Factors, Multiples and Primes

Transcription

1 MathsWatch Clip Grade D questions Factors, Multiples and Primes ) Write the factors of a) 6 b) 6 c) 8 d) 0 ) In a pupil s book the factors of are listed as The above list contains a mistake. Cross it out from the list and replace it with the correct number. ) The factors of 0 and 0 are listed 0:,,,, 6, 0,, 0 0:,,,, 8, 0, 0, 0 Write the common factors of 0 and 0 (the numbers that are factors of 0 and 0). ) Write the first four multiples of a) b) c) 0 d) ) In a pupil s book the first 7 multiples of 8 are listed as The above list contains mistakes. Cross them out and replace them with the correct numbers. 6) The first five multiples of and 0 are listed :, 8,, 6, 0 0: 0, 0, 0, 0, 0 From the two lists above, write the common multiple of and 0. 7) List the first five prime numbers 8) Using just this list of numbers: find the following: a) The prime numbers b) The factors of 8 c) The multiples of Page

2 MathsWatch Clip Grade D questions Evaluate Powers ) Evaluate the following: a) b) c) 0 ) Evaluate the following: a) 8 b) 6 c) 6 ) Find the value of a) + b) c) + + ) Find the value of a) + 6 b) c) 9 6 ) Find the value of Page

3 MathsWatch Clip 6 Grade D questions Understanding Squares, Cubes & Roots ) What is the value of? ) What is the value of 8? ) These are the first five square numbers:,, 9, 6, a) What is the sith square number? b) What is the 0th square number? ) Which square number lies between 60 and 70? ) What is the value of? 6) What is the value of? 7) Work out + + 8) Work out 9) Work out 9 0) Work out the value of ) Match together cards with the same answer Page 6

4 MathsWatch Clip 7 Grade D questions Equivalent Fractions ) Each of the grids below has a fraction written at the side of it. a) Shade the grids to show these fractions. 8 6 b) What do ou notice about how man little squares are shaded in each grid? ) Each of the grids below has a fraction written at the side of it. a) Shade the grids to show these fractions b) What do ou notice about how man little squares are shaded in each grid? ) Find the missing values in these equivalent fractions. = = = ) Find the missing values in these equivalent fractions. 6 = = = 0 ) How do ou know that is not equivalent to? 7 6 Page 7

5 MathsWatch Clip 8 Grade D questions Simplification of Fractions ) Write the following fractions in their simplest forms a) b) c) d) e) f) g) ) Write the following fractions in their simplest forms a) b) c) d) e) f) g) Page 8

6 MathsWatch Clip 9 Grade D questions Ordering Fractions ) Put these fractions in order of size, smallest to largest. Show our working for each question. a) b) c) 8 ) Put these fractions in order of size, smallest to largest. Show our working for each question. a) 8 b) c) 6 ) Put these fractions in order of size, smallest to largest. Show our working for each question. a) 7 6 b) 8 7 c) ) Ben spent his pocket mone this wa: on magazines on chocolates on games Order the items Ben bought b value, largest first. Show all our working. Page 9

7 MathsWatch Clip Grade D questions Find a Percentage without a Calculator ) Work out: a) 0% of 70 b) 0% of 6800 c) 0% of 9 d) 0% of 6 ) Work out: a) 0% of 60 b) 0% of 90 c) % of 800 d) % of 68 ) Work out: a) % of 80 b) 90% of 60 c) 7.% of 600 d) 7.% of 80 ) Work out: a) % of.60 b) 0% of.80 c) 7.% of.0 d) 97.% of ) The normal price of a jacket is. In a sale, the price is reduced b 0% What is the sale price? 6) A football costs plus 0% VAT. How much is the football? Page

8 MathsWatch Clip Grade D questions Change to a Percentage without a Calculator ) Write the following as percentages. a) out of 0 b) out of c) 8 out of 0 d) out of 0 e) out of f) out of 0 g) out of 80 h) 60 out of 800 i) 6 out of 60 ) Tim got 7 out of 0 in a French test. Write 7 out of 0 as a percentage. ) Write 9 as a percentage of ) Work out as a percentage of 0 ) A baker burnt loaves out of the 00 loaves he baked. What percentage of the 00 loaves did he burn? 6) What is 80 as a percentage of 00? 7) What is as a percentage of 0? 8) If there are 9 girls and bos in a class, what percentage of the class are girls? Page

9 MathsWatch Clip Grade D questions Finding a Fraction of an Amount ) Work out these amounts. a) of 0 b) of 60 kg c) 8 d) 0 e) 9 of 80 cm f) 9 7 g) 60 h) 8 of 8 i) ) There are 600 apples on a tree and there are maggots in of them. How man apples have maggots in them? ) Liz and Lee are travelling in a car from Glasgow to Poole (770 km). At midda the had alread travelled 7 of the total distance. What distance, in km, had the travelled b midda? ) A digital camera that cost 9 was sold on eba for 7 of the original price. What was the selling price? ) Yesterda Thomas travelled a total of 7 miles. He travelled of this distance in the morning. How man miles did he travel during the rest of the da? 6) Debra received her pocket mone on Saturda. She spent of her pocket mone on magazines. She spent of her pocket mone on a necklace. How much of the did she have left? Page

10 MathsWatch Clip 6 Grade D questions Addition and Subtraction of Fractions In all the questions on this page, please give our answers in their simplest form. ) Work out the following: a) b) ) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) ) Work out the following: ) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) 8 7) Ted received his pocket mone on Frida. He spent of his pocket mone on games. He spent of his pocket mone on magazines. 0 What fraction of his pocket mone did he have left? a) b) c) d) ) Maisie bus a bag of flour. She uses to bake a cake and to make a loaf. a) What fraction of the bag of flour was used? b) What fraction of the bag of flour is left? 9) Work out the total length of this shape. Give our answer as a mied number. inches inches Page 6

11 MathsWatch Clip 7 Grade D questions Multiplication and Division of Fractions In all the questions on this page, please give our answers in their simplest form. ) Work out the following: ) Work out the following: a) a) b) b) 7 c) 7 c) 9 d) 7 9 d) 0 9 ) Work out the following: ) Work out the following: a) a) b) 8 b) 7 7 c) 9 c) 9 d) d) 0 ) Work out the following: 6) Work out the following: a) a) b) b) c) c) d) 7 d) Page 7

12 MathsWatch Clip 8 Grade D questions Change Fractions to Decimals Write the following fractions as decimals ) 0 ) 7 0 ) 9 00 ) ) 6) 7) 7 0 8) 9) 8 0) 8 Page 8

13 MathsWatch Clip 9 Grade D questions BODMAS Work out the following. for all questions. ) 6 + ) + 6 ) ) 8 ( ) ) 7 ( + 6) 6) ) (9 + ) + 8) ( + ) 6 9) 6 0) 9+ + ) ) 7 ) + 7 ) 6 ) 8 + 6) 7 7) 0 0 ( + ) 8) Page 9

14 MathsWatch Clip 60 Grade D questions Long Multiplication with Decimals ) Work out a). b).6 7 c) 6 d).0 ) David bus books for 8.7 each. How much does he pa? ) A DVD costs.. Work out the cost of 9 of these DVDs. ) John takes 7 boes out of his van. The weight of each bo is.7 kg. Work out the total weight of the 7 boes. ) Nina bought tedd bears at 9. each. Work out the total amount she paid. 6) Elliott goes shopping. He bus 0. kg of pears at 0.8 per kg.. kg of grapes at.89 per kg. 6 kg of potatoes at 0. per kg. How much does he pa? 7) Brian hires a car for das. Tariffs are:.80 for the first da and 7.0 for each etra da. How much does he pa? Page 60

