ESSENTIAL REVISION QUESTIONS. MathsWatch Foundation. Book

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

2 CONTENTS Grades G to E... to 0 D to C... to 8

3 Essential Questions at E to G (All Non-Calculator) T) a) Write the number five thousand seven hundred and ninety two in figures. b) Write the number 700 in words. c) What is the value of the 6 in the number 60? Grades E to G Clip S) a) Write the number two thousand five hundred and seventy in figures. b) Write the number 609 in words. c) What is the value of the in the number 87? a) 79 b) seven thousand and forty c) six thousand a) 70 b) sixteen thousand three hundred and nine c) twenty thousand T) The pictogram shows information about some fruit that Sara buys. Apples Bananas Oranges Key: represents 8 fruit Grades E to G Clip a) How many apples does she buy? b) How many bananas does she buy? c) Sara buys oranges. Complete the pictogram. a) 6 apples b) 6 bananas c) oranges S) The pictogram shows information about some fruit that Jane buys. Apples Bananas Oranges Key: represents fruit a) How many apples does she buy? b) How many bananas does she buy? c) Jane buys oranges. Complete the pictogram. a) 0 apples b) bananas c) oranges Page MathsWatch Ltd info@mathswatch.com Page

4 T) Put these numbers in order of size starting with the smallest. a) b) c) S) Put these numbers in order of size starting with the smallest. a) 96 8 b) c) Grades E to G Clip a) b) c) a) 8 96 b) c) T) a) Harry buys a newspaper for 70p and a magazine for.99. How much change does he get from a note? b) The total cost of two pens is 80p. What is the cost in pounds of of the pens? Grades E to G Clip S) a) Fred buys a newspaper for 90p, a magazine for.0 and a pencil for p. How much change does he get from a 0 note? b) The total cost of three pens is 96p. What is the cost in pounds of of the pens? a). b).00 a). b).8 T) Here is a list of numbers: From this list, write down a) An odd number b) A multiple of c) A square number d) A factor of 0 S) Here is a list of numbers: 8 From this list, write down a) A cube number b) A multiple of 6 c) Three prime numbers d) A factor of Grades E to G Clip 9 a) or 7 b) 6 c) d) or a) 8 b) c),, d) Page MathsWatch Ltd info@mathswatch.com Page

5 6T) The numbers in this distance table are in km. Hull 00 Leeds 6 7 Manchester Sheffield York a) What is the distance between Leeds and York? b) Which city is nearest to Hull? c) Which city is 8km from York? 6S) The numbers in this distance table are in km. Alim 7 Brow 8 6 Thrum Gredge 0 8 Sork a) What is the distance between Brow and Gredge? b) Which city is furthest from Sork? c) Which city is 78km from Thrum? 7T) Some plants are measured as follows: 0cm cm cm cm cm a) What is the mean height? b) What is the median height? c) What is the modal height? d) What is the range of heights? 7S) Some plants are measured as follows: 8cm 6cm 8cm 7cm cm cm a) What is the mean height? b) What is the median height? c) What is the modal height? d) What is the range of heights? Grades E to G Clip Grades E to G Clip 8T) 8 8 a) Write down the next two terms of the sequence. b) If the 0th term is 8, what is the st term? 8S) a) Write down the next two terms of the sequence. b) What is the 0th term? c) If the 0th term is what is the 9th term? Grades E to G Clip 9 a) 0km b) York c) Manchester a) 0km b) Thrum c) Gredge a) cm b) cm c) cm d) cm a) 8cm b) 7cm c) 8cm d) cm a) 8 b) a) b) c) Page MathsWatch Ltd info@mathswatch.com Page

6 9T) y A B a) Write down the coordinates of point A. b) Write down the coordinates of point B. c) On the grid, plot the point (, ) and label it P. d) On the grid, plot the point (-, -) and label it Q. y 9S) O x Grades E to G Clip 8 a) (, ) b) (-, 0) c) Q O P A a) Write down the coordinates of point A. b) Write down the coordinates of point B. c) On the grid, plot the point (-, ) and label it P. d) On the grid, plot the point (0, -) and label it Q. O B x a) (-, ) b) (, -) c) P O Q Page 6 MathsWatch Ltd info@mathswatch.com Page 6

7 0T) Here is part of a railway timetable. Bristol Bath Chippenham Swindon Didcot Reading London Euston a) At what time does the train from Bristol arrive at Didcot? b) How long does the train which leaves Bath at 07 take to travel to Swindon? c) If Jane gets to the Bath station at 08 0, how long will she have to wait for the next train to Reading? d) What is the journey time from Didcot to London? Grades E to G Clip 0S) Here is part of a railway timetable. a) 08 b) minutes c) minutes d) 0 minutes Bristol Bath Chippenham Swindon Didcot Reading London Euston a) At what time does the 09 0 train from Bristol arrive at Reading? b) How long does the train which leaves Didcot at 0 8 take to travel to London Euston? c) If Jane gets to the Bath station at 09 9, how long will she have to wait for the next train to Reading? d) What is the journey time from Bath to London? a) 08 b) 8 minutes c) 9 minutes d) hr 8 minutes T) a) Write the number 896 to the nearest thousand. b) Write the number 896 to the nearest hundred. c) Write the number 97 to the nearest ten. S) a) Write the number 96 to the nearest ten. b) Write the number 7 to the nearest hundred. c) Write the number 0678 to the nearest thousand. a) 000 b) 900 c) 00 a) 960 b) 800 c) 0000 Grades E to G Clip Page 7 MathsWatch Ltd info@mathswatch.com Page 7

