Edexcel GCSE 1387 Mathematics A Paper 6 (Calculator) HIGHER Tier MOCK Paper Time: 2 hours

Transcription

1 Centre No. Paper Reference Candidate No / 0 6 Surname Signature Initial(s) Paper Reference(s) 1387/06 Edexcel GCSE 1387 Mathematics A Paper 6 (Calculator) HIGHER Tier MOCK Paper Time: 2 hours Examiner s use only Team Leader s use only 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 In the boxes above, write your Centre Number and Candidate Number, your surname, initial(s) and signature. Check that you have the correct question paper. 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 the various parts of questions are shown in round brackets, e.g.:. Calculators may be used. This paper has 20 questions. There is 1 page. Advice to Candidates Work steadily through the paper. Do not spend too long on one question. Show all stages in any calculations. If you cannot answer a question, leave it and attempt the next one. Return at the end to those questions you have left out. Turn over This publication may only be reproduced in accordance with Edexcel copyright policy. Edexcel Foundation is a registered charity Edexcel

2 Answer ALL TWENTY questions. Write your answers in the spaces provided. You must write down all stages in your working. 1. Jack and Jill share 18 in the ratio 2:3 Work out how much each person gets. Jack.. Jill.. (Total 2 marks) 2. (a) Express the following numbers as products of their prime factors. (i) 56 (ii) 84. Find the Highest Common Factor of 56 and 84.. (4) (1) (Total 5 marks) 2

3 3. The equation x 3 + 3x 2 = 65 has a solution between x = 3 and x = 4. Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working. x = (Total 4 marks) 4. John records the time, in minutes, between successive aircraft passing over his house. The table shows the results. Time, t minutes Frequency 0 < t < t < t < t < t (a) Calculate the class interval in which the median lies.. John claims that his results show that the mean time is 10 minutes. Is John correct? Explain briefly your answer. (1) (Total 3 marks) 3 Turn over

4 5. In a sale all the normal prices are reduced by 18%. In the sale Mandy pays for a hat. Calculate the normal price of the hat... (Total 3 marks) cm Diagram NOT accurately drawn 10 cm The diagram shows a solid cylinder. The radius of the cylinder is 54 cm. The height of the cylinder is 10 cm. (a) Calculate the curved surface area of the cylinder. Give your answer correct to three significant figures... 4

5 The diagrams show the circular top of the cylinder and a piece of plastic in the shape of a right-angled triangle. The two shorter sides of the triangle have lengths76 cm and 77 cm. Show that the triangular piece of plastic cannot completely fit on the top of the cylinder without overlapping. Diagrams NOT accurately drawn 54 cm 76 cm 77 cm (4) (Total 7 marks) 5 Turn over

6 7. Simplify fully (i) 4 m m 5.. (ii) 6 p p 2 (iii) 3 8 5x y 2xy (iv) ( k+ 8) 4 k (Total 5 marks) 6

7 8. C 12.6 m A 41 B The diagram shows a right-angled triangle ABC. AC = 12.6 m. Angle CAB = 41 Angle ABC = 90 Find the length of the side AB. Give your answer correct to 3 significant figures. m (Total 3 marks) 9. Solve the simultaneous equations 2x + 3y = 6 3x 2y = 22 x = y = (Total 4 marks) 7 Turn over

8 10. A 8 cm B Diagram NOT accurately drawn E 5 cm D 6 cm C AB is parallel to DC. The lines AC and BD intersect at E. AB = 8cm EC = 5 cm DC = 6 cm (a) Explain why triangle ABE and triangle CDE are similar Calculate the length of AC... cm (Total 5 marks) 8

9 11. A straight line has equation y = 4x 5. (a) Write down the equation of the straight line that is parallel to y = 4x 5 and passes through the point (0, 3). Rearrange the equation y = 4x 5 to find x in terms of y... x =.. (Total 4 marks) 12. x= p q pq 5 p = 4 10 q = (a) Calculate the value of x. Give your answer in standard form. Make q the subject of the formula x= p q pq q =. (4) (Total 6 marks) 9 Turn over