15 MathsWatch Clip 6 Grade D questions Ratio ) Write the following ratios in their simplest form: a) 6 : 9 b) 0 : c) 7 : d) : e) : 0 f) : : 8 g) 8 : 6 : 9 ) Write the missing value in these equivalent ratios: a) : = : b) : 9 = : 7 c) : 7 = 6 : ) The ratio of girls to bos in a class is :. What fraction of the class are girls? ) A model of a plane is made using a scale of :. a) If the real length of the plane is 0 m, what is the length of the model? b) If the wings of the model are. m long, what is the actual length of the wings on the plane? Page 6

16 MathsWatch Clip 6 Grade D questions Proportion Recipe Tpe Questions ) Here are the ingredients needed to make 8 pancakes. James makes pancakes. Pancakes Ingredients to make 8 pancakes 0 ml milk egg 0 g flour g butter a) Work out how much milk he needs. Kate makes pancakes. b) Work out how much flour she needs. ) Here are the ingredients for making fish pie for 6 people. Fish pie for 6 people 80 g flour 0 g fish 80 g butter eggs 80 ml milk Jill makes a fish pie for people. a) Work out how much flour she needs. Tim makes a fish pie for people. b) Work out how much milk he needs. ) Here are the ingredients for making pineapple sorbet for 6 people. Pineapple sorbet for 6 people 800 g of pineapple egg whites ½ lemon 00 g caster sugar Trevor makes pineapple sorbet for 8 people. a) Work out how much caster sugar he uses. Sid makes a pineapple sorbet. He uses lemons. b) Work out how man people he makes pineapple sorbet for. Page 6

17 MathsWatch Clip 6 Grade D questions Generate a Sequence from the Nth Term ) The nth term of a number sequence is n + Write down the first three terms of the sequence. ) The nth term of a number sequence is n Write down the first four terms of the sequence. ) The nth term of a number sequence is n + Write down the first four terms of the sequence. ) The nth term of a number sequence is n 7 Write down the first four terms of the sequence. ) The nth term of a number sequence is n Write down the first three terms of the sequence. 6) The nth term of a number sequence is n + Write down the first three terms of the sequence. 7) The nth term of a number sequence is n a) Find the third term of this sequence. b) Find the fifth term of this sequence. 8) The nth term of a number sequence is n + n a) Find the third term of this sequence. b) Find the fifth term of this sequence. Page 6

18 MathsWatch Clip 67 Grade D questions Parallel Lines ) Line PQ is parallel to line RS. If angle PQR is equal to 6 a) What is the size of angle QRS? b) Give a reason for our answer. P 6 Q R S ) Line DCE is parallel to line AB a) Find the size of angle ABC b) Find the size of angle DCA c) Calculate the size of angle ACB D C E A 68 B ) a) Find the size of angle DBF b) Find the size of angle HGC D E C 6 F B G H Page 67A

19 MathsWatch Clip 67 Grade D questions Parallel Lines ) A 67 9 B C D AB is parallel to CD. (i) Write down the value of. (ii) Give a reason for our answer. ) Q 80 S O P 0 R PQ is parallel to RS. OSQ and ORP are straight lines. a) (i) Write down the value of. (ii) Give a reason for our answer. b) Work out the value of. Page 67B

20 MathsWatch Clip 67 Grade D questions ) Parallel Lines a (i) Write down the size of the angle marked a. (ii) Give a reason for our answer. L ) A N B ANB is parallel to CMD. LNM is a straight line. Angle LMD = 67 (i) Work out the size of the angle marked. (ii) Give reasons for our answer. C M 67 D ) D C A B 6 E ABCD is a rhombus. BCE is an isosceles triangle. ABE is a straight line. Work out the size of angle DCA. Page 67C

21 MathsWatch Clip 68 Grade D questions Angle Sum of a Triangle ) Work out the size of angle a. 6 7 a ) Work out the size of angle b. 9 b ) Work out the size of angle c. 8 7 c ) Work out the size of angle d. d 0 Page 68

22 MathsWatch Clip 69 Grade D questions ) ABC is a triangle. a) Find the size of angle A. Properties of Special Triangles C 60 Diagram NOT accuratel drawn b) Triangle ABC is equilateral. Eplain wh. A 60 B ) BCD is a triangle. ABC is a straight line. Angle CBD = 70. BD = CD. D Diagram NOT accuratel drawn a) (i) Work out the value of. (ii) Give a reason for our answer. 70 A B C b) (i) Work out the value of. (ii) Give reasons for our answer. ) The diagram shows a -sided shape. All the sides of the shape are equal in length. a) (i) Find the value of. (ii) Give a reason for our answer. b) (i) Work out the value of. (ii) Eplain our answer. Page 69

23 All transformations on pages 77A to 77K MathsWatch Clip 7 Grade D questions ) a) Rotate triangle T 90 anti-clockwise about the point (0, 0). Label our new triangle U. b) Rotate triangle T 80 about the point (, 0). Label our new triangle V. Rotations T O ) Describe full the single transformation which maps triangle T to triangle U. T U O Page 7

24 All transformations on pages 77A to 77K MathsWatch Clip 7 Grade D questions = - Reflections ) a) Reflect triangle T in the ais. Label our new triangle U. b) Reflect triangle T in the line with equation = -. Label our new triangle V. T O ) a) Describe full the single transformation which maps triangle T to triangle U. T b) Describe full the single transformation which maps triangle T to triangle V O - - U - V - - Page 7

25 All transformations on pages 77A to 77K MathsWatch Clip 76 Grade D questions ) a) Enlarge triangle T b scale factor using point (-, ) as the centre of enlargement. Label our new triangle U. b) Enlarge triangle V b scale factor a half using the point (-, -) as the centre of enlargement. Label our new triangle W. Enlargements T O V - - ) Describe full the single transformation which maps triangle S to triangle T S T O Page 76

26 MathsWatch Clip 77 Grade D questions Translations ) - a) Translate triangle T b vector and label it U. b) Translate triangle T b vector - and label it V. 6 T O ) a) Describe full the single transformation which maps triangle A to triangle B. b) Describe full the single transformation which maps triangle A to triangle C. 6 A B O C Page 77A

27 MathsWatch Clips 7-77 Grade D questions Transformations ) O 6 - P a) Rotate triangle P 80 about the point (-, ). Label the new triangle A. b) Translate triangle P b the vector Label the new triangle B. ( ( 6 - ) ) = c) Reflect triangle Q in the line =. Label the new triangle C. Q O Page 77B

28 MathsWatch Clips 7-77 Grade D questions Transformations ) 8 = 6 A O Triangle A is reflected in the -ais to give triangle B. Triangle B is reflected in the line = to give triangle C. Describe full the single transformation that takes triangle A to triangle C. ) A a) Reflect shape A in the -ais O - b) Describe full the single transformation which takes shape A to shape B. - B Page 77C

29 MathsWatch Clips 7-77 Grade D questions Transformations ) O a) Rotate the shaded shape 90 clockwise about the point S T O - b) Describe full the single transformation that will map shape S onto shape T. Page 77D

30 MathsWatch Clips 7-77 Grade D questions Transformations ) a) On the grid, draw an enlargement, scale factor, of the shaded shape. A B O - - b) Describe full the single transformation that maps triangle A onto triangle B. Page 77E

31 MathsWatch Clips 7-77 Grade D questions Transformations ) T Triangle T has been drawn on a grid. a) On the grid, draw an enlargement of the triangle T with scale factor. U O Triangle U has been drawn on a grid. b) On the grid, rotate triangle U 90 clockwise about the centre O. Page 77F

32 MathsWatch Clips 7-77 Grade D questions Transformations ) A O B Describe full the single transformation that maps triangle A onto triangle B. ) T O Triangle T has been drawn on the grid. Rotate triangle T 80 about the point (, 0) Label the new triangle A. Page 77G

33 MathsWatch Clips 7-77 Grade D questions Transformations ) T S O Describe full the single transformation which maps shape S onto shape T. ) 7 6 P O Q Triangle P and triangle Q are drawn on the grid. a) Describe full the single transformation which maps triangle P onto triangle Q. b) Translate triangle P b the vector Label the new triangle R. ( ( - ) ) Page 77H