8 T) What are the names of these angles? a) b) Grades E to G Clip a) acute angle b) right angle S) What are the names of these angles? a) b) a) obtuse angle b) reflex angle T) a) The temperature in the morning is - C. It rises by degrees. What is the new temperature? b) If a temperature of 7 C falls by 9 degrees, what is the new temperature? c) How much would a temperature of -6 C have to rise to reach C? Grades E to G Clip 6 S) a) The temperature in the morning is - C. It rises by degrees. What is the new temperature? b) If a temperature of - C falls by 6 degrees, what is the new temperature? c) How much would a temperature of -8 C have to rise to reach C? a) 9ºC b) -ºC c) 0ºC a) ºC b) -8ºC c) ºC T) a) Express as a power of. b) Express as a power of. c) Express 7 as a power of. S) a) Express as a power of. b) Express 6 as a power of. c) Express as a power of. Grades E to G Clip 6 a) b) c) a) b) 0 c) T) What is the reciprocal of 7? S) What is the reciprocal of? Grades E to G Clip 7 6T) What number is in the middle of and? 6S) What number is in the middle of and 8? Grades E to G Clip 9 0 Page 8 MathsWatch Ltd info@mathswatch.com Page 8

9 7T) Two of the shapes below are congruent. Which ones? A B C A and C 7S) Two of the shapes below are similar. Which ones? B A Grades E to G Clip C A and B 8T) a) Round the number.68 to decimal place. b) Round the number 699 to significant figure. c) Round the number to significant figure. 8S) a) Round the number to decimal places. b) Round the number 98 to significant figures. c) Round the number to significant figures. Grades E to G Clip 0 a).7 b) 0000 c) 0.00 a) 0.79 b) 000 c) T) a) What is 7 6? b) What is 8? 9S) a) What is 7? b) What is 06? Grades E to G Clip 7 a) b) 8778 a) 77 b) 97 0T) a) What is 0? b) What is.78 00? c) What is 0 lots of.6? d) What is 96 0? Grades E to G Clip e) If 00 pencils cost find the cost of pencil. 0S) a) What is 8 0? b) What is. 00? c) What is 0 lots of.78? d) What is 86 00? e) If 0 pencils cost.0 find the cost of pencil. a) 0 b) 78. c).60 d) 96. e) 0. a) 80 b) 0 c) 7.80 d).86 e) 0. Page 9 MathsWatch Ltd info@mathswatch.com Page 9

10 T) a) If bananas cost., how much will of them cost? b) If 7 pencils cost.68, how much will 0 cost? S) a) If 6 bananas cost.6, how much will 8 of them cost? b) If 9 pencils cost.06, how much will 0 cost? Grades E to G Clip T) a) What are the names of shapes A and B? b) How many vertices, edges and faces does shape A have? B A a).90 b).0 a).8 b).0 a) A cuboid B cylinder b) 8 vertices edges 6 faces Grades E to G Clip 7 S) a) What are the names of shapes A and B? b) How many vertices, edges and faces does shape A have? B A a) A triangular prism B sphere b) 6 vertices 9 edges faces T) a) b) 7 0. c) d) e) 8 0. S) a) b) c) d) e) 0. T) a) -6 - b) -7 c) - S) a) 7 - b) -0-8 c) - - Grades E to G Clip 9 Grades E to G Clip 7 a) 0.07 b). c) 0. d) e) 0 a) 0. b) 7. c) 0.6 d) 0 e) 0 a) b) -8 c) - a) -8 b) 80 c) Page 0 MathsWatch Ltd info@mathswatch.com Page 0

11 T) a) Shade in two thirds of shape A. b) What fraction of shape B is shaded? A B a) Grades E to G Clip S) a) Shade in three fifths of shape A. b) What fraction of shape B is shaded? b) a) 7 A B b) 8 6T) a) Find the area of these two shapes. A B cm 6cm a) A 8cm B 7cm b) cm 7cm 9cm b) Find the perimeter of the rectangle. 6S) a) Find the area of these two shapes. A B 7cm cm a) A 70cm B 6cm b) cm 0cm 8cm b) Find the perimeter of the rectangle. Grades E to G Clip Page MathsWatch Ltd info@mathswatch.com Page