10 13. Kevin regularly travels from Manchester to Oxford. He travels on two different trains. His first train is from Manchester to Birmingham and his second train is from Birmingham to Oxford. On the first train, the probability that a seat has a table is 5 3. On the second train, the probability that a seat has a table is Kevin is travelling from Manchester to Oxford tomorrow. (a) Complete the probability tree diagram to show the outcomes of Kevin s seating on the two trains. Label clearly the branches of the probability tree diagram. The probability tree diagram has been started in the space below. Seat on the first train Seat on the second train 3 5 with a table without a table Calculate the probability that Kevin will have a seat with a table on both the first train and the second train. (c) Calculate the probability that Kevin will have a seat with a table on at least one of the two trains.. (Total 8 marks) 10

11 14. A Diagram NOT accurately drawn 8.1 cm 7.5 cm B 30 C In triangle ABC, AB = 8.1 cm, AC = 7.5 cm, angle ACB = 30. (a) Calculate the size of angle ABC. Give your answer correct to 3 significant figures. Calculate the area of triangle ABC. Give your answer correct to 3 significant figures....cm 2 (Total 6 marks) 11 Turn over

12 15. Peter cuts a square out of a rectangular piece of metal. 2x + 3 Diagram NOT accurately drawn x + 2 x + 4 x + 2 The length of the rectangle is 2x + 3. The width of the rectangle is x + 4. The length of the side of the square is x + 2. All measurements are in centimetres. The shaded shape in the diagram shows the metal remaining. The area of the shaded shape is 20 cm 2. 2 (a) Show that x + 7x 12= 0 (i) 2 Solve the equation x + 7x 12= 0 Give your answers correct to 4 significant figures. (4).. 12

13 (ii) Hence, find the perimeter of the square. Give your answer correct to 3 significant figures... cm (1) (Total 8 marks) 16. There are 800 pupils at Hightier School. The table shows information about the pupils. Year group Number of boys Number of girls An inspector is carrying out a survey into pupil s views about the school. She takes a sample, stratified both by Year group and by gender, of 50 of the 800 pupils. (a) Calculate the number of Year 9 boys to be sampled.. Toni stated There will be twice as many Year 7 boys as Year 11 girls to be sampled. Is Toni s statement correct? You must show how you reached your decision. (Total 4 marks) 13 Turn over

14 17. The graph of y = f(x) is sketched in the diagrams below. x Diagram A (2,6) 0 4 y (a) On Diagram A sketch the graph of y = f(x) Diagram B x (2,6) 0 4 y On Diagram B sketch the graph of y = f(x 1) (Total 4 marks) 14

15 18. Error! C Diagram NOT accurately drawn A B The diagram shows a triangle ABC. Angle ABC is exactly 90. AB = 83 mm correct to 2 significant figures. BC = 90 mm correct to 1 significant figures. (a) Calculate the upper bound for the area of triangle ABC. Angle CAB = x... mm 2 Calculate the lower bound for the value of tan x. ABC is the cross section of a triangular prism... The upper bound for the volume of the prism is mm 3. The lower bound for the volume of the prism is mm 3. (d) Write down the volume of the prism, in cm 3, to an appropriate degree of accuracy. 19. C a cm 3 15 Turn over D (Total 6 marks)

16 Error! CDEF is a quadrilateral with CD = a, DE = b and FC = a b. (a) Express CE in terms of a and b. Prove that FE is parallel to CD... (1)... M is the midpoint of DE. (c) Express FM in terms of a and b. X is the point on FM such that FX : XM = 4 : 1.. (1) (d) Prove that C, X and E lie on the same straight line. 20. The expression x can be written in the form ( ) x p x q, (Total 7 marks) 16

17 for all values of x. (a) Find the value of p and the value of q. p =.. q =.. The expression 2 8x x has a maximum value. (i) Find the maximum value of 2 8x x. (ii) State the value of x for which this maximum value occurs. (Total 6 marks) TOTAL FOR PAPER: 100 MARKS 17

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