34 MathsWatch Clips 7-77 Grade D questions Transformations ) = O a) Reflect the shaded shape in the line =. O b) On the grid, enlarge the shaded shape b a scale factor of, centre O. Page 77I

35 MathsWatch Clips 7-77 Grade D questions Transformations ) 6 A O a) On the grid above, reflect shape A in the line = - P Q O b) Describe full the single transformation that will map shape P onto shape Q. Page 77J

36 MathsWatch Clips 7-77 Grade D questions Transformations ) Q a) On the grid, enlarge the shape with scale factor, centre Q O - - b) Rotate the shape 90 clockwise, centre O. - Page 77K

37 MathsWatch Clip 78 Grade D questions Finding the Midpoint of a Line ) Find the midpoint of A and B where A has coordinates (-, ) and B has coordinates (, -) O - - ) Find the midpoint of A and B where A has coordinates (, 0) and B has coordinates (8, 6). ) Find the midpoint of A and B where A has coordinates (-, -) and B has coordinates (, ). ) Find the midpoint of A and B where A has coordinates (-, -) and B has coordinates (7, ). ) Find the midpoint of A and B where A has coordinates (, -) and B has coordinates (7, ). 6) Find the midpoint of A and B where A has coordinates (-7, -) and B has coordinates (-, -). 7) The midpoint of A and B is at (, ). The coordinates of A are (-, ). Work out the coordinates of B. 8) The midpoint of A and B is at (.,.). The coordinates of A are (, ). Work out the coordinates of B. Page 78

38 MathsWatch Clip 8 Grade D questions Plans and Elevations ) The diagram shows a prism drawn on an isometric grid. Front a) On the grid below, draw the front elevation of the prism from the direction marked b the arrow. b) On the grid below draw a plan of the prism. Page 8A

39 MathsWatch Clip 8 Grade D questions Plans and Elevations ) Here is the plan and front elevation of a prism. The front elevation shows the cross section of the prism. Plan Front Elevation On the grid below, draw the side elevation of the prism. Page 8B

40 MathsWatch Clip 8 Grade D questions Plans and Elevations ) The diagram shows a solid prism made from centimetre cubes. a) On the centimetre square grid, draw the front elevation of the solid prism from the direction shown b the arrow. b) On the centimetre square grid below, draw the plan of the solid prism. Page 8C

41 MathsWatch Clip 8 Grade D questions Plans and Elevations ) The diagram shows a solid prism. cm cm cm cm a) On the grid below, draw the front elevation of the prism from the direction of the arrow. b) On the grid below, draw the plan of the prism. Page 8D

42 MathsWatch Clip 8 Grade D questions Nets ) Sketch nets of these solids. a) b) ) On squared paper draw accurate nets of these solids. a) Cube b) Cuboid cm cm cm cm 8 cm 6 cm c) Right-angled triangular prism d) Triangular prism cm cm cm cm 8 cm 7 cm 7 cm cm ) The two nets, below, are folded to make cubes. Two other vertices will meet at the the dot, A. Mark them with As. One other verte will meet the dot B. Mark it with B. a) A b) B Page 8

43 MathsWatch Clip 8 Grade D questions Smmetries ) Draw all the lines of smmetr on the triangle and the rectangle. ) What is the order of rotational smmetr of the two shapes below? S ) The diagram below, shows part of a shape. P The shape has rotational smmetr of order about point P. Complete the shape. ) On each of the shapes below, draw one plane of smmetr. Page 8

44 MathsWatch Clip 90 Grade D questions Simple Probabilit ) A blue dice and a red dice are rolled. a) How man different outcomes are possible? b) List the possible outcomes. ) Three coins are flipped. One possible outcome is H, H, H List all the outcomes. ) If five coins are flipped, how man possible outcomes are there? ) A dice is rolled and a coin is flipped. List all the possible outcomes. ) A bo contains gre counters and white counters. A counter is taken from the bo at random. What is the probabilit of choosing a white counter? 6) There are blue counters, red counters and 7 green counters in a bag. A counter is taken from the bag at random. a) What is the probabilit that a green counter will be chosen? b) What is the probabilit that a blue or red counter will be chosen? 7) In a class there are 0 bos and girls. A teacher chooses a student at random from the class. Eric sas that the probabilit a bo will be chosen is 0. because a student can be either a bo or a girl. Jenn sas that Eric is wrong. Decide who is correct - Eric or Jenn - giving reasons for our answer. 8) Spinner A has numbers to on it. Spinner B has numbers to on it. Both spinners are spun and the numbers on each are added together to give a score. What is the probabilit that the score will be a) 7? b) or? Page 90

45 MathsWatch Clip 9 Grade D questions Mutuall Eclusive Events ) If the probabilit of passing a driving test is 0., what is the probabilit of failing it? ) The probabilit that a football team will win their net game is. The probabilit the will lose is. What is the probabilit the game will be a draw? ) On the school dinner menu there is onl ever one of four options. Some of the options are more likel to be on the menu than others. The table shows the options available on an da, together with three of the probabilities. Food Curr Sausages Fish Casserole Probabilit a) Work out the probabilit of the dinner option being Fish. b) Which option is most likel? c) Work out the probabilit that it is a Curr or Sausages on an particular da. d) Work out the probabilit that it is not Casserole. ) Julie bus a book ever week. Her favourite tpes are Novel, Drama, Biograph and Romance. The table shows the probabilit that Julie chooses a particular tpe of book. Tpe of book Novel Drama Biograph Romance Probabilit a) Work out the probabilit that she will choose a Novel or a Drama. b) Work out the probabilit that she will choose a Biograph or a Romance. The probabilit that she will choose a Biograph is the same as the probabilit she will choose a Romance. c) Work out the probabilit that she will choose a Biograph. Page 9

46 MathsWatch Clip 9 Grade C questions Increase/Decrease b a Percentage ) Increase: a) 00 b 0% c) 80 b % b) 0 b 0% d) 7 b 0% ) Decrease: a) 00 b 0% c) 0 b % b) 80 b 0% d) b 0% ) The price of a laptop is increased b %. The old price of the laptop was 00. Work out the new price. ) The price of a 6800 car is reduced b 0%. What is the new price? ) Increase: a) 6 b % c) 600 b 7.% b) 0 b % d) 70 b 7.% 6) Decrease: a) b % c) b 8.% b) 79 b % d) 8900 b 8% 7) The price of a mobile phone is 78.0 plus VAT. VAT is charged at a rate of 7.%. What is the total price of the mobile phone? 8) In a sale, normal prices are reduced b 7%. The normal price of a camera is 89. Work out the sale price of the camera. 9) A car dealer offers a discount of 0% off the normal price of a car, for cash. Peter intends to bu a car which usuall costs He intends to pa b cash. Work out how much he will pa. 0) A month ago, John weighed 97. kg. He now weighs.% more. Work out how much John now weighs. Give our answer to decimal place. Page 9

47 MathsWatch Clip 9 Grade C questions Product of Prime Factors ) List the first seven prime numbers. ) Epress the following numbers as the product of their prime factors: a) b) 0 c) 0 d) ) Epress the following numbers as the product of their prime factors: a) 6 b) 00 c) 0 ) Epress the following numbers as the product of their prime factors: a) 7 b) 9 c) ) The number 96 can be written as m n, where m and n are prime numbers. Find the value of m and the value of n. 6) The number 7 can be written as, where and are prime numbers. Find the value of and the value of. Page 9

48 MathsWatch Clip 96 Grade C questions HCF and LCM ) Find the Highest Common Factor of 6 and. ) Find the Highest Common Factor of and 8. ) Find the Highest Common Factor of 60 and 0. ) Find the Highest Common Factor of 96 and 08. ) Find the Lowest Common Multiple of 0 and 60. 6) Find the Lowest Common Multiple of 8 and 7. 7) Find the Lowest Common Multiple of 70 and 0. 8) Find the Lowest Common Multiple of and. 9) (i) Write and 6 as products of their prime factors. (ii) Work out the Highest Common Factor of and 6. (iii) Work out the Lowest Common Multiple of and 6. Page 96A

