ESSENTIAL REVISION QUESTIONS. MathsWatch Higher. Book

Transcription

1 GCSE Mathematics ESSENTIAL REVISION QUESTIONS MathsWatch Higher Book with answers to all questions enquiries to

2 CONTENTS Grades C/D... to 0 B... to A/A*... to 7

3 T) a) t + 7t b) t 7t c) + w d) t e) e e f) m 7 m g) 8 Essential Questions at C to D ( to 7 are non-calculator) Grade C Clip 0 a) t b) 8t c) + w d) 8t or 8t e) e f) m g) h) h) S) a) t + 8t b) t 9t c) + w d) t e) e e 7 f) g) r r 7 a) t b) 8t c) 7 + w d) 8t or 8t e) e f) g) r h) r h) r r T) a) Epand ( ) b) Epand ( + ) c) Epand and simplif ( + ) ( ) d) Epand and simplif ( ) + ( ) e) ( + )( ) Grade C Clip 0 S) a) Epand ( ) b) Epand ( + ) c) Epand and simplif ( + ) ( ) d) Epand and simplif ( ) + ( ) e) ( )( ) a) b) + c) + d) 7 e) a) b) + 0 c) + d) 8 e) + Page MathsWatch Ltd info@mathswatch.com Page

4 T) Find the nth term of the following patterns a),, 7, 9,..... b) 8,, 8,, 8,..... c) 9,,, 0,,..... Grade C Clip a) n + b) n + c) n + S) Find the nth term of the following patterns a),, 0,, b) 7,,,,,..... c),,,, 7,..... a) n b) 9n c) n + 8 T) Number of smarties Frequenc 9 0 a) From the table above, find the mean number of smarties in a tube. b) Find the median number of smarties in a tube. Grade C Clip a) 0. b) 0 S) Number of smarties Frequenc 9 0 a) From the table above, find the mean number of smarties in a tube. b) Find the median number of smarties in a tube. a) 0.7 b) Page MathsWatch Ltd info@mathswatch.com Page

5 T) Factorise the following: a) + b) + 8 c) + d) + e) + f) g) 9h + h h) 8 0 Grade C Clip 0 a) ( + ) b) ( + ) c) ( + ) d) ( + ) e) ( + ) f) ( ) g) h(h + ) h) ( ) S) Factorise the following: a) t + 0 b) m c) + 8 d) + e) t + t f) t + 0t g) 7t t h) 9h 0h a) (t + ) b) (m ) c) ( + ) d) ( + ) e) t(t + ) f) t(t + ) g) 7t(t ) h) h(h 0) T) a) If a piece of wood is measured as 8cm to the nearest cm, what is the greatest possible length and the least possible length? b) If a piece of wood is measured as 9.8cm to the nearest tenth of a cm, what is the greatest possible length and the least possible length? Grade C Clip S) a) If a piece of wood is measured as cm to the nearest cm, what is the greatest possible length and the least possible length? b) If a piece of wood is measured as.7cm to the nearest tenth of a cm, what is the greatest possible length and the least possible length? a) Greatest is 8.cm Least is 7.cm b) Greatest is 9.8cm Least is 9.7cm a) Greatest is.cm Least is.cm b) Greatest is.7cm Least is.cm Page MathsWatch Ltd info@mathswatch.com Page

6 7T) a) If a = and t = find the value of (i) a (ii) a (iii) a (iv) a t (v) (a + t) (vi) a t 7 Grade D Clip b) Colin said when =, then the value of is Sue said when =, then the value of is Who was right? Eplain wh. a) (i) 9 (ii) 9 (iii) (iv) (v) (vi) b) Sue because is 7S) a) If a = and t = find the value of (i) a (ii) a (iii) a (iv) a t (v) (a + t) (vi) a t 7 b) Colin said when =, then the value of is 00 Sue said when =, then the value of is 00 Who was right? Eplain wh a) (i) (ii) (iii) 80 (iv) (v) (vi) b) Sue because is 8T) Using the information that 7 = 8 Write down the value of: a) 7.. = b) 7 0 = c).8 7. = Grade C Clip 97 8S) Using the information that 8 = 7 Write down the value of: a) 8. = b) = c).7.8 = a).8 b) 80 c) a) 7. b) 7. c). Page MathsWatch Ltd info@mathswatch.com Page

7 9T) Write the following numbers as the product of their prime factors Grade C a) 8 b) 0 Clips 9 & 9 c) Find the Highest Common Factor of 8 and 0 d) Find the Lowest Common Multiple of 8 and 0 9S) Write the following numbers as the product of their prime factors a) 90 b) 0 c) Find the Highest Common Factor of 90 and 0 d) Find the Lowest Common Multiple of 90 and 0 0T) a) Draw an angle of 70 degrees and then use ruler and compasses to bisect it. b) Draw a line of length 9cm and then bisect it using compasses. c) Use compasses to draw a triangle ABC with AB equal to 9cm, AC 7cm and BC cm a) b) c) d) 0 a) b) c) 0 d) 0 Grade C Clip 7 Grade C Clip 9 Grade D Clip 80 0S) a) Draw an angle of 0 degrees and then use ruler and compasses to bisect it. b) Draw a line of length cm and then bisect it using compasses. c) Use compasses to draw an isosceles triangle with the base equal to 8cm and the other two sides of length cm T) What is + 7? S) Work out the answer to 8 Grade D Clip 9 T) What is. 0.? S) What is.7 0.? Grade D Clip 0 Grade C Clip 08 T) < < is an integer. Write down all the possible values. S) < < is an integer. Write down all the possible values ,,, 0,,,,, 0,,, Page 7 MathsWatch Ltd info@mathswatch.com Page 7

8 T) Here are the front elevation, side elevation and the plan of a -D shape. Draw a sketch of the -D shape. Front elevation Side elevation Grade D Clip 8 Plan S) Here are the front elevation, side elevation and the plan of a -D shape. Draw a sketch of the -D shape. Front elevation Side elevation Plan T) a) Work out b) Work out 0 8 of 00 of 800 Grade D Clip a) 80 b) 00 c) Work out 7 c) 0 S) a) Work out 7 0 of 00 a) 80 b) Work out 9 of 900 b) 00 c) Work out 8 c) Page 8 MathsWatch Ltd info@mathswatch.com Page 8

