# 1MA0/3H Edexcel GCSE Mathematics (Linear) 1MA0 Practice Paper 3H (Non-Calculator) Set C Higher Tier Time: 1 hour 45 minutes

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2 GCSE Mathematics (Linear) 1MA0 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of prism = area of cross section length Volume of sphere 4 πr Surface area of sphere = 4πr Volume of cone 1 πr h Curved surface area of cone = πrl In any triangle ABC The Quadratic Equation The solutions of ax+ bx + c = 0 where a 0, are given by x = b ( b a 4ac) Sine Rule a sin A b sin B c sin C Cosine Rule a = b + c bc cos A Area of triangle = 1 ab sin C

3 Answer ALL TWENTY ONE questions Write your answers in the spaces provided. You must write down all the stages in your working. 1. A postman delivers mail on Bolton Road. Each house number on one side of the road is an even number. The postman delivers to houses from house number 08 to house number 400 Work out the greatest number of houses between house number 08 and house number 400 On the opposite side of the road each house number is an odd number. The postman delivers mail to n houses on this side of the road. He delivers mail to is house number 1, house number, and so on. Write down an expression, in terms of n, for the least number of the final house.. (). () (Total 4 marks)

4 . A village fair has stalls to raise money for charity. On one stall there is a game where you roll a 6-sided dice and spin a 4-sided spinner. The dice is labelled 1,,, 4, 5, 6 The spinner is labelled 1,,, The score on the dice and the score on the spinner are added to get the total score. The table shows some of the possible total scores (a) Complete the table of possible total scores. () People pay 50p to play the game. The prizes are: 1 for a total score of 7 or 8 for a total score of 9 or 10 During one day of the fair, exactly 60 people played the game. *(b) Did the stall make a profit or a loss on this day? You must fully explain your answer. (5) (Total 7 marks) 4

5 . (a) Solve x = 48 x =. () (b) Solve x + 4 = 6(x 1) x = () (Total 5 marks) 4. 0 cm Diagram NOT accurately drawn 9 cm 4 cm 8 cm The diagram shows a shape. Work out the area of the shape. cm (Total 4 marks) 5

6 5. Gordon is going to open a restaurant. He wants to know how often people eat out at a restaurant. He designs a questionnaire. He uses this question on a questionnaire. "How often do you go to a restaurant?" Never Sometimes Often (a) Write down two things that are wrong about this question () (b) Design a more suitable question Gordon could use to find out how often people eat out at a restaurant. Gordon asks his family Do you agree that pizza is better than pasta? () This is not a good way to find out what people who might use his restaurant like to eat. (c) Write down two reasons why this is not a good way to find out what people who might use his restaurant like to eat. 1st reason nd reason () (Total 6 marks) 6

7 6. Mr Green buys a garden spade. The spade costs plus 0% VAT. (a) Calculate the total cost of the spade. Garden spade % VAT... () Mr Green makes some compost. He mixes soil, manure and leaf mould in the ratio :1: Mr Green makes 7 litres of compost. (b) How many litres of leaf mould does he use?... litres () (Total 6 marks) 7

8 7. Here is a 4-sided spinner. The sides of the spinner are labelled 1,, and 4. The spinner is biased. The probability that the spinner will land on each of the numbers and is given in the table. The probability that the spinner will land on 1 is equal to the probability that it will land on 4 Number 1 4 Probability x x Sarah is going to spin the spinner 00 times. Work out an estimate for the number of times it will land on 4. (Total 4 marks) 8

9 8. Work out the surface area of the triangular prism.. (Total 4 marks) 9

10 9. (a) Complete the table of values for y = x x 1. x y 1 (b) On the grid below, draw the graph of y = x x 1. () () (c) Use your graph to find an estimate for the minimum value of y. y 10 (1) O x 4 5 (Total 5 marks) 10

11 10. (a) Work out the value of 4 Give your answer as a fraction in its simplest form. (b) Work out the value of 1 4. () Give your answer as a fraction in its simplest form.. () (Total 5 marks) 11. The mass of 5 m of copper is kg. (a) Work out the density of copper. The density of zinc is 710 kg/m. kg/m () (b) Work out the mass of 5 m of zinc. kg () (Total 4 marks) 11