12 7T) a) b) c) d) 8 09 e)..6 7S) a) b) c) d) 78 9 e) Grades E to G Clip 6 a) b) 6.6 c).0 d) 9 e) 8.8 a) 8 b).8 c) 9.9 d) 88 e).77 8T) Tessellate this shape. Draw at least ten shapes. Grades E to G Clip 8 8S) Show how the shape below tessellates. You need to draw at least six more shapes T) a) b) of Grades E to G Clip 8 a) 6 b) 8 9S) a) b) 7 of 8 8 a) 9 b) 0 Page MathsWatch Ltd info@mathswatch.com Page

13 0T) a) Find the volume of this cuboid. a) 6cm Grades E to G Clip 7cm cm cm b) 6cm b) The volume of this cuboid is 80cm Work out its height. x cm 0cm cm 0S) a) Find the volume of this cuboid. cm a) 90cm b) cm 6cm cm b) The volume of this cuboid is 8cm Work out its depth. cm 8cm x cm T) What number is the arrow pointing at? S) What number is the arrow pointing at? Grades E to G Clip 9 T) Place these numbers in order of size from low to high. 0. 0% S) Place these numbers in order of size from low to high. 78% Grades E to G Clip 7 0 0% 0. 78% 0.79 Page MathsWatch Ltd info@mathswatch.com Page

14 T) Complete the table INPUT OUTPUT 0 7 Grades E to G Clip 0 INPUT OUTPUT S) Complete the table + INPUT OUTPUT 0 + INPUT OUTPUT 8 0 T) Complete the table Fraction Decimal Percentage 0. S) Complete the table 60% 90% Grades E to G Clip 0 Fraction Decimal Percentage 0. 0% Fraction Decimal Percentage 0.7 7% 0. 0% % 90% Fraction Decimal Percentage % 0. % %. 66.6% Page MathsWatch Ltd info@mathswatch.com Page

15 T) Estimate the answer to S) Estimate the answer to.8 Grades E to G Clip 000 6T) a) Change.m to cm. b) Change km to m. c) Change m to cm 6S) a) Change cm to m. b) Change 986m to km. c) Change 8km to m Grades E to G Clip a) 0cm b) 000m c) 0000cm a).m b).986km c) m 7T) On the number line, put arrows to indicate the following probabilities: c b a 0 0 a) Getting a head if a coin is flipped. b) Getting a or if a dice is rolled. c) Snow falling in London in June. 7S) On the number line, put arrows to indicate the following probabilities: b a c 0 0 a) Getting an even number if a dice is rolled. b) Getting two heads if two coins are flipped. c) Rain falling in London sometime in the year. Grades E to G Clip 0 8T) Use the information that = 78 to work out a).. b). 0 c) 78 Grades E to G Clip 8S) Use the information that 8 = 06 to work out a).8. b) 80 0 c) a) 7.8 b) 78. c) a).06 b) 0600 c). Page MathsWatch Ltd info@mathswatch.com Page

16 9T) Draw the following cuboid on the isometric grid. cm cm cm Grades E to G Clip 9 other diagrams are also correct 9S) Draw the following cuboid on the isometric grid. cm cm cm other diagrams are also correct Page 6 MathsWatch Ltd info@mathswatch.com Page 6

17 0T) If identical text books cost 6. how much will one text book cost? 0S) If identical text books cost 7.60 how much will one text book cost? Grades E to G Clip T) Name the following shapes: A B A B Parallelogram Hexagon C Equilateral triangle C Grades E to G Clip 6 S) Name the following shapes: A B A B Trapezium Isosceles triangle C Pentagon C Page 7 MathsWatch Ltd info@mathswatch.com Page 7

18 T) The graph shows the average temperature in a city for a year. 0 Temperature in C 0 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month a) Which month had the highest average temperature? b) How much warmer was it in June than February? c) The average temperatures in October, November and December were 0 C, 8 C and C, respectively. Plot this information on the graph. Grades E to G Clip 7 S) The graph shows the average sales per month of a particular type of computer in a shop. a) July b) 0ºC 00 Computers sold Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month a) What was the total number of sales in March, April and May? b) How many more computers were sold in June compared to March? c) The average sales in October, November and December were 0, 00 and. Plot this information on the graph. a) 7 computers b) 7 more Page 8 MathsWatch Ltd info@mathswatch.com Page 8

19 T) Litres Gallons S) a) Fred buys gallons of petrol. How many litres is this? b) How many gallons is 70 litres? Grades E to G Clip a) litres b) approx Distance in miles Distance in kilometres a) Change 60 miles to kilometres. b) How many miles is 90 km? c) How much more is 00 miles than 60 miles, in kilometres? a) 96km b) 6 miles c) 6km Page 9 MathsWatch Ltd info@mathswatch.com Page 9