9 T) If ou share out 0 between Alice and Bill in the ratio :, how much more does Alice get compared with Bill? Grade C Clip 9 S) If ou share out 0 between Alice and Bill in the ratio :, how much does each of them get? 7T) Sara and Fred share tips from their job in the ratio :. If Fred receives how much does Sara get? Grade C Clip 9 7S) Sara and Fred share tips from their job in the ratio :. If Sara receives 8 how much does Fred get? 0 for Alice and for Bill 8T) Some plant heights are measured as shown in the table, below. Height in cm Frequenc 0 < h < 0 0 < h < 0 0 < h < 0 0 < h < 80 a) Find an estimate for the mean height of a plant. b) In which interval does the median height lie? a) 0 b) 0 < h 0 8S) Some plant heights are measured as shown in the table, below. Height in cm Frequenc 0 < h < 0 0 < h < 0 0 < h < 0 0 < h < 80 a) Find an estimate for the mean height of a plant. b) In which interval does the median height lie? Grade C Clip a) 8 b) 0 < h 0 Page 9 MathsWatch Ltd info@mathswatch.com Page 9

10 9T) a) Reflect the shaded shape in the ais and label it T b) Rotate T 90º anticlockwise using (0, 0) as the centre of rotation and label the new shape U c) Decribe full the single transformation that will move U back on to the shaded shape T U c) Reflection in = Grade D Clips 7, 7, 77 9S) a) Reflect the shaded shape in the ais and label it T b) Rotate T 90º clockwise using (0, 0) as the centre of rotation and label the new shape U c) Decribe full the single transformation that will move U back on to the shaded shape U T c) Reflection in = Page 0 MathsWatch Ltd info@mathswatch.com Page 0

11 0T) a) Enlarge triangle A scale factor using (, ) as centre of enlargement b) Enlarge triangle A scale factor ½ using (, 0) as centre of enlargement Grade D Clip 7 0S) a) Enlarge triangle A scale factor using (, ) as centre of enlargement b) Enlarge triangle A scale factor ½ using (-, ) as centre of enlargement Page MathsWatch Ltd info@mathswatch.com Page

12 T) Find the eterior angle of this regular octagon Grade D Clip 70 degrees S) Find the eterior angle of this regular heagon 0 degrees T) a) In the triangle below, find an epression, in terms of, for the perimeter of the triangle. Simplif our epression. a) + 8 b) = 9 cm b) If the perimeter of the triangle is cm, find the value of. Grade C Clip 0 8 S) a) In the rectangle below, find an epression, in terms of, for the perimeter of the rectangle. Simplif our epression. a) 8 + b) = cm + b) If the perimeter of the rectangle is cm, find the value of. Page MathsWatch Ltd info@mathswatch.com Page

13 T) Find the size of angle n, giving reasons A B C Grade D Clips 8, 9 S) Find the size of angles and, giving reasons A B C ABC = 0 (angles on st. line = 80) n = 78 (angles in add up to 80) = (angles in =80, base angles are equal) ABC = (base angles of isos. are equal) = (angles on st. line = 80 ) T) Find the size of angle, giving reasons Grade D Clip 7 BRS = 0 (angles on straight line add up to 80 ) = 0 (alternate angles) S) Find the size of angles and, giving reasons = 8 = 7 (angles in quadrilateral add up to 0 ) (alternate angles) Page MathsWatch Ltd info@mathswatch.com Page

14 T) Solve the following equations a) = 7 b) 8 = c) + = d) + = 7 e) ( ) = f) = g) + = S) Solve the following equations a) = b) 9 = c) + = d) + = e) ( + ) = f) = g) + = Grade C Clip 0 a). b) c) d) e) f) g). a) b) c) d) e) 7 f) 7. g) T) Draw a stem and leaf diagram to show the following information. The heights of plants in cm are:.,.,.,.,.8,.,.7,.,.7,.,.,.9 S) Draw a stem and leaf diagram to show the following information. The weights of 0 people in kg are: 9,, 8, 7, 7,, 0,, 8, 7 7T) a) Change 7 m to cm b) Change cm to mm c) Change 9 m to cm 7S) a) Change cm to mm b) Change m to cm c) Change cm to mm Grade D Clip 89 Grade C Clip Ke means Ke means a) cm b) 00 mm c) cm a) 00 mm b) 0000 cm c) 000 mm Page MathsWatch Ltd info@mathswatch.com Page

15 8T) a) Anne bus litres of diesel at. per litre. How much does she spend altogether on diesel? b) James spends.7 on litres of petrol. How much was each litre of petrol? Grade D Clip 0 & Grade C Clip 00 8S) a) Sara bus litres of diesel at. per litre. How much does she spend altogether on diesel? b) Sid spends 7. on litres of petrol. How much was each litre of petrol? a) 0.7 b). a) 8. b). 9T) a) b) c) d) Grade D Clips and 7 a) b) c) d) 7 0 9S) a) + a) b) 7 b) c) 0 8 c) 9 0 d) 0 d) 0T) Draw a pie chart to show the following information Crisp flavour Frequenc Cheese 8 Plain 9 Beef Prawn Grade D Clip 8 0S) Draw a pie chart to show the following information Crisp flavour Frequenc Cheese 8 Plain Beef Prawn P B C Plain Cheese Plain Beef Prawn B P Plain Cheese Plain Beef Prawn C Page MathsWatch Ltd info@mathswatch.com Page

16 T) Find the areas of the following shapes a) 7m b) a) m m cm b) 0cm cm c) 0cm c) 8cm cm cm cm Grade D Clip 7 S) Find the areas of the following shapes a) 9m b) a) m m 7cm b) cm cm c) cm c) cm cm cm cm Page MathsWatch Ltd info@mathswatch.com Page

17 T) Find the surface area of this cuboid. 9cm cm 8cm cm Grade C Clip 0 S) Find the surface area of this cuboid. 90cm cm 0cm cm T) Make the letter in the bracket the subject of the formula. a) v = u + at (a) b) a t = bc () S) Make the letter in the bracket the subject of the formula. a) v = u + as (a) b) a + = c () Grade C Clip 07 a) b) = a(bc + t) a) a = a = v - u t v - u s b) = a(c ) T) Find the following: a) 0% of 700 b) % of 80 c) % of 00 d) 7.% of 8 Grade D Clip a) 70 b) c) 0 d) 8.0 S) Find the following: a) 0% of 0 b) % of 900 c) 8% of 800 d) 7.% of 0 a) 0 b) c) 80 d) Page 7 MathsWatch Ltd info@mathswatch.com Page 7