49 MathsWatch Clips 9, 96 Grade C questions Product of Prime Factors, HCF & LCM ) a) Epress 8 as a product of its prime factors. b) Find the Highest Common Factor (HCF) of 8 and. ) Epress 7 as the product of its prime factors. ) Epress 80 as the product of its prime factors. ) a) Epress 66 as a product of its prime factors. b) Epress as a product of its prime factors. ) Epress as a product of its prime factors. 6) Find the Lowest Common Multiple (LCM) of and 6. 7) a) Write 6 as a product of its prime factors. b) Find the Highest Common Factor (HCF) of 6 and. 8) a) Epress as a product of its prime factors. b) Find the Highest Common Factor (HCF) of and 0. 9) a) Find the Highest Common Factor (HCF) of and 0. b) Find the Lowest Common Multiple (LCM) of, and 6. Page 96B

50 MathsWatch Clip 97 Grade C questions Using Place Value ) Using the information that write down the value of a) 7 b).7. c) = 9.8 ) Using the information that write down the value of a)..8 b) c).8 8 = ) Using the information that write down the value of a) 70 b) 7. 7 = 708 ) Using the information that write down the value of a) 7 6 b) c) =. ) Using the information that write down the value of a) 7.9. b) c) = 6 Page 97A

51 MathsWatch Clip 97 Grade C questions Using Place Value ) Use the information that to write down the value of (i)..7 (ii).7 7 = ) Use the information that to write down the value of (i)..8 (ii) 0 80 (iii) (iv). (v) = ) Use the information that to write down the value of (i) 7 8 (ii).7 80 (iii) (iv) (v) = 76. ) Use the information that to write down the value of (i) (ii) (iii) (iv) 6..7 (v) = 6 Page 97B

52 MathsWatch Clip 98 Grade C questions Recurring Decimals into Fractions ) Write each recurring decimal as an eact fraction, in its lowest terms. a) 0. b) 07. c) 0. d) 0. e) 07. f) 08. g) h) 06. i) 07. j) 0. k) l) 0. 6 Page 98

53 MathsWatch Clip 99 Grade C questions Four Rules of Negatives ) Work out the following: a) 7 b) 6 c) 8 d) 0 ) Work out the following: a) - + b) -7 + c) d) -9 + ) Work out the following: a) - b) - c) -7 8 d) - ) Work out the following: a) 6 - b) - - c) -9 - d) - ) Work out the following: a) - b) - c) - - d) -6-6) Work out the following: a) - b) -0 - c) - d) Page 99

54 MathsWatch Clip 00 Grade C questions Division b Decimals ) Work out the following: a) 0. b) 0. c) 0. ) Work out the following: a) 0. b) 0. c) 8 0. ) Work out the following: a) 6 0. b) 0.8 c) ) Work out the following: a) 0. b) 8 0. c) 0 0. ) Work out the following: a) b) c) ) Work out the following: a) b) c) Page 00

55 MathsWatch Clip 0 Grade C questions Significant Figures ) Round the following numbers to significant figure: a) 8 b) 78 c) 608 d) e) 999 f) 79 0 ) Round the following numbers to significant figures: a) 86 b) 67 c) d) 6 87 e) 89 7 f) 9 08 ) Round the following numbers to significant figures: a) 9 9 b) 6 8 c) 08 d) 89 e) 7 76 f) 997 ) Work out the following and give our answer to significant figures: a) 6 8 b) c) ) Round the following numbers to significant figure: a) b) c) d) ) Round the following numbers to significant figures: a) 0.08 b) c) d) ) Round the following numbers to significant figures: a) b) c) d) ) Round the following numbers to significant figures: a) 7.8 b) c).9 9) Work out the following and give our answer to significant figures: a) 0.8 b) c) Page 0A

56 MathsWatch Clip 0 Grade C questions Estimating Answers ) Work out an estimate for ) Work out an estimate for ) Work out an estimate for.9 0. ) Work out an estimate for ) Work out an estimate for Page 0B

57 MathsWatch Clip 0 Grade C questions Estimating Answers ) Work out an estimate for the value of a) b) c) d) ) a) Work out an estimate for b) Use our answer to part (a) to find an estimate for ) a) Work out an estimate for b) Use our answer to part (a) to find an estimate for Page 0C

58 MathsWatch Clip 0 Grade C questions ) Simplif the following a) + b) + c) t t d) 7 6 e) + + f) g g + 6g g) h) + 6 Algebraic Simplification ) Simplif the following a) b) c) ) Simplif the following a) b) c) d) e) ) Simplif the following a) + b) c) + d) e) + f) 6a bc + a bc a bc ) Simplif the following a) b) c) a + b a + b d) + e) f) g) t + u + t 7u h) + t t 6) Simplif the following a) b) c) t t d) e) 7) Simplif the following a) b) c) r s t d) 6 z 8) Simplif the following a) b) c) d) 6 e) f) tu t u tu Page 0A

59 MathsWatch Clip 0 Grade C questions Algebraic Simplification ) a) Simplif p 6q b) Simplif d d d d c) Simplif t t 8) a) Simplif a + c a + c b) Simplif c) Simplif ) a) Simplif a + c a + c b) Simplif 6c + c 9) Simplif ) a) Simplif b) Simplif ) a) Simplif t + t t b) Simplif + + c) Simplif m m m d) Simplif n t ) Simplif ) a) Simplif pq + pq b) Simplif + ) a) Simplif 6a + b b + a b) Simplif + ) Simplif ) a) Simplif b) Simplif t + t + t 6) a) Simplif t t b) Simplif a a a ) a) Simplif a a b) Simplif 7) a) Simplif 6 b) Simplif ) a) Simplif d + e d + e b) Simplif c) Simplif t + 8d t d d) Simplif t q Page 0B

60 MathsWatch Clip 0 Grade C questions Epanding and Simplifing Brackets ) Epand these brackets a) ( + ) b) ( + ) c) (p q) d) ( + ) e) 6(r r ) ) Epand and simplif a) ( + ) + ( + ) b) ( + ) + ( + ) c) ( + ) + ( + ) d) (c + d) + (c + d) e) (p + q) + (p + q) ) Epand these brackets a) ( ) b) ( + ) c) p(p 7q) d) ( + 6 ) e) (r + r ) 6) Epand and simplif a) ( + ) + ( ) b) ( + ) + ( ) c) ( ) + ( + ) d) 6(c d) + (c d) e) (p q) + (p q) ) Epand these brackets a) ( ) b) ( + ) c) p(p q) d) ( + ) e) ( + r ) 7) Epand and simplif a) ( + ) ( ) b) ( ) ( ) c) 7( ) ( + ) d) 6( ) ( + ) e) (p q) (p q) ) Epand these brackets a) ( ) b) ( + ) c) p (p ) d) ( + ) e) ( + ) Page 0A

61 MathsWatch Clip 0 Grade C questions Epanding and Simplifing Brackets ) Epand and simplif a) ( + )( + ) b) ( + )( + ) c) ( + )( + ) d) ( + 6)( + ) e) ( + )( + 7) ) Epand and simplif a) ( 7)( + ) b) (p 6)(p + ) c) (e )(e 7) d) ( + 8)( + ) e) ( )( ) ) Epand and simplif a) ( + )( ) b) ( 7)( + ) c) ( )( + ) d) ( + )( ) e) ( )( + ) ) Epand and simplif a) ( + )( + ) b) (p )(p + ) c) (e )(e ) d) ( 6)( + ) e) ( )( + ) ) Epand and simplif a) ( )( ) b) ( )( 6) c) ( )( ) d) ( 7)( ) e) ( )( ) 6) Epand and simplif a) ( + )( + ) b) (p q)(p + q) c) (e f )(e f ) d) (6 )(6 + ) e) ( )( ) Page 0B