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21 T) a) t + 7t b) t 7t c) 6y + w y d) 6y t e) e e f) m 7 m g) 8 Essential Questions at C to D y y ( to 7 are non-calculator) Grade C Clip 0 a) t b) 8t c) y + w d) 8yt or 8ty e) e f) m g) y h) y h) 6y y S) a) t + 8t b) t 9t c) y + w y d) y t e) e e 7 f) x x g) r r 7 a) t b) 8t c) 7y + w d) 8yt or 8ty e) 6e f) x g) r h) r h) 6r r T) a) Expand (y ) b) Expand x(x + ) c) Expand and simplify (x + ) (x ) d) Expand and simplify (y ) + (y ) e) (x + )(x ) Grade C Clip 0 S) a) Expand (y ) b) Expand x(x + ) c) Expand and simplify (x + ) (x ) d) Expand and simplify (y ) + (y ) e) (x )(x ) a) y b) 6x + x c) 6x + 6 d) y 7 e) x x a) 6y b) x + 0x c) x + d) 8y e) 6x x + Page MathsWatch Ltd info@mathswatch.com Page

22 T) Find the nth term of the following patterns a),, 7, 9,..... b) 8,, 8,, 8,..... c) 9, 6,, 0,,..... Grade C Clip a) n + b) n + c) n + S) Find the nth term of the following patterns a), 6, 0,, b) 7, 6,,,,..... c),,,, 7,..... a) n b) 9n c) n + 8 T) Number of smarties Frequency 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 Frequency 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

23 T) Factorise the following: a) x + 6 b) x + 8 c) x + d) x + 6 e) x + x f) x 6x g) 9h + 6h h) 8x 0x Grade C Clip 0 a) (x + ) b) (x + ) c) (x + 6) d) (x + ) e) x(x + ) f) x(x ) g) h(h + ) h) x(x ) S) Factorise the following: a) t + 0 b) m c) y + 8 d) x + 6 e) t + t f) t + 0t g) 7t t h) 9h 0h a) (t + ) b) (m ) c) (y + ) d) (x + ) e) t(t + ) f) t(t + ) g) 7t(t ) h) h(h 0) 6T) 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 6S) 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 6.7cm 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 6.7cm Least is 6.6cm Page MathsWatch Ltd info@mathswatch.com Page

24 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 66 b) Colin said when x =, then the value of x is Sue said when x =, then the value of x is 6 Who was right? Explain why. a) (i) 9 (ii) 9 (iii) (iv) 6 (v) (vi) b) Sue because x is x 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 x =, then the value of x is 00 Sue said when x =, then the value of x is 00 Who was right? Explain why a) (i) (ii) 6 (iii) 80 (iv) 6 (v) (vi) b) Sue because x is x 8T) Using the information that 76 = 68 Write down the value of: a) 7.6. = b) 76 0 = c) = Grade C Clip 97 8S) Using the information that 8 6 = 76 Write down the value of: a) 8.6 = b) = c).76.8 = a).68 b) 680 c) a) 7.6 b) 7.6 c).6 Page MathsWatch Ltd info@mathswatch.com Page

25 9T) Write the following numbers as the product of their prime factors Grade C a) 8 b) 60 Clips 9 & 96 c) Find the Highest Common Factor of 8 and 60 d) Find the Lowest Common Multiple of 8 and 60 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) 60 Grade C Clip 7 Grade C Clip 9 Grade D Clip 80 0S) a) Draw an angle of 60 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 6 T) What is. 0.? S) What is.7 0.? Grade D Clip 60 Grade C Clip 08 T) < x < x is an integer. Write down all the possible values. S) < x < x is an integer. Write down all the possible values ,,, 0,,,,, 0,,, Page MathsWatch Ltd info@mathswatch.com Page

26 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 600 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 6 c) Page 6 MathsWatch Ltd info@mathswatch.com Page 6

27 6T) If you share out 0 between Alice and Bill in the ratio :, how much more does Alice get compared with Bill? Grade C Clip 9 6S) If you share out 60 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? 60 for Alice and 6 for Bill 8T) Some plant heights are measured as shown in the table, below. Height in cm Frequency 0 < h < 0 0 < h < 0 0 < h < < 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 Frequency 0 < h < 0 0 < h < 0 0 < h < < 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 60 Page 7 MathsWatch Ltd info@mathswatch.com Page 7

28 9T) a) Reflect the shaded shape in the y axis 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 fully the single transformation that will move U back on to the shaded shape T U c) Reflection in y = x Grade D Clips 7, 7, 77 9S) a) Reflect the shaded shape in the x axis 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 fully the single transformation that will move U back on to the shaded shape U T c) Reflection in y = x Page 8 MathsWatch Ltd info@mathswatch.com Page 8

29 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 76 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 9 MathsWatch Ltd info@mathswatch.com Page 9

30 T) Find the exterior angle of this regular octagon Grade D Clip 70 degrees S) Find the exterior angle of this regular hexagon 60 degrees T) a) In the triangle below, find an expression, in terms of x, for the perimeter of the triangle. Simplify your expression. a) x + 8 b) x = 9 cm b) If the perimeter of the triangle is cm, find the value of x. Grade C Clip 06 x 8 x S) a) In the rectangle below, find an expression, in terms of x, for the perimeter of the rectangle. Simplify your expression. a) 8x + 6 b) x = cm x + x b) If the perimeter of the rectangle is 6 cm, find the value of x. Page 0 MathsWatch Ltd info@mathswatch.com Page 0