18 T) Sall s mother lives 80km from Sall. This is the journe to her mother s house. a) Sall has a rest at 8.0. What speed had she been travelling at until 8.0? b) How long did she rest for? c) What speed did she travel at for the last part of the journe to her mother s house? d) For the return journe, Sall travelled at 0km/h without a break. Complete the travel graph to show this. S) Sall s mother lives 90km from Sall. This is the journe to her mother s house. Distance in km from home Distanc e in km from home Time Grade C Clip 7 a) 00km/h b) 0 mins c) 0km/h a) 0km/h b) 0km/h Time a) What speed did Sall travel at until her first rest? b) What speed did she travel at for the last part of the journe to her mother s house? c) For the return journe, Sall travelled at 80km/h without a break. Complete the travel graph to show this. Page 8 MathsWatch Ltd info@mathswatch.com Page 8

19 T) a) Complete the table for the equation = Grade C Clip b) Draw the graph of = on the aes at the bottom of the page c) Use our graph to find the value of when =. d) Use our graph to find the value of when =. e) Use our graph to solve = f) Use our graph to solve = 8 c). d) 9 e) = and =. f) =. and = O - - Page 9 MathsWatch Ltd info@mathswatch.com Page 9

20 S) a) Complete the table for the equation = 0 Grade C Clip b) Draw the graph of = on the aes at the bottom of the page c) Use our graph to find the value of when =. d) Use our graph to find the value of when =. e) Use our graph to solve = 0 c). d) 8. e) =.7 and = O - - Page 0 MathsWatch Ltd info@mathswatch.com Page 0

21 7T) Draw a set of aes going from to + a) Draw the graph of = b) What is the gradient? 7S) Draw a set of aes going from to + a) Draw the graph of = + b) What is the gradient? Grade C Clip b) b) = O = - 8T) The table below shows the probabilit of an oddl shaped -sided dice landing on,,, or. a) Work out the value of b) If the dice is rolled 000 times how man s would ou epect to get? Grade C Clip 8S) The table below shows the probabilit of an oddl shaped -sided dice landing on,,, or. a) Work out the value of b) If the dice is rolled 000 times how man s would ou epect to get? a) 0. b) 70 a) 0. b) 0 9T) Draw a plane of smmetr on this shape Grade D Clip 8 other answers are possible 9S) Draw a plane of smmetr on this shape other answers are possible Page MathsWatch Ltd info@mathswatch.com Page

22 0T) Height Frequenc 0 to 0 0 to 0 0 to 0 0 to 0 a) On the first set of aes, draw a frequenc diagram b) On the second set of aes, draw a frequenc polgon Grade D Clip 88 0S) Height Frequenc 0 to 0 0 to to 0 0 to 0 ANSWERS for 0T a) On the first set of aes, draw a frequenc diagram b) On the second set of aes, draw a frequenc polgon 7 Frequenc Height 7 7 Freq ue nc Height Frequenc Height 7 Freq ue nc 7 Frequenc Height 7 7 Freq ue nc Height Frequenc Height 7 Freq ue nc ANSWERS for 0S Height Page MathsWatch Ltd info@mathswatch.com Height Page

23 T) a) In a room there are 7 bos and girls. What percentage of the people are bos? b) In a room there are bos and 7 girls. What percentage of the people are girls? c) Sall scores marks out of 0 in a Science test. What was her percentage score? Grade D Clip S) a) In a room there are bos and 9 girls. What percentage of the people are bos? b) In a room there are bos and girls. What percentage of the people are girls? c) Emma scores marks out of 0 in a Science test. What was her percentage score? a) 70% b) % c) 0% a) % b) 8% c) 90% T) A point, P, moves so that the locus of P is alwas cm from the line AB. Draw the locus of P. Grade C Clip 0 A B S) A point, P, moves so that the locus of P is alwas equidistant from lines AB and AC. Draw the locus of P. A B Page MathsWatch Ltd info@mathswatch.com C Page

24 T) a) Sketch a scatter diagram with positive correlation hair length, hair colour, intelligence, circumference of wrist, height, ice cream sales, weight, outside temperature sale of etra-warm jackets, ee colour b) From the list above select two sets of data which would have (i) a positive correlation (ii) no correlation Grade D Clip 87 S) a) Sketch a scatter diagram with negative correlation hair length, hair colour, intelligence, circumference of wrist, height, ice cream sales, weight, outside temperature sale of etra-warm jackets, ee colour b) From the list above select two sets of data which would have (i) a negative correlation (ii) no correlation T) a) What are the first four multiples of 7? b) Write down all the factors of 0. c) What are the first si prime numbers? S) a) What are the first four multiples of? b) Write down all the factors of 0. c) Which two prime numbers come net, after? Grade D Clip T) Solve the inequalit + < S) Solve the inequalit 7 > Grade C Clip 09 T) Evaluate S) Evaluate Grade D Clip a) b) (i) height and weight or Ice cream sales and temp. (ii) hair length and hair colour or hair colour and intelligence etc a) b) (i) temp. and sale of jackets (ii) ee colour and intelligence or hair length and weight etc a) 7 8 b) 0 0 c) 7 a) 0 0 b) c) 7 9 < > 0 Page MathsWatch Ltd info@mathswatch.com Page

25 7T) Find the volume of this triangular prism. cm cm 7cm 7S) Find the volume of this triangular prism. Grade C Clip Volume = 8cm cm 8cm 8T) a) Write as a power of b) Write as a power of 8 0cm Grade C Clip Volume = 0cm a) 7 8 b) 8S) a) Write as a power of b) Write as a power of 9 a) 7 b) 9T) Complete the two-wa table which shows the favourite soup of 00 people. Otail Tomato Chicken Total Male Female 8 Total 00 Grade D Clip 8 Otail Tomato Chicken Total Male Female Total S) 0 students studied Histor and Geograph as shown in the two-wa table. Histor Geograph Both Total Female Male 8 Total males studied both subjects. of the students were male. Complete the two-wa table. Histor Geograph Both Total Female 8 Male 8 0 Total Page MathsWatch Ltd info@mathswatch.com Page

26 0T) Measure this angle. 8 0S) Measure this angle. Grade D Clip 79 T) The price of a pair of shoes is 7. How much are the after a price increase of 0%? Grade C Clip 9 S) A new car costs If the price is reduced b % what is the new price? T) S) Grade C Clip 00 0 T) What are the first terms of the number sequence with the nth term of n +? Grade D Clip S) What are the first terms of the number sequence with the nth term of n? Page MathsWatch Ltd info@mathswatch.com Page

27 T) Translate triangle A b vector Grade D Clip 77 S) Describe full the transformation which maps triangle A onto triangle B. Translation b vector - B.. T) Change the recurring decimal 0.7 into a fraction in its simplest form. S) Change the recurring decimal 0. into a fraction in its simplest form... Grade C Clip 98 7 Page 7 MathsWatch Ltd info@mathswatch.com Page 7