62 MathsWatch Clip 0 Grade C questions Factorisation ) Factorise a) + b) + 0 c) + d) 6 e) ) Factorise a) p + 7p b) + c) d) p p e) + ) Factorise a) + 6 b) 8 c) p + 0p d) 7c c e) ) Factorise a) b) t + 0tu c) 6 8 d) + 9 Page 0

63 Solving equations and inequalities on pages 09A to 09C MathsWatch Clip 0 Grade C questions Solving Equations ) Solve = 7 7) Solve ( + ) = + 9 ) Solve + = 8) Solve 7 = ( ) ) Solve 7 = 9) Solve ( + ) = ( + 6) ) Solve + 7 = 9 0) Solve ( + ) = ( ) ) Solve = 0 ) Solve 7 = ( + ) 6) Solve + = 7) Solve ( + ) = 8 8) Solve ( ) = 9) Solve (t ) = 0 ) Solve ) Solve ) Solve ) Solve = = 6 = = 0) Solve ( + ) = 6 6) Solve = ) Solve + 7 = + 7) Solve + = 7 ) Solve = + 0 ) Solve + = 0 ) Solve p = p ) Solve d + = 0 d 6) Solve e = e 8 8) Solve 9) Solve 0) Solve ) Solve ) Solve = = = + = = Page 0

64 MathsWatch Clip 06 Grade C questions Forming Equations ) The width of a rectangle is centimetres. The length of the rectangle is ( + ) centimetres. + a) Find an epression, in terms of, for the perimeter of the rectangle. Give our answer in its simplest form. The perimeter of the rectangle is 8 centimetres. b) Work out the length of the rectangle. ) Diagram NOT accuratel drawn The sizes of the angles, in degrees, of the quadrilateral are a) Use this information to write down an equation in terms of. b) Use our answer to part (a) to work out the size of the smallest angle of the quadrilateral. ) Sarah bus 6 cups and 6 mugs A cup costs A mug costs ( + ) a) Write down an epression, in terms of, for the total cost, in pounds, of 6 cups and 6 mugs. b) If the total cost of 6 cups and 6 mugs is 8, write an equation in terms of. c) Solve our equation to find the cost of a cup and the cost of a mug. Page 06A

65 MathsWatch Clip 06 Grade C questions Forming Equations ) + 9 In the diagram, all measurements are in centimetres. The lengths of the sides are a) Find an epression, in terms of, for the perimeter of the triangle. Give our epression in its simplest form. The perimeter of the triangle is 9 cm. b) Find the value of. ) The diagram shows a right-angled triangle and a rectangle. cm 7 cm cm 8 cm cm The area of the right-angled triangle is equal to the area of the rectangle. Find the value of. Page 06B

66 MathsWatch Clip 06 Grade C questions Forming Equations ) A shop sells small boes and large boes for storing CDs. A small bo stores CDs. A large bo stores CDs. Emma bus 8 small boes and large boes. Emma can store a total of T CDs in these boes. Write down a formula for T in terms of and. ) Batteries are sold in packets and boes. Each packet contains batteries. Each bo contains 0 batteries. Ton bus p packets of batteries and b boes of batteries. Ton bus a total of N batteries. Write down a formula for N in terms of p and b. ) Compasses cost c pence each. Rulers cost r pence each. Write down an epression for the total cost, in pence, of compasses and rulers. ) P + 0 ABC is a straight line. Angle APB = + 0 Angle PAB = 0 Angle PBC = 0 A B C a) Show that = + 0 Give reasons for each stage of our working. b) Given that equals degrees (i) Work out the value of. (ii) Work out the size of the largest angle in triangle APB. Page 06C

67 MathsWatch Clip 07 Grade C questions Changing the Subject of a Formula ) Make c the subject of the formula. a = b + cd ) Make t the subject of the formula. u = v + t ) Make n the subject of the formula. M = n + ) Make z the subject of the formula. = + z ) r = s + t a) Make t the subject of the formula. b) Make s the subject of the formula. 6) Rearrange = + to make the subject. 7) Rearrange = + to make the subject. 8) Rearrange = + to make the subject. Page 07

68 MathsWatch Clip 08 Grade C questions Inequalities ) Represent this inequalit on the number line - < < ) Represent this inequalit on the number line - < < ) Write down the inequalit shown ) Write down the inequalit shown ) If is an integer, write down all the possible values of - < < 6) If is an integer, write down all the possible values of -9 < < - Page 08

69 MathsWatch Clip 09 Grade C questions Solving Inequalities ) Solve a) > b) c) d) + > 7 e) 8< p f) + g) h) 6 > + i) p 9< 6 p j) < 0 ) a) Solve the inequalit z + > 7 b) Write down the smallest integer value of z which satisfies the inequalit z + > 7 ) + < 0 and are both integers. Write down two possible pairs of values that satisf this inequalit. =..., =... and =..., =... Page 09A

70 MathsWatch Clips 0/09 Grade C questions Solving Equations & Inequalities ) Solve the inequalit 6 < 9 ) Solve + = + ) a) Solve the inequalit t + < t + b) If t = 7 find a value of t ) Solve ( + ) = 8 ) Solve the inequalit 6 > + 0 6) Solve ( ) = + 7 7) h = t + Work out the value of t when h = 8 8) Solve (p ) = p + 9) Solve the equation + = 9 0) Solve 9 = + ) Solve 0 = + 0 ) Solve the inequalit > + 7 ) Solve the inequalit < 0 Page 09B

71 d) + Page A MathsWatch Clip Grade C questions Inde Notation for Multiplication and Division ) Write as a power of 8 a) 8 8 b) ) Write as a power of a) 9 b) 0 ) Simplif a) k k b) c) k k 6 d) (k 8 ) ) Simplif eg. ( ) = = 6 a) ( ) b) ( ) c) ( ) d) ( ) ) = 0 and = Work out the value of and the value of. 6) = and = 6 Work out the value of and the value of. 7) a =, b = Epress in terms of a and b a) + b) c)

72 MathsWatch Clip Grade C questions Inde Notation for Multiplication and Division ) a) Simplif d d d d b) Simplif t t c) Simplif m m ) a) Simplif ( ) b) Simplif ) a) Simplif t t b) Simplif 8 c) Simplif (c ) ) a) Simplif 6 b) Simplif 8 c) Simplif (t) d) Simplif ) a) Simplif b) Simplif t 7 t c) Simplif 6) a) Simplif b) Simplif Page B

73 MathsWatch Clip Grade C questions Finding the Nth Term ) Here are the first five terms of an arithmetic sequence. 7 9 Find, in terms of n, an epression for the nth term of this sequence. ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an epression for the nth term of this sequence. ) Here are the first five terms of an arithmetic sequence. 7 0 Find, in terms of n, an epression for the nth term of this sequence. ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an epression for the nth term of this sequence. ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an epression for the nth term of this sequence. Page A

74 MathsWatch Clips 6, Grade C questions Nth Term ) Here are the first four terms of an arithmetic sequence. 7 0 Find an epression, in terms of n, for the nth term of the sequence. ) The nth term of a number sequence is n + Write down the first three terms of the sequence. ) Here are the first five terms of an arithmetic sequence. 7 7 a) Find, in terms of n, an epression for the nth term of this sequence. b) An epression for the nth term of another sequence is n (i) Find the third term of this sequence. (ii) Find the fifth term of this sequence. ) The nth term of a sequence is n (i) (ii) Find the th term of the sequence. Is the number 00 a term of the sequence? Give reasons for our answer. Page B

75 MathsWatch Clips 6, Grade C questions Nth Term ) The nth term of a number sequence is given b n + a) Work out the first two terms of the number sequence. Here are the first four terms of another number sequence. 7 0 b) Find, in terms of n, an epression for the nth term of this number sequence. ) Here is a number pattern. Line Number a) Complete Line Number of the pattern. b) Complete Line Number 0 of the pattern. c) Use the number pattern to find the answer to Page C