31 T) Find the size of angle n, giving reasons A B C Grade D Clips 68, 69 S) Find the size of angles x and y, giving reasons A B C ABC = 60 (angles on st. line = 80) n = 78 (angles in add up to 80) x = 6 (angles in =80, base angles are equal) ABC = 6 (base angles of isos. are equal) y = (angles on st. line = 80 ) T) Find the size of angle x, giving reasons Grade D Clip 67 BRS = 0 (angles on straight line add up to 80 ) x = 0 (alternate angles) S) Find the size of angles x and y, giving reasons x = 86 y = 7 (angles in quadrilateral add up to 60 ) (alternate angles) Page MathsWatch Ltd info@mathswatch.com Page

32 T) Solve the following equations a) x = 7 b) x 8 = c) x + = d) x + = 7 e) (x ) = 6 f) x = g) x + = x S) Solve the following equations a) x = b) x 9 = c) x + = d) x + 6 = e) (x + ) = 6 f) x 6 = g) x + = x Grade C Clip 0 a). b) c) d) 6 e) f) g). a) b) c) d) 6 e) 7 f) 7. g) 6T) Draw a stem and leaf diagram to show the following information. The heights of plants in cm are:.6,.,.,.,.8, 6.,.7,.,.7, 6.,.,.9 6S) Draw a stem and leaf diagram to show the following information. The weights of 0 people in kg are: 9,, 8, 67, 7, 6, 0, 6, 68, 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 Key means Key 6 means 6 a) cm b) 00 mm c) cm a) 00 mm b) 0000 cm c) 000 mm Page MathsWatch Ltd info@mathswatch.com Page

33 8T) a) Anne buys 6 litres of diesel at. per litre. How much does she spend altogether on diesel? b) James spends 6.7 on litres of petrol. How much was each litre of petrol? Grade D Clip 60 & Grade C Clip 00 8S) a) Sara buys 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) 60.7 b). a) 8.6 b).6 9T) a) b) c) d) Grade D Clips 6 and 7 a) b) c) d) 7 0 9S) a) + a) b) 7 b) c) c) 9 0 d) 0 d) 0T) Draw a pie chart to show the following information Crisp flavour Frequency Cheese 8 Plain 9 Beef 6 Prawn Grade D Clip 86 0S) Draw a pie chart to show the following information Crisp flavour Frequency Cheese 8 Plain 6 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

34 T) Find the areas of the following shapes a) 7m b) a) m m cm b) 0cm cm c) 60cm c) 8cm cm cm cm Grade D Clip 7 S) Find the areas of the following shapes a) 9m b) a) m 6m 7cm b) cm cm c) cm c) cm cm cm cm Page MathsWatch Ltd info@mathswatch.com Page

35 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) x a t = bc (x) S) Make the letter in the bracket the subject of the formula. a) v = u + as (a) b) x a + y = c (x) Grade C Clip 07 a) b) x = a(bc + t) a) a = a = v - u t v - u s b) x = a(c y) T) Find the following: a) 0% of 700 b) % of 80 c) % of 600 d) 7.% of 8 Grade D Clip a) 70 b) c) 0 d) 8.0 S) Find the following: a) 0% of 60 b) % of 900 c) 8% of 800 d) 7.% of 0 a) 0 b) c) 680 d) Page MathsWatch Ltd info@mathswatch.com Page

36 T) Sally s mother lives 80km from Sally. This is the journey to her mother s house. a) Sally 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 journey to her mother s house? d) For the return journey, Sally travelled at 60km/h without a break. Complete the travel graph to show this. S) Sally s mother lives 90km from Sally. This is the journey 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 Sally travel at until her first rest? b) What speed did she travel at for the last part of the journey to her mother s house? c) For the return journey, Sally travelled at 80km/h without a break. Complete the travel graph to show this. Page 6 MathsWatch Ltd info@mathswatch.com Page 6

37 6T) a) Complete the table for the equation y = x x Grade C Clip 6 x 0 0 y 0 9 b) Draw the graph of y = x x on the axes at the bottom of the page c) Use your graph to find the value of y when x =. d) Use your graph to find the value of y when x =. e) Use your graph to solve x x = f) Use your graph to solve x x = 8 c).6 d) 9 e) x = and x =. f) x =. and x =.9 y O x - - Page 7 MathsWatch Ltd info@mathswatch.com Page 7

38 6S) a) Complete the table for the equation y = x x x 0 y Grade C Clip b) Draw the graph of y = x x on the axes at the bottom of the page c) Use your graph to find the value of y when x =. d) Use your graph to find the value of y when x =. e) Use your graph to solve x x = 0 c). d) 8. e) x =.7 and x = y O x - - Page 8 MathsWatch Ltd info@mathswatch.com Page 8