12 1. (a) Solve the inequality x + 1 > (b) Expand and simplify (x 7)(x + ) () () (Total 4 marks) *1. Pictures NOT accurately drawn A 0 Euro note is a rectangle 1 mm long and 7 mm wide. A 500 Euro Note is a rectangle 165 mm long and 8 mm wide. Show that the two rectangles are not mathematically similar. (Total marks) 1

13 14. y A O 1 4 x Enlarge triangle A by scale factor 1 1, centre O. (Total marks) 15. (a) Solve x 5 = (x ) (b) Solve x x 18 = 0 x = (4) () (Total 7 marks) 1

14 16. Work out the value of (a) ( )... (1) (b) ( ) (c) (1) (d) 4... ()... (1) (Total 5 marks) 17. The force, F, between two magnets is inversely proportional to the square of the distance, x, between them. When x =, F = 4. (a) Calculate F when x =. (b) Calculate x when F = (4)... () (Total 6 marks) 14

15 18. Jenni has a box of chocolates. The box contains 6 plain, 4 milk and 5 white chocolates. Jenni takes two chocolates at random from the box. Work out the probability that at least one of these chocolates will be a milk chocolate. (Total 4 marks) 15

16 19. ( 5 + 0) Diagram NOT accurately drawn 8 5 A large rectangular piece of card is ( 5 + 0) cm long and 8 cm wide. A small rectangle cm long and 5 cm wide is cut out of the piece of card. Express the area of the card that is left as a percentage of the area of the large rectangle....% (Total 4 marks) 16

17 0. R p P S Diagram NOT accurately drawn O q Q OPQ is a triangle. R is the midpoint of OP. S is the midpoint of PQ. OP = p and OQ = q (i) Find OS in terms of p and q. OS =... (ii) Show that RS is parallel to OQ. (Total 5 marks) 17

18 1. The diagram shows a sector of a circle with a radius of x cm and centre O. PQ is an arc of the circle. Angle POQ = 10 O 10 x cm P Diagram NOT accurately drawn Q (a) Write down an expression in terms of and x for (i) the area of this sector,... (ii) the arc length of this sector.... () 18

19 The sector is the net of the curved surface of this cone. Arc PQ forms the circumference of the circle that makes the base of the cone. h cm x cm The curved surface area of the cone is A cm. The volume of the cone is V cm. The height of the cone is h cm. Given that V = A, (b) find the value of h.... () (Total 5 marks) END TOTAL FOR PAPER: 100 MARKS 19

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21 GCSE MATHEMATICS 1MA0 LINEAR PRACTICE PAPERS SET C HIGHER TIER H Question Working Answer Mark Notes 1(a) (400 08)/ M1 for (400 08)/ or 46 seen 1(c) (a) n B cao [B1 for n ± k where k -1] B for a fully correct table [B1 at least 5 correct entries] (b) P(7 or 8) = 7/4 P(9 or 10) = /4 7/4 x 60 x 1 = 105 /4 x 60 x = 90 Takings = 60 x 0.5 = 180 (a) (b) (48/) x + 4 = 6(x 1) x + 4 = 6x 6 10 = 4x A loss of 15 ±4.5 5 M1 for P(7 or 8) {= 7/4}or P(9 or 10) {= /4} oe M1 for 7/4 x 60 x 1( = 105) or /4 x 60 x (= 90) M1 for 60 x 0.5 (= 180) A1 for 180 and 195 seen C1 for a loss of 15 oe M1 for (48/) A1 for 4 or -4 or ±4 M1 for x + 4 = 6(x 1) M1 for = 6x x 4 9 x 8 + ½ x 5 x M1 for splitting M1 for either 9 x 8 or ½ x 5 x 1 oe M1 for 9 x 8 + ½ x 5 x 1

