Mock GCSE Paper Calculator allowed for all questions

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1 Foundation Higher Mock GCSE Paper Calculator allowed for all questions MATHSWATCH Time: 1 hour 45 minutes Name: Question number Marks Score Question number Marks Score Out of 100 TOTAL SCORE % FINAL PERCENTAGE MathsWatch mathswatch@aol.co.uk Page 1

2 FORMULAE SHEET HIGHER TIER MathsWatch Volume of a prism = Area of cross section Length Volume of sphere 4 = r 3 3 π π Surface area of sphere = 4 r 2 Volume of cone 1 = r 2 h 3 π Curved surface area of cone = π rl In any triangle ABC The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a = 0, are given by Sine Rule a b sin A = c sin B = sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle 1 ab sin C 2 x b b ac = ± ( 2 4 ) 2a MathsWatch mathswatch@aol.co.uk Page 2

3 1. There are 2 blue coins, 3 green coins and 6 black coins in a bag. Jason takes a coin, at random, from the bag. (a) Write down the probability that he takes a green coin. (b) Write down the probability that Jason takes a coin that is not blue. 2. Use your calculator to work out Write down all the figures on your calculator display. (1) (Total 3 marks) 3. (Total 2 marks) A B Diagram NOT accurately drawn C x D AB is parallel to CD. (i) Write down the value of x. (ii) Give a reason for your answer.... (Total 2 marks) MathsWatch mathswatch@aol.co.uk Page 3

4 4. The scatter graph shows information about an indoor softball playground. It shows the maximum outside temperature and the number of people visiting the playground on ten saturdays in summer. Number of people O Maximum outside temperature C The table shows this information for two more Saturdays. Maximum outside temperature ( C) Number of people (a) Plot this information on the scatter graph. (b) What type of correlation does this scatter graph show? (c) Draw a line of best fit on the scatter graph. (1) (1) (1) The weather forecast for next Saturday gives a maximum temperature of 17 C (d) Estimate the number of people who will visit the softball playground. (1) On another Saturday, 350 people were recorded to have visited the playground. (e) Estimate the maximum outside temperature on that day. (1) (Total 5 marks) MathsWatch mathswatch@aol.co.uk Page 4

5 5. Here are the first four terms of an arithmetic sequence Find an expression, in terms of n, for the nth term of the sequence. 6. Here are the front elevation, side elevation and the plan of a 3-D shape. (Total 2 marks) Front elevation Side elevation Plan In the space below, draw a sketch of the 3-D shape. (Total 2 marks) MathsWatch mathswatch@aol.co.uk Page 5

6 7. 70 students take a Maths test. The test is marked out of 50. This table shows information about the students marks. Maths mark Frequency On the grid, draw a frequency polygon to show this information Frequency Maths mark (Total 2 marks) MathsWatch mathswatch@aol.co.uk Page 6

7 8. The equation x 3 + 5x = 117 has a solution between 4 and 5 Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show all your working. x = (Total 4 marks) MathsWatch mathswatch@aol.co.uk Page 7

8 9. D 3x Diagram NOT accurately drawn A x C 4x B In this quadrilateral, the sizes of the angles, in degrees, are x x 20 3x (a) Use this information to write down an equation in terms of x. (b) Work out the value of x. x = (Total 5 marks) MathsWatch mathswatch@aol.co.uk Page 8

9 10. A dealer sells cars and motorbikes. The ratio of the number of cars sold to the number of motorbikes sold is 5 : 2 The garage makes 35 sales in one week. (a) Work out the number of motorbikes the garage sold that week. A car tyre costs 90 plus VAT at 17.5%. (b) Work out the total cost of the tyre. The value of a new motorbike is 7500 The value of the motorbike depreciates by 15% per year. (c) Work out the value of the motorbike after 3 years. (Total 8 marks) MathsWatch mathswatch@aol.co.uk Page 9

10 11.(a) Simplify 2a + 3b a + 4b (1) 1 (b) M = pz Find the value of M when p = and z = 2 4 M = (c) Factorise 2x 2 4x (d) Expand and simplify (x + 4)(x + 5) (e) Factorise x 2 + 7x + 10 (Total 9 marks) MathsWatch mathswatch@aol.co.uk Page 10