39 7T) Draw a set of axes going from to + a) Draw the graph of y = x b) What is the gradient? 7S) Draw a set of axes going from to + a) Draw the graph of y = x + b) What is the gradient? Grade C Clip b) b) y = x O y = x - 8T) The table below shows the probability of an oddly shaped -sided dice landing on,,, or. a) Work out the value of x b) If the dice is rolled 000 times how many s would you expect to get? x Grade C Clip 8S) The table below shows the probability of an oddly shaped -sided dice landing on,,, or. a) Work out the value of x b) If the dice is rolled 000 times how many s would you expect to get? x a) 0. b) 70 a) 0. b) 0 9T) Draw a plane of symmetry on this shape Grade D Clip 8 other answers are possible 9S) Draw a plane of symmetry on this shape other answers are possible Page 9 MathsWatch Ltd info@mathswatch.com Page 9

40 0T) Height Frequency 0 to 0 0 to 0 0 to 0 0 to 0 a) On the first set of axes, draw a frequency diagram b) On the second set of axes, draw a frequency polygon Grade D Clip 88 0S) Height Frequency 0 to 0 0 to to 0 0 to 0 ANSWERS for 0T a) On the first set of axes, draw a frequency diagram b) On the second set of axes, draw a frequency polygon 7 6 Frequenc y Height Freq ue nc y Height Frequenc y Height 7 6 Freq ue nc y 7 6 Frequenc y Height Freq ue nc y Height Frequenc y Height 7 6 Freq ue nc y ANSWERS for 0S Height Page 0 MathsWatch Ltd info@mathswatch.com Height Page 0

41 T) a) In a room there are 7 boys and girls. What percentage of the people are boys? b) In a room there are boys and 7 girls. What percentage of the people are girls? c) Sally scores marks out of 0 in a Science test. What was her percentage score? Grade D Clip S) a) In a room there are boys and 9 girls. What percentage of the people are boys? b) In a room there are boys and girls. What percentage of the people are girls? c) Emma scores marks out of 60 in a Science test. What was her percentage score? a) 70% b) % c) 60% a) % b) 8% c) 90% T) A point, P, moves so that the locus of P is always 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 always equidistant from lines AB and AC. Draw the locus of P. A B Page MathsWatch Ltd info@mathswatch.com C Page

42 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 extra-warm jackets, eye 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 extra-warm jackets, eye 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 six 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 next, after? Grade D Clip T) Solve the inequality x + < S) Solve the inequality x 7 > Grade C Clip 09 6T) Evaluate 6S) 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) eye colour and intelligence or hair length and weight etc a) 7 8 b) c) 7 a) 0 0 b) c) 7 9 x < x > 0 6 Page MathsWatch Ltd info@mathswatch.com Page

43 7T) Find the volume of this triangular prism. 6cm 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 = 60cm a) 7 8 b) 6 8S) a) Write as a power of b) Write as a power of 9 a) 7 b) 9T) Complete the two-way table which shows the favourite soup of 00 people. Oxtail Tomato Chicken Total Male Female 8 Total 6 00 Grade D Clip 8 Oxtail Tomato Chicken Total Male Female Total S) 0 students studied History and Geography as shown in the two-way table. History Geography Both Total Female Male 8 Total males studied both subjects. of the students were male. Complete the two-way table. History Geography Both Total Female 8 Male 8 0 Total Page MathsWatch Ltd info@mathswatch.com Page

44 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 they after a price increase of 0%? Grade C Clip 9 S) A new car costs If the price is reduced by % 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 6 S) What are the first terms of the number sequence with the nth term of n? Page MathsWatch Ltd info@mathswatch.com Page

45 T) Translate triangle A by vector Grade D Clip 77 S) Describe fully the transformation which maps triangle A onto triangle B. Translation by vector -6 B.. T) Change the recurring decimal 0.7 into a fraction in its simplest form. S) Change the recurring decimal 0.6 into a fraction in its simplest form... Grade C Clip 98 7 Page MathsWatch Ltd info@mathswatch.com Page

46 6T) What is the equation of the line? y y = x O - x - - 6S) What is the equation of the line? y Grade C Clip y = x O T) List all of the outcomes if you roll a dice and flip a coin. 7S) List all of the outcomes if you flip three coins. Grade D Clip 90 H H H H H 6H T T T T T 6T HHH HHT HTH THH TTT TTH THT HTT Page 6 MathsWatch Ltd info@mathswatch.com Page 6

47 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 06 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 60T) A map has a scale of : If town A is cm away from town B on the map, what is the actual distance between them in kilometres? 60S) A map has a scale of : If town A is cm away from town B on the map, what is the actual distance between them in kilometres? Grade D Clip km km 6 0 Page 7 MathsWatch Ltd info@mathswatch.com Page 7

48 6T) a) - - b) 7 - c) - d) -8 6 e) 9 - f) g) Grade C Clip 99 6S) a) 6 - b) -0 - c) - d) 8 e) - f) + -7 g) T) Use the graph to solve the simultaneous equations y = 7 x and y = x 8 7 y y = 7 x y = x a) b) - c) - d) - e) f) g) -9 x = and y = a) -8 b) 0 c) - d) -6 e) f) - g) S) Use the graph to solve the simultaneous equations y = 8 x and y = ½x y Grade C Clip y = 8 x x y = ½x + x = and y = x Page 8 MathsWatch Ltd info@mathswatch.com Page 8