28 T) What is the equation of the line? = O S) What is the equation of the line? Grade C Clip = O T) List all of the outcomes if ou roll a dice and flip a coin. 7S) List all of the outcomes if ou flip three coins. Grade D Clip 90 H H H H H H T T T T T T HHH HHT HTH THH TTT TTH THT HTT Page 8 MathsWatch Ltd info@mathswatch.com Page 8

29 8T) Use a protractor to work out the bearing of A from B. Grade C Clip Bearing of A from B is 9 A A N B B 8S) Use a protractor to work out the bearing of B from A. N B Bearing of B from A is 0 B A A 9T) In the list of fractions, below, which two are equivalent to? S) In the list of fractions, below, which two are equivalent to? Grade D Clip 7 0T) A map has a scale of : If town A is cm awa from town B on the map, what is the actual distance between them in kilometres? 0S) A map has a scale of : If town A is cm awa from town B on the map, what is the actual distance between them in kilometres? Grade D Clip km km 0 Page 9 MathsWatch Ltd info@mathswatch.com Page 9

30 T) a) - - b) 7 - c) - d) -8 e) 9 - f) g) Grade C Clip 99 S) a) - b) -0 - c) - d) 8 e) - f) + -7 g) T) Use the graph to solve the simultaneous equations = 7 and = 8 7 = 7 = a) b) - c) - d) - e) f) g) -9 = and = a) -8 b) 0 c) - d) - e) f) - g) S) Use the graph to solve the simultaneous equations = 8 and = ½ Grade C Clip = 8 = ½ + = and = Page 0 MathsWatch Ltd info@mathswatch.com Page 0

31 T) Estimate the answer to S) Estimate the answer to Grade C Clip 0 T) A triangular prism has sides as shown. Find the surface area of the prism cm cm cm 7 cm S) A triangular prism has sides as shown. Find the surface area of the prism. Grade C Clip 70 cm 8 m 0 m m m m T) If the probabilit of passing a driving test is 0. what is the probabilit of failing the test? 0.8 Grade D Clip 9 S) The probabilit of a school football team winning a football match is 0. and the probabilit of losing is 0.. What is the probabilit of the team drawing the match? 0. Page MathsWatch Ltd info@mathswatch.com Page

32 T) Draw the net of this right-angled triangular prism. squares squares Grade D Clip 8 squares squares S) Draw the net of this cuboid squares squares squares Page MathsWatch Ltd info@mathswatch.com Page

33 7T) Write the following fractions in their simplest forms. a) b) c) Grade D Clip 8 7S) Write the following fractions in their simplest forms. a) 0 b) 7 c) 0 8T) Here are the ingredients needed to make salmon fishcakes for four people. 0g potatoes 900g of salmon g butter g dill 0g flour eggs 0g breadcrumbs a) What weight of salmon would be needed to use the recipe for si people? b) For seven people, what weight of flour is needed? 8S) Here are the ingredients needed to make shepherd's pie for five people. 00g potatoes 0g of cheese 0g butter onion carrots 00ml stock kg of lamb a) What weight of cheese would be needed to use the recipe for eight people? b) For si people, how much stock is needed? c) For nine people, what weight of lamb should be used? Grade D Clip a) b) c) a) b) c) 8 a) 0g b) 87.g a) 80g b) 0ml c).8kg Page MathsWatch Ltd info@mathswatch.com Page

34 9T) Put these fractions in order of size, smallest to largest S) Put these fractions in order of size, smallest to largest Grade D Clip T) a) What is the square of? b) Find the cube of. c) What is the square root of 9? d) What is the cube root of 7? e) Evaluate 70S) a) What is the square of 8? b) Find the cube of. c) What is the square root of 00? d) What is the cube root of? e) Evaluate 9 Grade D Clip a) b) c) 7 d) e) a) b) 8 c) 0 d) e) 7T) Sara wishes to find out how much pocket mone people in her class received. Design a suitable question she could use on a questionnaire. You should include some tickboes. 7S) Fred wants to know which sports are watched b pupils in his class. Design a suitable data collection sheet he can use to find out. Grade D Clip 8 Grade C Clip 7T) Change the following fractions to decimals. a) b) 8 How much pocket mone do ou receive each week? Less than Between.0 and More than Sport Tall Frequenc Football Cricket Tennis Athletics Rugb Other a) 0.8 b) 0.7 7S) Change the following fractions to decimals. a) b) 0 8 a) 0. b) 0. Grade D Clip 8 Page MathsWatch Ltd info@mathswatch.com Page

35 Questions 7 to 8 are all calculator questions 7T) Find the length of sides A, B and C giving our answers to one decimal place. cm A.9cm cm A cm B B C 8.cm.cm 7cm Grade C Clip 8 C.9cm.8cm 7S) Find the length of sides A, B and C giving our answers to one decimal place. A 7cm cm 8cm A B C.cm.9cm.7cm 9cm B 9.cm 8.cm C 7T) The equation + = 0 has a solution between and. Use a trial and improvement method to find this solution. Give our answer to decimal place and show all workings. 7S) The equation = 88 has a solution between and. Use a trial and improvement method to find this solution. Give our answer to decimal place and show all workings. Grade C Clip 0 = + = Too low = + = Too big =.. +. = 8. Too low =.. +. = 0. Too big =.. +. = 9.0 Too low =. to decimal place. = = 8 Too low = = 0 Too big = = 8.0 Too low = = 9.9 Too big = = Too big =.7 to decimal place. Page MathsWatch Ltd info@mathswatch.com Page

36 7T) a) % of 8.7 = b) 7% of 900 = c) Reduce.0 b.% 7S) a) 9% of.0 = b) % of 00 = c) Reduce 0 b 0% 7T) If =. Euros, a) Change 8 to Euros. b) Change 0 Euros to pounds ( ). 7S) If =.7 Euros, a) Change 000 to Euros. b) Change 9 Euros to pounds ( ). Grade D Clip Grade D Clip a) 9.78 b) 8 c) 9.8 a) 8. b) 0 c) 8 a).7 Euros b) 8. a) 0 Euros b) T) a) Find the area of the following circles. Give both answers to decimal place. (i) (ii) a) (i).9cm 7cm cm (ii).cm b) Find the area of this quarter circle. Grade D Clip 7 77S) a) Find the area of the following circles. Give both answers to decimal place. (i) cm (ii) 7.cm 0cm b) 78.cm a) (i) 80.cm (ii).cm b) Find the area of this semicircle. 9cm b).8cm Page MathsWatch Ltd info@mathswatch.com Page

