Excel / Education GCSE Mathematics Paper 5B (Calculator) Higher Tier Time: 2 hours 5B Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Items included with question papers Formulae sheet Instructions to Candidates Answer ALL the questions in the spaces provided in this question paper. Supplementary answer sheets may be used. Information for Candidates The total mark for this paper is 100. The marks for questions and parts of questions are shown in round brackets: e.g.. Calculators may be used. Advice to Candidates Show all your working.
1. (a) Simplify 3x 4y + 7x + 8y (b) Expand 3 (4 9x) (c) Factorise 8xy 12y (d) Simplify (2x 2 x 4 ) 3.... 2. A child s puzzle consists of several wooden blocks like the one shown below. 12.7 cm 5.1cm 6.9cm A 9.3 cm 1.8cm
(a) Calculate the area of the L shaped face of the block, marked A in the diagram. Give your answer to a sensible degree of accuracy. cm 2 (b) Calculate the volume of the block. Remember to state the units in your answer. 3. A group of people were asked to throw a basketball into a hoop, the number of tries it took them to do it are shown in the bar chart below
(a) Complete the frequency table below. (b) People Tries 1 3 2 3 4 5 6 Total Calculate the mean number of tries per person. (c) If a person is chosen at random from the group, what is the probability that it took them 3 throws? (d) The throws were taken from 30 feet away from the hoop. Given that 1 foot is 12 inches and one inch is 2.6cm, how many metres is this?
4. (a) Given that x is an integer and -1 < x 4, list all of the possible values of x. (b) Solve 3 4x 15. 5. A.. (a) In the space below draw a sketch of the net of this cylinder. 12 cm 10cm The cylinder has radius 10cm and height 12cm.
(b) Find, to 4 sig fig, the circumference of the top of the cylinder. (c) Find the total surface area of the cylinder cm 6. (a) Make y the subject of 3y! 2x z = 7 cm 2 (4) (b) (i) What is the gradient of the line 4x + 2y = 10?
(ii) Write down the coordinates of the point where the line 4x + 2y = 10 crosses the y axis. 7. A curve has equation y = x 2-5x + 6 (1) (a) Complete the following table of values for this equation. x -1 0 1 2 3 4 5 y 2 2 6 (b) Use the grid below to plot the graph of y = x 2-5x + 6 y 10 8 6 4 2-4 -3-2 -1 1 2 3 4 x -2-4 -6-8
8. Solve; (a) 2x + 3 = 10 (b) 4(x 1) = 40 x = (c) x 2! 5 =1 x = (d) 5x! 3 2 =11 x = x = 9. An opera is attended by 768 people. One sixth of them had free seats. The rest paid 12.25 each. How much did they pay in total?
10. John invests 2,400 in an account paying 6% compound interest per year. (a) How much is it worth after 1 year? (b) How much is it worth after 3 years? 11. The diagram shows a tent whose front is an isosceles, right angled triangle with a side of length 1.6m. The tent is 2.5m long. b b 1.6m 2.5m (a) Calculate the length of the sloping side of the front triangle (both marked b in the diagram) m
(b) Use your answer to part (a) to find the area of the triangle (c) Hence find the volume of the tent m 2 12. 5m 40 o Gill stands 5m from a tree. The angle of elevation from the ground to the tree is 40 o (a) Find the height of the tree.
(b) Gill moves further away from the tree until the angle of elevation has changed to 30 o. How far is Gill from the tree now? 13. (a) Describe how to take a stratified sample of 20 people from a group of 60 men and 20 women. (b) State an advantage of using a stratified sample rather than a simple random sample of these men and women. 14. A number sequence begins as follows; 3, 6, 11, 18, 27,..,.. (a) Write down the next two terms of the sequence...
(b) Find an expression for the nth term of the sequence... 15. T A 40 o 70 o 12 m B The diagram shows a tall building. At A the angle of elevation to the top of the building is 40 o. At B the angle of elevation to the top of the building is 70 o. The distance AB is 12m. Calculate the height of the building...m (5)
16. B 110 o C E A D The diagram shows a circle containing a cyclic quadrilateral ABCD. A tangent, DE, meets the circle at D. Angle BCD is 110 o. Triangle CBD is isosceles. (a) Find the size of angle BAD. Give a reason for your answer. (a).. Find the size of angle CDE. Give a reason for your answer...
17. Solve the following simultaneous equations; x = 1 2y 2x 2 5 xy = 0 (5) End of Questions (Total Marks: 100)