49 6T) Estimate the answer to S) Estimate the answer to Grade C Clip 0 6T) A triangular prism has sides as shown. Find the surface area of the prism cm cm cm 7 cm 6S) A triangular prism has sides as shown. Find the surface area of the prism. Grade C Clip 70 cm 8 m 0 m 6 m 6 m m 6T) If the probability of passing a driving test is 0. what is the probability of failing the test? 0.8 Grade D Clip 9 6S) The probability of a school football team winning a football match is 0. and the probability of losing is 0.. What is the probability of the team drawing the match? 0. Page 9 MathsWatch Ltd info@mathswatch.com Page 9

50 66T) Draw the net of this right-angled triangular prism. squares squares Grade D Clip 8 squares squares 66S) Draw the net of this cuboid squares squares squares Page 0 MathsWatch Ltd info@mathswatch.com Page 0

51 67T) Write the following fractions in their simplest forms. a) b) c) Grade D Clip 8 67S) Write the following fractions in their simplest forms. a) 0 b) 7 c) T) 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 six people? b) For seven people, what weight of flour is needed? 68S) 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 six people, how much stock is needed? c) For nine people, what weight of lamb should be used? Grade D Clip 6 a) b) c) a) b) c) 8 a) 0g b) 87.g a) 80g b) 60ml c).8kg Page MathsWatch Ltd info@mathswatch.com Page

52 69T) 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 6? 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 69 Grade D Clip 6 a) 6 b) 6 c) 7 d) e) a) 6 b) 8 c) 0 d) e) 7T) Sara wishes to find out how much pocket money people in her class received. Design a suitable question she could use on a questionnaire. You should include some tickboxes. 7S) Fred wants to know which sports are watched by 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 money do you receive each week? Less than Between.0 and More than Sport Tally Frequency Football Cricket Tennis Athletics Rugby Other a) 0.8 b) 0.7 7S) Change the following fractions to decimals. a) 6 b) 0 8 a) 0.6 b) 0.6 Grade D Clip 8 Page MathsWatch Ltd info@mathswatch.com Page

53 Questions 7 to 8 are all calculator questions 7T) Find the length of sides A, B and C giving your answers to one decimal place. cm A.9cm cm A cm B B C 8.cm.6cm 7cm Grade C Clip 8 C.9cm 6.8cm 7S) Find the length of sides A, B and C giving your answers to one decimal place. A 7cm 6cm 8cm A B C.cm.9cm.7cm 9cm B 9.cm 8.cm C 7T) The equation x + x = 0 has a solution between and. Use a trial and improvement method to find this solution. Give your answer to decimal place and show all workings. 7S) The equation x x = 88 has a solution between and. Use a trial and improvement method to find this solution. Give your answer to decimal place and show all workings. Grade C Clip 0 x = + = Too low x = + = Too big x =.. +. = 8.6 Too low x =.. +. = 0.6 Too big x =.. +. = Too low x =. to decimal place. x = = 8 Too low x = = 0 Too big x = = 8.0 Too low x = = 9.9 Too big x = = Too big x =.7 to decimal place. Page MathsWatch Ltd info@mathswatch.com Page

54 7T) a) % of 8.76 = b) 76% of 900 = c) Reduce.0 by.% 7S) a) 9% of.60 = b) % of 00 = c) Reduce 60 by 0% 76T) If =. Euros, a) Change 8 to Euros. b) Change 60 Euros to pounds ( ). 76S) If =.7 Euros, a) Change 000 to Euros. b) Change 9 Euros to pounds ( ). Grade D Clip Grade D Clip 6 a) 9.78 b) 68 c) 9.8 a) 68. b) 0 c) 8 a) 6.7 Euros b) 8.6 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) 7.6cm 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

55 78T) Which is the best value for money 00g of sausages for.7 or 60g of the same type of sausages for.70? You must show all your working. 0.p per gram 0.7p per gram 00g for.7 best value 78S) Which is the best value for money 800ml of orange juice for 0.8 or 0ml of orange juice for 0.6? You must show all your working. Grade D Clip p 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) 7.6cm b).7cm a) (i) 69.cm (ii).cm b) 8.8cm b) Find the perimeter of this semicircle to decimal place. 9cm Page MathsWatch Ltd info@mathswatch.com Page

56 80T) a) Change the following to percentages. Give your answers to decimal place. (i) 7 out of 67 (ii) out of 86 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 your answers to decimal place. (i) out of 78 (ii).6 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) 68.% a) (i) 6.% (ii).% b) 8.7% 8T) Find the volume of this cylinder. Give your answer to decimal place. 9cm cm Grade C Clip Volume = 607.cm 8S) Find the volume of this cylinder. Give your answer to decimal place. 0cm Volume = 76.cm 7cm 8T) Evaluate 8S) Evaluate (. 7.) Grade D Clip = = Page 6 MathsWatch Ltd info@mathswatch.com Page 6