37 78T) Which is the best value for mone 00g of sausages for.7 or 0g of the same tpe of sausages for.70? You must show all our working. 0.p per gram 0.7p per gram 00g for.7 best value 78S) Which is the best value for mone 800ml of orange juice for 0.8 or 0ml of orange juice for 0.? You must show all our working. Grade D Clip 0 0.0p per ml 0.p per ml 800ml for 0.8 best value 79T) a) Find the circumference of the following circles. Give both answers to decimal place. (i) (ii) a) (i).0cm (ii) 7.cm 7cm cm b) Find the perimeter of this quarter circle to decimal place. Grade D Clip 7 0cm 79S) a) Find the circumference of the following circles. Give both answers to decimal place. (i) cm (ii) 7.cm b).7cm a) (i) 9.cm (ii).cm b) 8.8cm b) Find the perimeter of this semicircle to decimal place. 9cm Page 7 MathsWatch Ltd info@mathswatch.com Page 7

38 80T) a) Change the following to percentages. Give our answers to decimal place. (i) 7 out of 7 (ii) out of 8 b) If Sue scores 8 marks out of a possible 0 marks, what was her score as a percentage? 80S) a) Change the following to percentages. Give our answers to decimal place. (i) out of 78 (ii). out of 9 b) If Sue scores marks out of a possible 7 marks, what was her score as a percentage? Grade D Clip a) (i).% (ii).7% b) 8.% a) (i).% (ii).% b) 8.7% 8T) Find the volume of this clinder. Give our answer to decimal place. 9cm cm Grade C Clip Volume = 07.cm 8S) Find the volume of this clinder. Give our answer to decimal place. 0cm Volume = 7.cm 7cm 8T) Evaluate 8S) Evaluate (. 7.) Grade D Clip = = Page 8 MathsWatch Ltd info@mathswatch.com Page 8

39 8T) Find the length of the line. Grade C Clip 9 cm O O 8S) Find the length of the line to decimal place..cm O O 8T) a) A cclist travels miles in hours. What is the cclist's speed in mph? b) Sue walks for minutes at mph. How far does she travel? c) A piece of lead has a mass of 0g and a volume of 0cm. Work out its densit in g/cm. Grade C Clip 8S) a) A cclist travels at.mph for hours. What distance does he cover? b) Sue drives at an average speed of 7mph and covers a distance of. miles. How long does the journe take in hours and minutes? c) A piece of lead has a densit of g/cm and a mass of kg. Work out its volume in cm. a) mph b) 0. miles c). g/cm a) 7. miles b) hours 0 minutes c).7cm Page 9 MathsWatch Ltd info@mathswatch.com Page 9

40 8T) The two triangles are similar. cm 7.8cm 8cm.cm a) Work out the size of. b) Work out the size of. a) = 7cm b) = 7cm 8S) BE is parallel to CD Find the length of BC. A Grade C Clip BC = 8cm 0cm B cm E C.cm D Page 0 MathsWatch Ltd info@mathswatch.com Page 0

41 Essential Questions at grade B (A calculator can be used on all questions apart from qu. ) T) Solve these two simultaneous equations r + s = r s = Grade B Clip S) Solve these two simultaneous equations h + t = 0 h t = 8 r = and s = h = and t = T) Mar recorded the heights, in centimetres, of the girls in her class. She put the heights in order Grade B Clip a) LQ = b) UQ = 77 a) Find the lower quartile b) Find the upper quartile c) On the grid, draw a boplot for this data. S) Mar recorded the heights, in centimetres, of the girls in her class. She put the heights in order. a) LQ = b) UQ = a) Find the lower quartile b) Find the upper quartile c) On the grid, draw a boplot for this data. Page MathsWatch Ltd info@mathswatch.com Page

42 T) Work out the lengths or angles indicated b the letters a to d. a cm b 8cm a =.cm b = 8. 8 Grade B Clip 7 cm c =.8cm d =. 0cm cm c d 8cm S) Work out the lengths or angles indicated b the letters e to h. cm cm e f e =.9 f =.cm cm g =.cm h =. h g cm 9.cm.cm Page MathsWatch Ltd info@mathswatch.com Page

43 T) TR and TQ are tangents to the circle a) Eplain wh angle PQR = º Grade B Clip 0 a) b) PQT = 90 (Tangent meets radius at 90 ) 90 8 = PRQ = 90 (angle in semicircle is 90 ) TRQ = 8 (tri. TRQ is isosceles and base angles are equal) PRT = = 8 b) Find the size of angle PRT giving reasons S) TR and TQ are tangents to the circle a) Eplain wh angle PQR = º a) PQT = 90 (Tangent meets radius at 90 ) 90 = b) PRQ = 90 (angle in semicircle is 90 ) TRQ = (tri. TRQ is isosceles and base angles are equal) PRT = 90 + = b) Find the size of angle PRT giving reasons T) Find angles a and b 0 a a = 8 (opp angles of cclic quad. add up to 80) Grade B Clip 0 9 b b = 7 (opp angles of cclic quad. add up to 80) S) Find angles a and b b a a = (opp angles of cclic quad. add up to 80 ) b = 7 (opp angles of cclic quad. add up to 80 ) Page MathsWatch Ltd info@mathswatch.com Page

44 T) Find the size of angle. = o S) Find the size of angle. Grade B Clip 0 = 8 8 o 7T) a) John places 000 in a bank which pas.% compound interest per ear. How much interest does he earn if he leaves the mone in the bank for ears? b) Sue bus a new car for Its annual rate of depreciation is % per ear. How much is it worth after ears? Grade B Clip 7 7S) a) Sarah bus a -ear bond which pas compound interest of.8% per ear. She bus the bond for How much can she cash the bond in for at the end of the ear period? b) Tom bus a house for 000. It will depreciate at the rate of.% per ear for the net three ears. How much will it then be worth? a) b).90 a) 00.9 b). Page MathsWatch Ltd info@mathswatch.com Page

45 8T) The heights of plants were measured and can be seen in this table. Height (cm) Frequenc 0 < h < 0 0 < h < 0 7 Grade B 0 < h < 0 Clip 0 < h < 0 0 < h < 0 0 < h < 0 a) Complete this cumulative frequenc table. a) CF Height (cm) 0 < h < 0 0 < h < 0 0 < h < 0 0 < h < 0 0 < h < 0 0 < h < 0 Cumulative Frequenc b) Draw a cumulative frequenc curve for our table. c) Use our graph to find an estimate for the b) 80 interquartile range of the heights of the plants. CF Height (cm) Cumulative Frequenc 0 < h < 0 0 < h < < h < 0 0 < h < < h < 0 0 < h < 0 UQ median LQ c) IR = UQ LQ =.. = cm Height (cm) Height (cm) Page MathsWatch Ltd info@mathswatch.com Page