11 12. A shop sells computers. The table shows the number of computers sold each month from September to January. Sep Oct Nov Dec Jan (a) Work out the percentage increase in the number of computers sold from November to December. Give your answer to 3 significant figures. (b) Work out the 4-month moving averages for the information in the table.... % 13. The mass of an oxygen atom is grams. Calculate the mass of 30 oxygen atoms. Give your answer in standard form (Total 5 marks) (Total 2 marks) MathsWatch mathswatch@aol.co.uk Page 11

12 14. x = -1 y A O x Triangle A is reflected in the x-axis to give triangle B. Triangle B is reflected in the line x = -1 to give triangle C. Describe the single transformation that takes triangle A to triangle C.... (Total 3 marks) MathsWatch mathswatch@aol.co.uk Page 12

13 15. Diagram NOT accurately drawn 12 cm 5 cm A solid cylinder has a radius of 5 cm and a height of 12 cm. (a) Work out the volume of the cylinder. Give your answer correct to 2 significant figures.... cm 3 The cylinder is made from steel. The density of the steel is 7.85 grams per cm 3. (b) Work out the mass of the cylinder. Give your answer correct to 2 significant figures.... cm 3 (Total 4 marks) MathsWatch mathswatch@aol.co.uk Page 13

14 16. ABC is a right-angled triangle. AB = 9 cm BC = 6 cm Diagram NOT accurately drawn C 6 cm A 9 cm B (a) Work out the area of the triangle.... cm 2 (b) Work out the length of AC. Give your answer correct to 2 decimal places. XYZ is another right-angled triangle. XY = 27 m YZ = 45 m 27 m X... cm Diagram NOT accurately drawn (c) Calculate the size of angle a. Give your answer correct to 1 decimal place. Y 45 m a Z... (Total 8 marks) MathsWatch mathswatch@aol.co.uk Page 14

15 17. (a) Express 420 as a product of its prime factors.... (b) Work out the Highest Common Factor (HCF) of 260 and (Total 6 marks) 18. The region R satisfies the inequalities x 3, y 1, x + y 7 On the grid below, draw straight lines and use shading to show region R. y O x (Total 3 marks) MathsWatch mathswatch@aol.co.uk Page 15

16 19. t is proportional to the square of r. When r = 6, t = 90 (a) Find a formula for t in terms of r. t =... (b) Calculate the value of t when r = (1) (Total 4 marks) 20. Diagram NOT accurately drawn The diagram shows a sector of a circle, centre O. The radius of the circle is 17 cm. The angle of the sector is 160. Calculate the area of the sector. Give your answer correct to 3 significant figures.... cm 2 (Total 2 marks) MathsWatch mathswatch@aol.co.uk Page 16

17 21. The incomplete table and histogram show information about the heights of a colony of giraffes living in Kenya. Height (h ) in cm Frequency 0 < h < h < h < h < h (a) Use the information in the histogram to complete the table. (b) Use the information in the table to complete the histogram. Frequency density Height (h) in cm 22. A car travels a distance of 45 m (correct to the nearest metre) in a time of 1.7 seconds (correct to the nearest tenth of a second). Find the upper and lower bounds of the average speed of the car. Give your answers correct to 1 decimal place. (Total 4 marks) Speed upper bound = m/s Speed lower bound = m/s (Total 3 marks) MathsWatch mathswatch@aol.co.uk Page 17

18 23. 5 m C 10 m Diagram NOT accurately drawn B A 12 m ABC is a triangle. AB = 12 m BC = 10 m CA = 5 m Calculate the size of angle BAC. Give your answer correct to 1 decimal place.... (Total 3 marks) MathsWatch mathswatch@aol.co.uk Page 18

19 24. (a) Show that the equation 4 5 2x x + 3 = x 2 can be rearranged to give 2x 2 + 5x 23 = 0 (b) Solve 2x 2 + 5x 23 = 0 Give your solutions correct to 2 decimal places. x =... or x =... (Total 6 marks) MathsWatch mathswatch@aol.co.uk Page 19

20 25. y (3, 294) Diagram NOT accurately drawn (1, 6) O x The sketch shows a curve with equation y = ka x where k and a are constants, and a > 0. The curve passes through points (1, 6) and (3, 294). Calculate the value of k and the value of a. k =... a =... (Total 3 marks) TOTAL FOR PAPER: 100 MARKS END MathsWatch mathswatch@aol.co.uk Page 20