For each question in this paper, less than 10% of Higher Tier students gained full marks can you do so? Instructions Information Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided there may be more space than you need. Calculators must not be used. The total mark for this paper is 76 The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end.
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 Area of trapezium = 2 1 (a + b)h Volume of sphere 34 πr 3 Surface area of sphere = 4πr 2 Volume of cone 31 πr 2 h Curved surface area of cone = πrl In any triangle ABC The Quadratic Equation The solutions of ax2+ bx + c = 0 where a 0, are given by x = b ( b 2 4ac) 2a Sine Rule a sin A b sin B c sinc Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 21 ab sin C 2
Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. You must NOT use a calculator. 1. (a) Rationalise the denominator of 12 3 (b) Work out the value of ( 2 + 8) 2... (2)... (2) (Total 4 marks) 3
2. Margaret has some goats. The goats produce an average total of 21.7 litres of milk per day for 280 days. Margaret sells the milk in 1 2 litre bottles. Work out an estimate for the total number of bottles that Margaret will be able to fill with the milk. You must show clearly how you got your estimate.... (Total 3 marks) 4
3. (a) Complete the table of values for y = x 2 2x 1. x 2 1 0 1 2 3 4 y 7 2 1 (b) On the grid, draw the graph of y = x 2 2x 1 for values of x from 2 to 4. (2) (c) Solve x 2 2x 1 = x + 3 (2)... (2) (Total 6 marks) 5
4. P and Q are two triangular prisms that are mathematically similar. Prism P Prism Q Prism P has triangle ABC as its cross section. Prism Q has triangle DEF as its cross section. AC = 6 cm DF = 12 cm The area of the cross section of prism P is 10 cm 2. The length of prism P is 15 cm. Work out the volume of prism Q. 6... (Total 4 marks)
*5. A and B are two points. Point A has coordinates ( 2, 4). Point B has coordinates (8, 9). D is the point with coordinates (100, 56). Does point D lie on the straight line that passes through A and B? You must show how you work out your answer. (Total 3 marks) 7
6. Fiza has 10 coins in a bag. There are three 1 coins and seven 50 pence coins. Fiza takes at random, 3 coins from the bag. Work out the probability that she takes exactly 2.50.... (Total 4 marks) 8
7. ABCD is a square with a side length of 4x. M is the midpoint of DC. N is the point on AD where ND = x. BMN is a right-angled triangle. Find an expression, in terms of x, for the area of triangle BMN. Give your expression in its simplest form.... (Total 4 marks) 9
8. (a) Simplify fully 2 x 2x 2 3x 4 5x 3... (3) (b) Write 4 x 2 + 3 x 2 as a single fraction in its simplest form.... (3) (Total 6 marks) 10
9. Colin took a sample of 80 football players. He recorded the total distance, in kilometres, each player ran in the first half of their matches on Saturday. Colin drew this box plot for his results. Colin also recorded the total distance each player ran in the second half of their matches. He drew the box plot below for this information. Compare the distribution of the distances run in the first half with the distribution of the distances run in the second half............. (Total 2 marks) 11
10. Here is a sketch of the curve y = a cos bx + c, 0 x 360 Find the values of a, b and c. a =... b =... c =... (Total 3 marks) 12
11. The graph of y = f(x) is shown on the grid. On this grid, sketch the graph of y = 2f(x) (Total 2 marks) 13
12. The diagram shows part of the curve with equation y = f(x). The coordinates of the maximum point of the curve are (3, 5). The curve with equation y = f(x) is transformed to give the curve with equation y = f(x) 4 Describe the transformation.... (Total 1 mark) 14
13. The diagram shows a sketch of the graph of y = cos x. (a) Write down the coordinates of the point A. (...,...) (1) (b) On the same diagram, draw a sketch of the graph of y = 2 cos x. (Total 2 marks) (1) 15
*14. B, C and D are points on the circumference of a circle, centre O. AB and AD are tangents to the circle. Angle DAB = 50 Work out the size of angle BCD. Give a reason for each stage in your working. (Total 4 marks) 16
15. Express the recurring decimal 0.28 1 as a fraction in its simplest form.... (Total 3 marks) 17
16. Sumeet has a pond in the shape of a prism. The pond is completely full of water. Sumeet wants to empty the pond so he can clean it. Sumeet uses a pump to empty the pond. The volume of water in the pond decreases at a constant rate. The level of the water in the pond goes down by 20 cm in the first 30 minutes. Work out how much more time Sumeet has to wait for the pump to empty the pond completely. 18... (Total 6 marks)
17. The expression x 2 8x + 21 can be written in the form (x a) 2 + b for all values of x. (a) Find the value of a and the value of b. a =... b =... (3) The equation of a curve is y = f(x) where f(x) = x 2 8x + 21 The diagram shows part of a sketch of the graph of y = f(x). The minimum point of the curve is M. (b) Write down the coordinates of M. (...,...) (1) (Total 4 marks) 19
18. 5 5can be written in the form 5 k (b) Find the value of k.... (Total 1 mark) 20
19. The diagram shows a solid metal cylinder. The cylinder has base radius 2x and height 9x. The cylinder is melted down and made into a sphere of radius r. Find an expression for r in terms of x.... (Total 3 marks) 21
20. There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes at random a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1 3. (a) Show that n 2 n 90 = 0 (b) Solve n 2 n 90 = 0 to find the value of n. (3)... (3) (Total 6 marks) 22
21. The diagram shows a container for grain. The container is a cylinder on top of a cone. The cylinder has a radius of 3 m and a height of h m. The cone has a base radius of 3 m and a vertical height of 4 m. The container is empty. The container is then filled with grain at a constant rate. After 5 hours the depth of the grain is 6 metres above the vertex of the cone. After 9 hours the container is full of grain. Work out the value of h. Give your answer as a fraction in its simplest form. You must show all your working.... (Total 5 marks) TOTAL FOR PAPER IS 76 MARKS 23
Original source of questions % of students scoring Mean score of students achieving grade Qn Paper 1H Qn 0 marks full marks A* A 1 June 2014 25 67.6 9.9 3.41 2.29 2 June 2013 8 21.2 9.5 2.15 1.72 3 June 2014 15 19.1 9.5 5.41 4.36 4 June 2013 22 38.3 8.2 3.34 2.16 5 June 2015 15(b) 87.8 7.4 2.09 0.66 6 June 2013 26 71.8 7.1 3.04 1.78 7 June 2013 20 81.1 6.0 2.43 1.27 8 June 2012 23 60.2 6.3 4.84 2.39 9 June 2014 16(c) 52.1 6.3 1.16 0.92 10 June 2014 26 92.7 5.7 1.30 0.37 11 June 2012 26(b) 89.9 5.3 0.98 0.26 12 June 2015 24(b) 94.7 5.3 0.35 0.11 13 June 2013 28 83.3 5.1 1.36 0.63 14 June 2012 21 58.6 4.7 3.00 1.94 13 June 2013 28 83.3 5.1 1.36 0.63 15 June 2012 24 78.3 4.3 1.74 0.74 16 June 2013 17 80.4 4.2 3.08 1.20 17 June 2013 25 80.6 3.5 2.88 1.19 18 June 2015 22(b) 96.9 3.1 0.28 0.04 19 June 2012 25 84.1 2.4 1.67 0.55 20 June 2015 19 65.3 2.2 1.95 0.99 21 June 2015 23 74.3 1.9 2.18 0.82 24