57 8T) Find the length of the line. y 6 Grade C Clip 9 cm 6 O 6 x O 6 8S) Find the length of the line to decimal place. y 6.cm 6 O 6 x O 6 8T) a) A cyclist travels miles in hours. What is the cyclist'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 density in g/cm. Grade C Clip 6 8S) a) A cyclist travels at.mph for hours. What distance does he cover? b) Sue drives at an average speed of 7mph and covers a distance of 6. miles. How long does the journey take in hours and minutes? c) A piece of lead has a density of g/cm and a mass of kg. Work out its volume in cm. a) 6mph b) 0. miles c). g/cm a) 7. miles b) hours 0 minutes c) 66.7cm Page 7 MathsWatch Ltd info@mathswatch.com Page 7

58 8T) The two triangles are similar. cm y x 7.8cm 8cm.cm a) Work out the size of x. b) Work out the size of y. a) x = 7cm b) y = 7cm 8S) BE is parallel to CD Find the length of BC. A Grade C Clip BC = 8cm 0cm B cm E x C.6cm D Page 8 MathsWatch Ltd info@mathswatch.com Page 8

59 Index Symbols D shapes 0 A addition alternate angles angles - names of 8 angles in triangle angles of polygons 0 area - finding area of circle area of compound shapes area of rectangle area of triangle averages B bearings - finding with protractor 7 best value for money bisect a line bisect an angle BODMAS bounds at grade C level C change the subject of a formula circles - area circles - circumference circumference of circle compound measures 7 compound shapes - area congruency 9 conversion graphs 9 converting metric measures, coordinates 6 cube numbers cubes, squares and roots cuboid - find volume curvy graphs 7, 8 cylinder - volume of 6 D decimal places 9 decimals - mult. and division 0 decimals to perc. and fractions density, mass, volume 7 dimensions directed numbers - four rules 8 directed numbers - mult. and div. 0 directed numbers in real life 8 distance tables divide by powers of 0 9 division - long 7 division with decimals 0 E edges 0 enlargements - positive scale factor 9 equations equivalent fractions 7 estimate for the mean 7 estimation, 9 evaluate with calculator 6 Evaluating numers with indices - simple Expanding brackets F factorising - simple factors factors, multiples and primes foreign currency conversion forming equations 0 forming expressions 0 fraction of an amount, 6 fractions - changing to decimal fractions - four rules fractions - putting in order fractions - shading fractions - simplifying fractions to perc. and dec. frequency diagrams 0 frequency polygons 0 G graphs - linear 9 graphs of quadratics 7, 8 H half-way values 8 hard calculator question 6 highest common factor I index notation - multiply and divide indices - simple 8 inequalities - integers inequalities - solving isometric drawing 6 L line graphs 8 linear graphs 9 loci long division 7, long diviso 7 long multiplication 9, lower bounds lowest common multiple M mean average mean from a table

60 measuring angles median average median from a table metric measures - converting, modal average money questions multiples, multiplication of decimals multiplication with decimals 0 multiply by powers of 0 9 N naming shapes 7 negative numbers - mult. and div. 0 negative numbers in real life 8 nets 0 nth term - finding from sequence nth term - generating a sequence from number machines number sequences O ordering decimals ordering fractions, decimals and perc. outcomes - listing 6 P percentages - change to % with calc. 6 percentages - change to % without calc. percentages - find % with calc. percentages - find % without calc. percentages - increase and reduction percentages to frac. and dec. perimeter - finding perimeter involving circles pictograms pie charts place value place value when multiplying, planes of symmetry 9 plans and elevations 6 powers - simple 8 prime numbers probability - experimental 9 probability - mutually exclusive events 9 probability scale product of prime factors proportion - simple 0 Pythagoras - in D Pythagoras - line on graph 7 Q questionnaires R range ratio - map scales 7 ratio - recipe questions ratio - sharing 7 reading scales real-life money questions recipes - ratio reciprocals 8 rectangles - finding area and perimeter recurring decimals - changing to fraction reflections 8 rotations 8 rounding numbers 7 rounding to decimal places 9 rounding to significant figures 9 S scales - reading scatter diagrams sequences shading fractions significant figures 9 similar shapes - simple 9 similar triangles 8 simplification of algebraic terms simultaneous equations - solving graphically 8 solids - names of 0 solving equations speed, distance, time 7 square and cube numbers squares, cubes and roots standard form stem and leaf diagrams straight lines - finding equation of 6 subject of a formula - simple substitution subtraction surface area of cuboids surface area of tirangular prisms 9 symmetry - planes of 9 T tessellations timetables 7 transformations 8 translations travel graph 6 trial and improvement triangles - drawing with compasses triangles - finding area and perimeter two-way tables U upper bounds V value for money vertices 0 volume of cuboid volume of cylinder 6 volume of prism