22 GCSE MATHEMATICS 1MA0 LINEAR PRACTICE PAPERS SET C HIGHER TIER H Question Working Answer Mark Notes 5(a) Vague response boxes B1 for a correct criticism of the question Question does not include a time period B1 for a correct criticism of the response boxes 5(b) How many times a month do you go to a restaurant? B1 for a relevant question inc. time period B1 for at least non-overlapping response boxes 5(c) A leading question Restricted/biased sample B1 for a leading/biased question oe B1 for small/biased sample oe 6(a) /5.40 M1 for 19.5/5 M1 for /5 oe 6(b) 7 6 = 1 1 x 4 M1 for 7 6 M1 for 1 x 7 ( )/ x M1 for M1 for ( )/ or 0.5 seen M1 for 0.5 x 00 8 ½ x 6 x 8 x + (8+6+10) x 9 64 cm 4 M1 for ½ x 6 x 8 or 8x9 or 6x9 or 10x9 M1 for ½ x 6 x 8 x + (8+6+10) x 9 oe A1 for 64 B1 ft for cm

23 GCSE MATHEMATICS 1MA0 LINEAR PRACTICE PAPERS SET C HIGHER TIER H Question Working Answer Mark Notes 9(a) 9,, -1, -, -, -1, B for fully correct table [B1 for 1 or correct entries] 9(b) Graph B ft for a fully correct graph through their points [B1 at least 6 of their correctly plotted points] 9(c) B1 for an answer in the range.1 to (a) 10(b) 6/1 ½ M1 for 6/1 oe M1 for M1 for 11(a) M1 for (b) 710 x M1 for 710 x 5 1(a) x > 1 x > -10/ oe M1 for x > 1 A1 for x > -10/ or better 1(b) x 7x + x 1 x 4x 1 M1 for correct out of 4 terms or 4 correct terms ignoring signs A1 for x 4x 1 oe

24 GCSE MATHEMATICS 1MA0 LINEAR PRACTICE PAPERS SET C HIGHER TIER H Question Working Answer Mark Notes > 1 8 < Since > and 1 8 <, the scale factors are different; so not similar M1 for considering or 1 8 oe A1 for correct estimated answers C1 for a correct conclusion based upon their answers 14 Triangle with coordinates (-,-1.5), (-4.5,-1.5) and (-,-4.5) B for a correct triangle [B for an enlargement of 1.5 about (0,0) or for an enlargement of -1 about (0,0) B1 for an enlargement of 1.5 about any point] 15(a) x 5 = x 6 /8 4 M1 for x 6 M1 for x 15 = 9x 18 M1 for rearranging so that numbers and x-terms or on opposite sides of the equation A1 for /8 oe 15(b) (x 6)(x + ) x= 6 and x = - M1 for (x ± 6)(x ± ) A1 for x = 6 and A1 for x = - 16(a) B1 cao 16(b) 1 B1 cao 16(c) ( 4 x ) = x 1 M1 for x oe 16(d) 1/4 1/16 1 B1 cao

25 GCSE MATHEMATICS 1MA0 LINEAR PRACTICE PAPERS SET C HIGHER TIER H Question Working Answer Mark Notes 17(a) 4 = k/ 9 4 M1 for F = k/x F = 6/x M1 for 4 = k/ 6/ M1 for 6 / 17(b) 64 = 6/x (6/64) /4 M1 for 64 = 6/x 18 10/1 M1 for M1 for M1 for A1 for 10/1 oe 19 8( 5 + 0) - 5 = ( 5 + 5) - 5 = 5-5 = = / 6 10 x / M1 for 8( 5 + 0) - 5 oe M1 for ( 5 + 5) - 10 M1 for 5 10 / 6 10 x 100 A1 for 8. 0(i) (ii) q + ½ (p q) RS = ½ (p+q) ½ p = ½ q RS = ½ OQ parallel ½ (p+q) Proof 5 M1 for QP = q p M1 for OS = q + ½ QP A1 for ½ (p+q) M1 for RS = ½ (p+q) ½ p C1 for conclusion of proof; ie RS = ½ q and relating this to OQ = q

26 GCSE MATHEMATICS 1MA0 LINEAR PRACTICE PAPERS SET C HIGHER TIER H Question Working Answer Mark Notes 1(a) πx / B1 for πx / oe πx/ B1 for πx/ oe 1(b) A = πx/ = πr r = x/ V = 1/ x π x (x/) x h = x πx / 1/ (1/) x h =1 7 M1 for πx/ = πr M1 for 1/ x π x (x/) x h = x πx /

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