76 MathsWatch Clip Grade C questions Drawing Straight Line Graphs ) a) Complete the table of values for = b) On the grid, draw the graph of =, for values of from - to. c) Use the graph to find the value of when =. d) Use the graph to find the value of when = O ) a) Complete the table of values for = b) On the grid, draw the graph of = O Page A

77 MathsWatch Clip Grade C questions ) On the grid, draw the graph of = Drawing Straight Line Graphs O ) a) Complete the table of values for + = b) On the grid, draw the graph of + = O - - c) Find the gradient of the graph of + = 6. Page B

78 MathsWatch Clip Grade C questions Drawing Straight Line Graphs ) a) Complete the table of values for = - 0 b) Using the aes on the right draw the graph of = c) Use our graph to work out the value of when =. d) Use our graph to work out the value of when =. - O - ) a) Complete the table of values for = b) Using the aes on the right, again, draw the graph of = - - ) a) Complete the table of values for = ½ b) Draw the graph of = ½ O - - c) Use our graph to find the value of when =. Page C

79 MathsWatch Clip Grade C questions Finding the Equation of a Straight Line ) Find the equations of lines A, B and C on the aes below 8 C A B 7 6 O ) Find the equations of lines A, B and C on the aes below C B 6 A O Page

80 MathsWatch Clip Grade C questions Solving Simultaneous Equations Graphicall ) On the aes below, the graphs of = + and = 6 have been drawn. Use the graphs to solve the simultaneous equations = + and = = + 6 = 6 O ) On the aes below draw the graphs of = + and = 7 Use our graphs to solve the simultaneous equations = + and = O Page

81 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) Complete the table of values for = On the grid, draw the graph of = O Page 6A

82 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) a) Complete the table of values for = b) On the grid, draw the graph of = O c) Use our graph to estimate the values of when = - Page 6B

83 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) a) Complete the table of values for = b) On the grid, draw the graph of = O Page 6C

84 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) a) Complete the table of values for = b) On the grid, draw the graph of = for values of from - to O c) Use the graph to find the value of when = -. d) Use the graph to find the values of when = - ) a) Complete the table of values for = b) On the grid, draw the graph of = for values of from - to O c) (i) On the same aes draw the straight line =. (ii) Write down the values of for which =. - Page 6D

85 MathsWatch Clip 6 Grade C questions Drawing Quadratic Graphs ) The diagram shows the graph of = O a) Use the graph to find estimates for the solutions of (i) = 0 (ii) = 6 b) Use the graph to find estimates for the solutions of the simultaneous equations = = Page 6E

86 MathsWatch Clip Grade C questions Converting Metric Units ) Change 9 m into cm ) How man square metres are there in square kilometres? ) Change cm into mm ) Convert 6. m into mm ) Change m into cm 6) How man cubic millimetres are there in cubic centimetres? 7) Change 7 m into mm 8) A tiler wants to tile a rectangular wall which measures m b. m. Each tile measures 6 cm b 0 cm. How man tiles will he need for the wall? Tile 0 cm. m 6 cm m 9) A carpet-fitter is laing carpet tiles on a rectangular floor which measures 7. m b. m. Each carpet tile measures 0 cm b 0 cm. How man carpet tiles will he need for the floor? Carpet tile. m 0 cm 0 cm 7. m Page

87 MathsWatch Clip Grade C questions Eperimental Probabilities ) Ahmad does a statistical eperiment. He throws a dice 600 times. He scores one, 00 times. Is the dice fair? Eplain our answer ) Chris has a biased coin. The probabilit that the biased coin will land on a tail is 0. Chris is going to flip the coin 0 times. Work out an estimate for the number of times the coin will land on a tail. ) On a biased dice, the probabilit of getting a si is. The dice is rolled 00 times. Work out an estimate for the number of times the dice will land on a si. ) On a biased dice, the probabilit of getting a three is 0. The dice is rolled 0 times. Work out an estimate for the number of times the dice will land on a three. ) Jenn throws a biased dice 00 times. The table shows her results. Score Frequenc a) She throws the dice once more. Find an estimate for the probabilit that she will get a four. b) If the dice is rolled 0 times, how man times would ou epect to get a five? Page

88 MathsWatch Clip 9 Grade B questions Four Rules of Fractions ) Work out the value of Give our answer as a fraction in its simplest form. ) a) Work out Give our answer in its simplest form. b) Work out 8 + ) Work out the value of Give our answer as a fraction in its simplest form. ) a) Work out 7 0 b) Work out ) a) Work out 6 Give our fraction in its simplest form. b) Work out 6) There are 00 people at a concert. of the 00 people are bos. 6 of the 00 people are girls. 0 The rest of the people are adults. Work out how man people are adults. Page 9

89 MathsWatch Clip Grade B questions Simultaneous Linear Equations ) Solve + = 6 = ) Solve + = 9 = 7 ) Solve + = + = 8 ) Solve + = = ) Solve a + b = a b = 0 6) Solve + = + = 9 7) Solve 6 = + = - 8) Solve a b = a + b = 9) Solve + = + 7 = 9 0) Solve 6 = 9 + = 6 Page

90 MathsWatch Clip Grade B questions Understanding = m + c gradient cuts the -ais ) a) Find the equation of line A on the grid below. b) Draw the line B, with equation =. c) Draw the line C, with equation =. A O ) A straight line passes through points (0, ) and (, ). What is its equation? ) A straight line passes through points (0, 7) and (, -). What is its equation? ) A straight line is parallel to = and goes through (, 8). What is its equation? ) A straight line is parallel to = + and goes through (, 6). What is its equation? 6) A is the point (-, ). B is the point (, 6). C is the point (0, -). Find the equation of the line which passes through C and is parallel to AB. A (-, ) C (0, -) B (, 6) Page

91 MathsWatch Clip Grade B questions Regions ) On the grid below, draw straight lines and use shading to show the region R that satisfies the inequalities > > + < O ) On the grid below, draw straight lines and use shading to show the region R that satisfies the inequalities > + < > O Page

92 MathsWatch Clip Grade B questions ) a) Complete this table of values for = + 0 b) On the grid, draw the graph of = + Graphs of Cubic and Reciprocal Functions O - - c) Use the graph to find the value of when = ) a) Complete this table of values for = b) On the grid, draw the graph of = + c) Use the graph to find the value of when = O - ) Sketch the graph of = Page

93 MathsWatch Clip 6 Grade B questions Recognise the Shapes of Functions ) Match each of the functions below, with the correct sketch of its graph. a) = b) = - c) = d) = e) = + f) = g) = h) = - Page 6

94 MathsWatch Clip 8 Grade B questions -D Coordinates ) A cuboid lies on the coordinate aes. U P Q O T z R S The point Q has coordinates (,, ) a) Write down the coordinates of the point P. b) Write down the coordinates of the point T. c) Write down the coordinates of the point S. d) Write down the coordinates of the point R. e) Write down the coordinates of the point U. ) A cuboid lies on the coordinate aes. C A P B O z Point P lies half wa between A and B and has coordinates (,, ). a) Write down the coordinates of B. b) Write down the coordinates of C. Page 8

95 MathsWatch Clip 0 Grade B questions Circle Theorems ) D A o C B In the diagram, A, B, C, and D are points on the circumference of a circle, centre O. Angle BAD =. Angle BOD =. Angle BCD =. a) (i) Work out the value of. (ii) Give a reason for our answer. b) (i) Work out the value of. (ii) Give a reason for our answer. B ) O C A The diagram shows a circle centre O. A, B and C are points on the circumference. DCO is a straight line and DA is a tangent to the circle. Angle ADO = a) Work out the size of angle AOD. b) (i) Work out the size of angle ABC. (ii) Give a reason for our answer. D Page 0A