46 8S) The weights of 7 boes of reccled metals can be seen in this table. Weight (kg) Frequenc 0 < w < < w < 0 Grade B 0 < w < 0 8 Clip 0 < w < 0 0 < w < < w < 0 a) Complete this cumulative frequenc table. a) CF Weight (kg) 0 < w < < w < 0 0 < w < 0 0 < w < 0 0 < w < 0 0 < w < 0 Cumulative Frequenc b) Draw a cumulative frequenc curve for our table. c) Use our graph to find an estimate for the b) 80 interquartile range of the weights of the boes. CF Weight (kg) Cumulative Frequenc 0 < w < < w < < w < < w < 0 0 < w < < w < 0 7 UQ 0 0 median LQ c) IR = UQ LQ =. 8. = 7.7kg Weight (kg) Weight (kg) Page MathsWatch Ltd info@mathswatch.com Page

47 9T) There are green sweets and 7 red sweets in a bag. Tom takes a sweet, at random, from the bag and eats it. He then takes another sweet, at random, and eats it. a) Draw a tree diagram in the space below to show all the possibilities. a) 0 Green Green Red 7 0 Red 9 Green Red b) What is the probabilit that Tom ate two Green sweets? c) What is the probabilit that Tom ate two different-coloured sweets? Grade B Clip 9S) There are ellow sweets and blue sweets in a bag. Joe takes a sweet, at random, from the bag and eats it. He then takes another sweet, at random, and eats it. a) Draw a tree diagram in the space below to show all the possibilities. b) c) a) = = 90 Yellow Yellow Blue 0 Blue 9 Yellow Blue b) What is the probabilit that Joe ate two blue sweets? c) What is the probabilit that Joe ate two different-coloured sweets? b) c) 0 9 = = T) a) Write 0000 in standard form. b) Write in standard form. c) Write as a normal number. d) Write.7 0 as a normal number. Grade B Clip a). 0 b). 0 c) d) S) a) Write in standard form. b) Write in standard form. c) Write as a normal number. d) Write 8. 0 as a normal number. a). 0 8 b) 7. 0 c) d) Page 7 MathsWatch Ltd info@mathswatch.com Page 7

48 T) a) In a sale, all the prices have been reduced b %. The sale price of a shirt is. What was the pre-sale price of the shirt? b) The price of a computer is 799. This price includes VAT which is 7.%. What is the cost of the computer before VAT is added? Grade B Clip 8 S) a) A bank pas interest of.8% per ear. Emma places some mone in the bank and, one ear later, after the interest has been paid, she has.80 in her account. How much did she put in the bank? b) After a reduction of.%, Sam pas 97.0 for a car. How much was the car before the reduction? T) In September 007, Jim weighed 8.0kg. In September 008, he weighed 8.7kg. What was his percentage increase in weight? Grade B Clip S) The price of a car decreases from 700 to 8 in one ear. What is the percentage depreciation in this ear? a) 7 b) 80 a) 00 b) 00 % % T) a) b) + a) b) c) d) Grade B Clip 9 S) a) b) 9 + c) d) 7 c) d) a) b) 8 c) d) 0 T) Factorise and solve the following equations: a) = 0 b) + 0 = 0 c) = 0 d) + 7 = 0 S) Factorise and solve the following equations: a) = 0 b) + 0 = 0 c) + = 0 d) 0 + = 0 Grade B Clip 0 a) ( + )( + ) = 0 = - or = - b) ( + )( ) = 0 = - or = c) ( )( ) = 0 = or = d) ( + )( ) =. 0 = -. or = 0. a) ( + )( + ) = 0 = - or = - b) ( + 8)( ) = 0 = -8 or = c) ( )( ) = 0 = or = d) ( + )( ) = 0 = -0. or = 0. Page 8 MathsWatch Ltd info@mathswatch.com Page 8

49 T) On the grid, draw straight lines and use shading to show the region R that satisfies the inequalities < + + < < O O Grade B Clip S) On the grid, draw straight lines and use shading to show the region R that satisfies the inequalities < + < < O O Page 9 MathsWatch Ltd info@mathswatch.com Page 9

50 T) A and B are two geometricall similar solids. The total surface area of shape A is 00cm The total surface area of shape B is 98cm The volume of shape A is 70cm Calculate the volume of shape B. Grade B Clip 9 S) C and D are two geometricall similar solids. The volume of shape C is 7cm The volume of shape D is cm The total surface area of shape C is 9.cm Calculate the total surface area of shape D. 7T) A, B and C are all towns. A is 7.8km due east of B. B is km due south of C. Calculate the bearing of A from C. Give our answer correct to decimal place. Grade B Clip 7c 7S) A, B and C are all towns. B is due south of A. C is 8km due east of B and on a bearing of from A. Calculate the distance between A and B. Give our answer correct to decimal place. 8T) a) Factorise (i) (ii) b) Simplif a 9b a + b c) Solve 9 = 00 Grade B Clip 8S) a) Factorise (i) (ii) 9 b) Simplif a b 8a b c) Solve = 0 9T) Work out the following, giving our answer in standard form. (7 0 ) (9 0 ) Grade B Clip 9S) Work out the following, giving our answer in standard form. (8 0 8 ) ( 0 ) 79.9cm 8.cm 7.0.9km a) (i) ( 8)( + 8) (ii) ( )( + ) a 7b b) c) (. 0)( + 0). = 0 =. or = -. a) (i) ( )( + ) (ii) ( )( + ) a + b b) c) ( )( + ) = 0 =. or = Page 0 MathsWatch Ltd info@mathswatch.com Page 0

51 0T) a) Complete this table of values for = + 0 a) b) On the grid, draw the graph of = + b) O O c) Use the graph to find the value of when = c) =. Grade B Clip Page MathsWatch Ltd info@mathswatch.com Page

52 0S) a) Complete this table of values for = 0 a) b) On the grid, draw the graph of = b) - - O O - - c) Use the graph to find the three values of when = c) = -.7 or -0. or.9 Grade B Clip Page MathsWatch Ltd info@mathswatch.com Page

53 T) a) A straight line is parallel to = and goes through (, 7). What is its equation? b) A straight line goes through points (, ) and (, ). What is its equation? Grade B Clip S) a) A straight line is parallel to = and goes through (, 7). What is its equation? b) A straight line goes through points (, ) and (, ). What is its equation? a) = + b) = + a) = + b) = T) Sketch the graphs of a) = b) = c) = + d) = - Grade B Clip S) Sketch the graphs of a) = - b) = c) = d) = = = a) b) = + = - c) d) = - = a) b) c) = d) = - Page MathsWatch Ltd info@mathswatch.com Page