96 MathsWatch Clip 0 Grade B questions Circle Theorems ) B C A O A, B and C are points on the circumference of a circle centre O. AC is a diameter of the circle. a) (i) Write down the size of angle ABC. (ii) Give a reason for our answer. E F O 0 D D, E and F are points on the circumference of a circle, centre O. Angle DOF = 0. b) (i) Work out the size of angle DEF. (ii) Give a reason for our answer. ) B, D and E are points on a circle centre O. ABC is a tangent to the circle. BE is a diameter of the circle. Angle DBE =. a) Find the size of angle ABD. Give a reason for our answer. A D E b) Find the size of angle DEB. Give a reason for our answer. B C Page 0B

97 MathsWatch Clip 0 Grade B questions ) In the diagram, A, B and C are points on the circumference of a circle, centre O. PA and PB are tangents to the circle. Angle ACB = 7. a) (i) Work out the size of angle AOB. (ii) Give a reason for our answer. b) Work out the size of angle APB. Circle Theorems B O C 7 A Diagram NOT accuratel drawn P ) P, Q, R and S are points on the circle. PQ is a diameter of the circle. Angle RPQ =. S b R Diagram NOT accuratel drawn a) (i) Work out the size of angle PQR. (ii) Give reasons for our answer. P a Q b) (i) Work out the size of angle PSR. (ii) Give a reason for our answer. ) The diagram shows a circle, centre O. AC is a diameter. Angle BAC =. D is a point on AC such that angle BDA is a right angle. B Diagram NOT accuratel drawn a) Work out the size of angle BCA. Give reasons for our answer. A O D C b) Calculate the size of angle DBC. c) Calculate the size of angle BOA. ) A, B, C and D are four points on the circumference of a circle. ABE and DCE are straight lines. Angle BAC =. Angle EBC = 8. a) Find the size of angle ADC. A B 8 Diagram NOT accuratel drawn b) Find the size of angle ADB. Angle CAD = 69. c) Is BD a diameter of the circle? You must eplain our answer. D C E Page 0C

98 MathsWatch Clip 0 Grade B questions All questions Circle Theorems ) a = ) b = ) c = a 6 O b O O c 88 6 ) d = ) e = f = 6) g = 9 e 8 f O O O g d 7) h = 8) i = 9) j = k = h k 6 O i O O j 0) l = m = ) n = p = q = ) r = s = 00 O m p q n O 8 O s l 0 r Page 0D

99 MathsWatch Clip 0 Grade B questions All questions Circle Theorems ) a = b = ) c = d = ) e = f = b a O O O d e c 0 f ) g = h = ) i = 6) j = g 8 0 O O O 88 h 00 i j 7) k = l = m = 8) n = p = q = 9) r = s = m O l k O p 0 O n q 0 r s 0) t = ) u = ) v = w = t O u 0 O O v 8 w Page 0E

100 MathsWatch Clip 0 Grade B questions All questions Circle Theorems ) a = ) b = c = ) d = e = b e 8 O O O a ) f = g = ) h = i = 6) j = k = l = m = g 0 O O 0 O 78 h 6 m k l j 7) n = 8) p = q = 9) r = s = t = r 6 O O q O 0 s t n p 76 0) u = v = w = ) = = z = 8 v O O u w z Page 0F

101 MathsWatch Clip Grade B questions Simple Tree Diagrams ) Jim and Sue each take a driving test. The probabilit that Jim will pass the driving test is 0.7 The probabilit that Sue will pass the driving test is 0.6 a) Complete the probabilit tree diagram. Jim Sue 0.6 Pass 0.7 Pass Fail 0.6 Pass Fail Fail b) Work out the probabilit that both Jim and Sue will pass the driving test. c) Work out the probabilit that onl one of them will pass the driving test. ) Terri has 7 pens in a bo. of the pens are blue. of the pens are red. Terri takes at random a pen from the bo and writes down its colour. Terri puts the pen back in the bo. Then Terri takes at random a second pen from the bo and writes down its colour. a) Complete the probabilit tree diagram. st pen nd pen..... Blue Blue Red..... Red..... Blue..... Red b) Work out the probabilit that Terri takes eactl one pen of each colour from the bo. Page A

102 MathsWatch Clip Grade B questions Simple Tree Diagrams ) Tim puts red counters and blue counters in a bag. He takes at random a counter from the bag. He writes down the colour of the counter. He puts the counter in the bag again. He then takes at random a second counter from the bag. a) Complete the probabilit tree diagram. st counter 7 nd counter Red 7 Red Blue Blue Red Blue b) Work out the probabilit that Tim takes two red counters. ) In a game of chess, a plaer can either win, lose or draw. The probabilit that Jane wins an game of chess is 0. The probabilit that Jane draws an game of chess is 0. Jane plas games of chess. st game nd game a) Complete the probabilit tree diagram Win Win..... Draw Lose..... Win 0. Draw..... Draw Lose Win Lose..... Draw b) Work out the probabilit that Jane will win both games Lose Page B

103 MathsWatch Clip Grade B questions Simple Tree Diagrams ) Luc throws a biased dice twice. Complete the probabilit tree diagram to show the outcomes. Label clearl the branches of the tree diagram. st Throw nd Throw 6 Si... Not Si ) A bag contains 0 coloured balls. 7 of the balls are blue and of the balls are green. Nathan is going to take a ball, replace it, and then take a second ball. a) Complete the tree diagram.... st Ball nd Ball... Blue Blue... Green... Green Blue Green b) Work out the probabilit that Nathan will take two blue balls. c) Work out the probabilit that Nathan will take one of each coloured balls. d) Work out the probabilit that Nathan will take two balls of the same colour. Page C

104 MathsWatch Clip Grade B questions Harder Tree Diagrams ) There are red pens, blue pens and green pens in a bo. Jerr takes at random a pen from the bo and gives the pen to his friend. Jerr then takes at random another pen from the bo. Work out the probabilit that both pens are the same colour. ) There are red sweets, blue sweets and green sweets in a bag. Jack takes a sweet at random. He eats the sweet. He then takes another sweet at random. Work out the probabilit that both sweets are the same colour. ) There are buttons in a bag. 9 buttons are white. buttons are black. Carol takes a button at random from the bag, and keeps it. She now takes another button from the bag. Work out the probabilit that Carol takes a button of each colour. Page A

105 MathsWatch Clip Grade B questions Harder Tree Diagrams ) A bag contains 7 green and ellow balls. A ball is taken from the bag at random and not replaced. Another ball is taken from the bag at random. a) Draw a tree diagram to show all the possibilities. b) What is the probabilit that both balls are different colours? ) A bo contains red counters and blue counters. A counter is taken from the bo at random and not replaced. Another counter is taken at random. a) Draw a tree diagram to show all the possibilities. b) What is the probabilit of choosing at least one blue counter? c) What is the probabilit of choosing two counters of the same colour? d) What is the probabilit of choosing two counters of different colours? ) A bo contains red counters and blue counters. A counter is taken from the bo at random and not replaced. A second counter is taken from the bo at random and not replaced. A third counter is taken from the bo. a) Draw a tree diagram to show all the possibilities. b) What is the probabilit that all three counters are the same colour? c) What is the probabilit that eactl two of the counters are red? Page B

106 MathsWatch Clip Grade B questions Harder Tree Diagrams ) Sara has two boes. There are 6 black and white counters in bo A. There are 7 black and white counters in bo B. Sara takes at random a counter from bo A and puts it in bo B. She then takes at random a counter from bo B and puts it in bo A. a) Complete the probabilit tree diagram. From A to B From B to A Black Black White White Black White b) Find the probabilit that after Sara has put the counters from bo B into bo A there will still be 6 black counters and white counters in bo A. Page C