54 T) Point P has coordinates (7,, ) Point T is the intersection of PR and SQ. Work out the coordinates of T. (.,, ) z S R... T.P. Q Grade B Clip 8 S) P. Point P has coordinates (8,, ) T. z S. a) Work out the coordinates of T. b) Work out the coordinates of S. a) (8,, 0) b) (0, 0, ) T) Two fair si sided dice are rolled. a) Complete the tree diagram to show the outcomes. Grade B Clip Red dice si not si Blue dice b) What is the probabilit of rolling a si on one dice and 'not a si' on the other dice? S) Two coins are flipped. a) Complete the tree diagram to show the outcomes. Coin Coin Head Tail b) What is the probabilit of flipping a head on one coin and a tail on the other coin? a) b) a) b) not + = 0 H T + = not not H T H T Page MathsWatch Ltd info@mathswatch.com Page

55 Essential Questions at grade A/A* (A calculator can be used on all questions unless told otherwise) T) (, ) = f() Grade A/A* Clip 7 0 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() c) = f( ) d) = f() e) = f(½) a) (, ) b) (, 0) c) (, ) d) (, ) e) (, ) S) = f() 0 (, -) The diagram shows part of the curve with equation = f(). The coordinates of the minimum point of this curve are (, -). Write down the coordinates of the minimum point of the curve with equation a) = ½f() b) = f() c) = f( + ) d) = f() + e) = f() a) (, -) b) (0., -) c) (-, -) d) (, 0) e) (, -) Page MathsWatch Ltd info@mathswatch.com Page

56 T) For each triangle find the side or angle marked with the letter. Give our answer correct to decimal place. a) b) 8 cm Grade A/A* Clip 7 9 cm 8 cm a). cm b) 0. c).7 cm c) d) cm d) 7. cm 0 9 cm cm 7 cm S) For each triangle find the side or angle marked with the letter. Give our answer correct to decimal place. a) b) 7 0 m m cm m c) d)* 8 cm 7 cm 98 9 cm a) 78. b). cm c) 0.0 cm d) 9. cm *A trick sine rule question. T) Solve + 7 = 0 Give our solutions correct to decimal places. S) Solve + = 0 Give our solutions correct to decimal places. Grade A/A* Clip =. or = -.8 =.8 or = 0. Page MathsWatch Ltd info@mathswatch.com Page

57 T) q is inversel proportional to the square of t. When t =, q = 9. a) Find a formula for q in terms of t. b) Calculate the value of q when t = 8. c) When q =., calculate the value of t. S) The distance d through which a bod falls from rest is proportional to the square of the time taken, t. The bod falls m in seconds. a) Find a formula for d in terms of t. b) How far will the bod fall in seconds? c) How long will the bod take to fall 0m? T) Grade A/A* Clip 9 0 a) q = t b) q =.7 c) t = 0 a) d = t b) d = 80 m c) t = seconds (, 00) (, 8) Grade A/A* Clip 70 0 The sketch shows a curve with function = ka where k and a are constants and a > 0. The curve passes through points (, 8) and (, 00). Calculate the value of k and the value of a. a = k =. S) (, 9) (, ) 0 The sketch shows a curve with function = ka where k and a are constants and a > 0. The curve passes through points (, ) and (, 9). Calculate the value of k and the value of a. a = k = 0.7 Page 7 MathsWatch Ltd info@mathswatch.com Page 7

58 T) Enlarge triangle A b scale factor -½, centre (0, 0) O A O A Grade A/A* Clip 7 S) Enlarge triangle B b scale factor -½, centre (, ) O B O B Page 8 MathsWatch Ltd info@mathswatch.com Page 8

59 7T) The maimum load a van can safel carr is 800kg. Fred transports metal bars in the van. Each bar weighs 90kg. Fred knows that the 800 is rounded correct to significant figures and 90 is rounded correct to significant figure. Calculate the greatest number of bars that Fred can safel carr in the van. Show all workings. 7S) Grade A/A* Clip 0 0. m m m m All measurements are rounded correct to decimal place. a) Find the largest possible value of the shaded area. b) Find the least possible value of the shaded area. 8T) Calculate the area of triangle ABC. Give our answer correct to decimal place. A 70 9 = 8. Greatest number of bars = 8 a). 7. =. m b) =.9 m Area =. cm 9 cm 0 cm B C 8S) Calculate the area of triangle ABC. Give our answer correct to decimal place. A Area =.8 cm. cm 78 B 8. cm Grade A/A* Clip 7 C Page 9 MathsWatch Ltd info@mathswatch.com Page 9

60 9T) Simplif full a) b) c) Show that the equation 9S) Simplif full a) b) + can be rearranged to give + = c) Show that the equation Grade A/A* Clip 7/8 Grade A/A* Clip = + can be rearranged to give + = 0 0T) a) Rationalise the denominator of b) Epand ( + )( + ) Give our answer in the form a + b, where a and b are integers. 0S) a) Rationalise the denominator of 7 b) Epand and simplif ( 7 )( 7 + ) T) Emma has blue pens and red pens in a pencil case. She picks a pen at random, notes its colour and then replaces it. She does this two more times. Work out the probabilit that when Emma takes three pens, eactl two are the same colour. Grade A/A* Clip 8 S) A bo contains toffees covered in either milk, plain or white chocolate. The probabilit of each is 0., 0. and 0. respectivel. Ton chooses a chocolate, notes the tpe of chocolate and replaces it. He then chooses again. What is the probabilit he chooses eactl one white chocolate toffee? = a) b) b) + 7( + ) ( + )( ) c) ( ) = ( )( + ) 0 = = 0 + = 0 a) + 7 9( + ) ( )( + ) c) ( )( + ) = ( ) + = 0 = = 0 a) b) 7 + a) 7 7 b) 0. Page 0 MathsWatch Ltd info@mathswatch.com Page 0

61 T) S) a a) Find, in terms of a and b, the vectors (i) a R A AB, (ii) RT, (iii) RS S O b B T b) Eplain wh RST is a straight line. The length of RS is cm. c) Find the length of RT. Grade A/A* Clip 80 P N OAB is a triangle. B is the midpoint of OT. S is the midpoint of AB. OR = a RA = a OB = b Q a) (i) a + b (ii) a + b (iii) ½a + ½b b) RS = ½( a + b) RT = ( a + b) RT = RS so RS is parallel to RT from the same point. So RST is a straight line. c) cm p M O OPQR is a parallelogram. M is the midpoint of RQ. N is the midpoint of PQ. OP = p OR = r a) Find, in terms of p and/or q, the vectors (i) MQ (ii) MN r b) Show that RP is parallel to MN R a) (i) ½p (ii) ½p ½r b) RP = p r MN = ½p ½r = ½(p r) So RP is parallel to MN.. T) Prove that the recurring decimal 0. =.. S) Prove that the recurring decimal 0. = Grade A/A* Clip Let = =. 99 = = = 99 Page MathsWatch Ltd info@mathswatch.com Let = =. 99 = = = 99 Page

62 T) Here is the graph of = sin, where 0º < < Grade A/A* Clip 9 What are the equations of these three graphs? Choose from = sin a) = sin = -sin = sin + = sin ½ 0 = -sin 0 a) = sin b) = sin c) = sin ½ b) c) S) Here is the graph of = sin, where 0º < < a) What are the equations of these three graphs? Choose from the same list as in T. b) a) = sin b) = sin c) = sin + c) 0 0 Page MathsWatch Ltd info@mathswatch.com Page

63 T) This unfinished table and histogram shows information about the takings per da in pounds (p) of a business which sells software. Takings in pounds (p) Frequenc 0 < p < < p < < p < < p < < p < < p < < p < Frequenc densit Takings in pounds (p) a) Use the information in the histogram to complete the table. b) Use the information in the table to complete the histogram. Grade A/A* Clip 8 Page MathsWatch Ltd info@mathswatch.com Page

64 Frequenc densit S) This histogram gives information about the paintings sold in a shop one Saturda Price (P) in pounds ( ) a) Use the histogram to complete the table. Price (p) in pounds ( ) Frequenc 0 < p < < p < 0 0 < p < 0 0 < p < 0 Grade A/A* Clip 8 0 < p < < p < 0 0 < p < 0 0 < p < This table gives information about the paintings sold in another shop on the same Saturda. Price (p) in pounds ( ) Frequenc 0 < p < < p < 0 0 < p < 0 0 < p < b) Draw a histogram to represent this information. Frequenc densit Price (p) in pounds ( ) Page MathsWatch Ltd info@mathswatch.com Page

65 T) A college has 0 students. Each student studies one of German, French, Spanish or Italian. This table shows how man students stud each of these languages. Language German French Spanish Italian Number of students German 7 French Spanish Italian An inspector wants to look at the work of a stratified sample of 80 of these students. Find the number of students studing each language that should be in the sample. Grade A/A* Clip 8 S) The table shows the number of bos and girls in each ear group of a secondar school. Year group No. of bos No. of girls 7 0 Yr Yr 8 Yr Yr Yr 8 Total James wants to take a stratified sample of 0 girls b ear group. Work out the number of girls in each ear group that should be in his sample. 7T) Make the subject of ( ) = ( ) 7S) Make the subject of the formula + t = m n Grade A/A* Clip = = + + mt n m Page MathsWatch Ltd info@mathswatch.com Page

66 8T) A B 0 cm 0 cm 0 O Grade A/A* Clip 78 OAB is a sector of a circle, centre O a) Work out the length of the arc AB Give our answer to decimal place. b) Work out the area of sector AOB. Give our answer to decimal place. a) Arc = 0. cm b) Sector =. cm 8S) A 8 cm 8 cm B OAB is a sector of a circle, centre O a) Work out the length of the arc AB Give our answer to decimal place. b) Work out the area of sector AOB. Give our answer to decimal place. O 9T) B eliminating, find the solutions to the simultaneous equations + = 0 = Grade A/A* Clip 9S) B eliminating, find the solutions to the simultaneous equations = + + = a) Arc =. cm b) Sector =. cm + ( ) = = 0 = 0 8 = 0 ( )( + ) = 0 = and = = - and = - + ( + ) = = + = 0 + = 0 ( + )( ) = 0 = - and = - = and = Page MathsWatch Ltd info@mathswatch.com Page

67 Non calculator question 0T) Here is the graph of = sin, where 0 < < Grade A/A* Clip 8 Given that sin 0 = (a) sin 0 (b) sin 0, write down the value of a) sin 0º = ½ b) sin 0 = -½ Non calculator question 0S) Here is the graph of = cos, where 0 < < 0 0. O Use the graph to find estimates of the solutions, in the interval 0 < < 0, of the equations (a) cos = 0. (b) cos = a) 08, b), 8 Page 7 MathsWatch Ltd info@mathswatch.com Page 7

68 T) Given that + 8 = ( + p) + q for all values of, a) find the value of p and the value of q. p =, q = -8 b) on the aes, draw a sketch of the graph = + 8 Grade A/A* Clip O - -8 S) Given that = ( p) + q for all values of, a) find the value of p and the value of q. p =, q = -9 b) on the aes, draw a sketch of the graph = O -9 Non calculator question T) Write down the value of a) 7 0 Non calculator question b) c) 8 S) Write down the value of a) 0 b) c) 8 Grade A/A* Clip a) b) c) a) b) c) 7 Page 8 MathsWatch Ltd info@mathswatch.com Page 8

69 T) B (, 7) Diagram NOT accuratel drawn A (0, ) Grade A/A* Clip 0 The equation of the straight line through A and B is = + a) Write down the equation of another straight line that is parallel to = + b) Write down the equation of another straight line that passes through the point (0, ). c) Find the equation of the line perpendicular to AB passing through B. a) = + an number eg = + 9 b) = anthing + eg = + c) = + S) B (8, 8) Diagram NOT accuratel drawn A (0, ) 0 The equation of the straight line through A and B is = + a) Write down the equation of another straight line that is parallel to = + b) Write down the equation of another straight line that passes through the point (0, ). c) Find the equation of the line perpendicular to AB passing through B. a) = + an number eg = + 9 b) = anthing + eg = 7 + c) = + Page 9 MathsWatch Ltd info@mathswatch.com Page 9

70 T) H G E F D cm C 8 cm A 9 cm B This is a cuboid, ABCDEFGH AB = 9 cm, BC = 8 cm, AG = cm S) a) Calculate the length AE. Give our answer to significant figures. b) Work out the angle between CE and the horizontal plane ABCD. Give our answer to significant figures. Grade A/A* Clips 7 and 7 X a) 0. cm b) º D C cm M 9 cm A 9 cm B The diagram shows a square-based pramid ABCDX. AB = BC = 9 cm. The point M is the centre of the square base. XM = cm. a) Calculate the length of AC. Give our answer to significant figures. b) Work out the angle between the edge AX and the horizontal plane ABCD. Give our answer to decimal place. a).7 cm b).º Page 70 MathsWatch Ltd info@mathswatch.com Page 70