107 MathsWatch Clip Grade A and A* questions Recurring Decimals ) a) Convert the recurring decimal 06. to a fraction in its simplest form. 8 b) Prove that the recurring decimal 07. = ) a) Change 9 to a decimal. 9 b) Prove that the recurring decimal 07. = ) a) Change to a decimal. b) Prove that the recurring decimal 0. = ) a) Change 6 to a decimal. b) Prove that the recurring decimal 0. = 7 ) a) Convert the recurring decimal 06. to a fraction in its simplest form. b) Prove that the recurring decimal 07. = 8 6) a) Convert the recurring decimal. to a fraction in its simplest form. b) Prove that the recurring decimal 06. = Page

108 MathsWatch Clip 6 Grade A and A* questions Fractional and Negative Indices ) Simplif the following: a) b) 6 c) (p ) d) ( ) e) ( ) f) ( ) g) 7 h) t t ) Work out the value of the following, leaving our answer in fraction form when necessar a) 0 b) c) d) 9 e) 8 f) g) 6 h) 7 i) 6 ) can be written in the form n. Calculate the value of n. ) 8 can be written in the form n. Calculate the value of n. ) a =, b = Epress in terms of a and b (i) (ii) + (iii) + Page 6

109 MathsWatch Clip 7 Grade A and A* questions Surds ) Simplif the following: a) 7 7 b) c) 0 d) e) 7 f) 00 g) ) Epand and simplif where possible: a) ( + )( ) b) ( + )( ) c) ( + )( + ) d) ( )( + ) e) ( + 7)( 7) f) ( 6 ) ) Simplif the following: ) Work out the following, giving our answer in its simplest form: a) 8 b) 8 c) 99 d) 0 e) 8 8 f) 8 7 ) Epand and simplif where possible: a) ( ) b) ( 6+ ) c) 7( + 7) d) ( 8) a) b) c) d) e) f) ( + )( ) ( )( + ) ( )( + ) ( + ) ( + ) 0 ( )( + ) 0 Page 7A

110 MathsWatch Clip 7 Grade A and A* questions Surds ) = k a) Write down the value of k. b) Epand and simplif ( + )( + ) Give our answer in the form a + b c where a, b and c are integers. ) The diagram shows a right-angled triangle with lengths of sides as indicated. The area of the triangle is A cm 6 cm Show that A = k giving the value of k. ) a) Find the value of 6 b) Given that 8 8 a + b find the value of a and the value of b. =, where a and b are integers, ) Work out ( + )( ) Give our answer in its simplest form. Page 7B

111 MathsWatch Clip 8 Grade A and A* questions Rationalising the Denominator ) Rationalise the denominator, simplifing where possible: a) b) c) 7 d) 0 e) 8 f) g) 7 ) Rationalise the denominator of ) Rationalise the denominator of 8 8 giving the answer in the form p Page 8

112 MathsWatch Clip 6 Grade A and A* questions Rearranging Difficult Fomulae ) Make c the subject of the formula. v = a + b + c ) Make t the subject of the formula. A = π t + t ) Make s the subject of the formula. R = s + π s + t l ) k = m l a) Make l the subject of the formula. b) Make m the subject of the formula. ) A k ( = + ) Make the subject of the formula. 6) R = u+ v u+ v Make u the subject of the formula. 7) + = 0+ Make the subject of the formula. 8) a = b Rearrange this formula to give a in terms of b. 9) S = πd h + d Rearrange this formula to make h the subject. Page 6

113 MathsWatch Clip 66 Grade A and A* questions Gradients of Lines ) B (0, 7) A (0, ) 0 A is the point (0, ) B is the point (0, 7) a) Write down the equation of the straight line which passes through points A and B. b) Find the equation of the line perpendicular to AB passing through B. ) A straight line has equation = The point P lies on the straight line. The coordinate of P is -6 a) Find the coordinate of P. A straight line L is parallel to = and passes through the point (, ). b) Find the equation of line L. c) Find the equation of the line that is perpendicular to line L and passes through point (, ). ) In the diagram A is the point (0, -) B is the point (-, ) C is the point (0, ) a) Find the equation of the line that passes through C and is parallel to AB. b) Find the equation of the line that passes through C and is perpendicular to AB. B C O - - A - Page 66

114 MathsWatch Clip 67 Grade A and A* questions Transformations of Functions ) The graph of = f() is shown on the grids. a) On this grid, sketch the graph of = f ( ) 6 = f() O b) On this grid sketch the graph of = f() 6 = f() O Page 67A

115 MathsWatch Clip 67 Grade A and A* questions Transformations of Functions ) (, ) = f() O The diagram shows part of the curve with equation = f(). The coordinates of the maimum point of this curve are (, ). Write down the coordinates of the maimum point of the curve with equation a) = f( ) b) = f() ) = f() - O 6 The curve with equation = f() is translated so that the point at (0, 0) is mapped onto the point (, 0). Find the equation of the translated curve. Page 67B

116 MathsWatch Clip 67 Grade A and A* questions Transformations of Functions ) The graph of = f() is shown on the grid. = f() graph G O The graph G is a translation of the graph of = f(). a) Write down, in terms of f, the equation of graph G. The graph of = f() has a maimum point at (-, ). b) Write down the coordinates of the maimum point of the graph = f(-). ) This is a sketch of the curve with the equation = f(). The onl minimum point of the curve is at P (, -). = f() o P (, -) a) Write down the coordinates of the minimum point of the curve with the equation = f( ) b) Write down the coordinates of the minimum point of the curve with the equation = f( + ) + 6 Page 67C

117 MathsWatch Clip 67 Grade A and A* questions Transformations of Functions ) This is a sketch of the curve with equation = f(). It passes through the origin O. The onl verte of the curve is at A (, -) a) Write down the coordinates of the verte of the curve with equation (i) = f( ) (ii) = f() (iii) = f() (iv) = f() A (, -) b) The curve = has been translated to give the curve = f(). Find f() in terms of. ) The graph of = f() is shown on the grids. a) On this grid, sketch the graph of = f( ) b) On this grid, sketch the graph of = f() ) Sketch the graph of = ( ) + State the coordinates of the verte. Page 67D

118 MathsWatch Clip 68 Grade A and A* questions Graphs of Trigonometric Functions ) On the aes below below, draw a sketch-graph to show = sin Given that sin 0 = 0., write down the value of: (i) sin 0 (ii) sin 0 ) On the aes below, draw a sketch-graph to show = cos Given that cos 60 = 0., write down the value of: (i) cos 0 (ii) cos 0 Page 68A

119 MathsWatch Clip 68 Grade A and A* questions Graphs of Trigonometric Functions ) On the aes below, draw a sketch-graph to show = tan ) The diagram below shows the graph of = cos a + b, for values of between 0 and 00. Work out the values of a and b. ) Here is the graph of the curve = cos for 0 < < 60. a) Use the graph to solve cos = 0.7 for 0 < < 60 b) Use the graph to solve cos = -0.7 for < < Page 68B

120 MathsWatch Clip 69 Grade A and A* questions Transformations of Trigonometric Functions ) The diagram below shows the graph of = sin, for values of between 0 and 60. B A The curve cuts the ais at the point A. The graph has a maimum at the point B. a) (i) Write down the coordinates of A. (ii) Write down the coordinates of B. b) On the same diagram, sketch the graph of = sin + for values of between 0 and 60. ) The diagram below shows the graph of = cos a + b, for values of between 0 and 00. Work out the values of a and b Page 69

121 MathsWatch Clip 70 Grade A and A* questions Graphs of Eponential Functions ) (, 7) (, ) The sketch-graph shows a curve with equation = pq. The curve passes through the points (, ) and (, 7). Calculate the value of p and the value of q. ) The graph shows the number of bacteria living in a petri dish. The number N of bacteria at time t is given b the relation: N = a b t The curve passes through the point (0, 00). a) Use this information to show that a = 00. The curve also passes through (, 900). b) Use this information to find the value of b. Number of bacteria N t c) Work out the number of bacteria in the dish at time t =. Time (hours) Page 70