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Centre Number Candidate Number For Examiner’s Use Surname Other Names Examiner’s Initials Candidate Signature Pages General Certificate of Secondary Education Higher Tier Mark 3 4–5 Mathematics 43602H 6–7 8–9 Unit 2 Higher Tier H Practice Paper Set 4 Specification 4360 For this paper you must have: mathematical instruments. 10 – 11 12 – 13 14 – 15 TOTAL You may not use a calculator. You may use a calculator. Time allowed 1 hour 15 minutes Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Fill in the boxes at the top of this page. Answer all questions. You must answer the questions in the space provided. Do not write outside the box around each page or on blank pages. Do all rough work in this book. Cross through any work that you do not want to be marked. Information The marks for questions are shown in brackets. The maximum mark for this paper is 66. The quality of your written communication is specifically assessed in questions 3 and 7 These questions are indicated with an asterisk () You may ask for more answer paper and graph paper. These must be tagged securely to this answer booklet. Advice In all calculations, show clearly how you work out your answer. Practice Paper Set 4/43602H 3 PP4/43602H 2 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED PP4/43602H 3 Do not write outside the box Answer all questions in the spaces provided. 1 Work out 8 1 – 9 6 ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 2 Manish has 100 millilitres of orange juice in a glass. During the next 12 seconds He fills the glass by adding some lemonade. He drinks from the glass. The graph shows this information. 300 200 Number of millilitres in the glass Turn over for the next question 100 5 10 Time, seconds Turn over for the next question 2 Turn over PP4/43602H 4 2 (a) When the glass is full, work out the ratio: orange juice: lemonade Write your answer in its simplest form. ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 2 (b) What percentage of the drink is left after 12 seconds? ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (3 marks) PP4/43602H 5 3 A market trader buys 100 scarves at £2.50 each and 200 hats at £4 each. He wants to sell them all and make 20% profit. He sells all the scarves at £3.25 each and 150 of the hats at £5 each. He can reduce the price of the remaining hats and still make 20% profit. Work out the reduced price of the hats. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer £............................................................. (6 marks) Turn over for the next question 11 Turn over PP4/43602H 6 4 (a) The nth term of a sequence is n2 – 4. Write down the first three terms of the sequence Answer ..................., ..................., ................. (1 marks) 4 (b) Here is a sequence. 3 8 13 18 23 ...... ...... Work out a formula for the nth term of the sequence. ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 5 Write 48 as the product of prime factors. Give your answer in index form. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (3 marks) PP4/43602H 7 6 (a) Solve 7x > 2x + 20 ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 6 (b) Circle the diagram that represents 1 2 3 1 2 3 1≤n<3 1 2 3 1 2 3 (1 mark) Turn over for the next question 9 Turn over PP4/43602H 8 7 Helga and Zara are goal shooters in netball. Information about the goals scored and goal attempts for each player are shown. Goals scored : Goal attempts Helga 9 : 24 Zara 12 : 28 Work out which player has the better ratio of goals scored to goal attempts. You must show your working. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (4 marks) PP4/43602H 9 8 (a) Solve 4(2w – 3) = 36 ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (3 marks) 8 (b) Solve 12 x = 5–x 3 ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer x = ........................................................ (3 marks) Turn over for the next question 10 PP4/43602H 10 9 (a) Do not write outside the box On the grid, draw the graph of y = 2x – 1 Use values of x from -1 to 2. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... y -1 0 1 2 x (3 marks) 9 (b) Line L is parallel to y = 2x – 1 and passes through the point (0, 3). Write down the equation of line L. Answer ............................................................. (2 marks) PP4/43602H 11 10 Here are two numbers. 2-3 1.5 × 10-1 Which is the larger? You must show your working. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (3 marks) 11 (a) Factorise fully 3y2 + 6y ....................................................................................................................................................... Answer ............................................................. (2 marks) 11 (b)(i) Factorise 3y2 + 13y + 14 ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 11 (b)(ii) Hence solve 3y2 + 13y + 14 = 0 ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (1 mark) Turn over for the next question 13 PP4/43602H 12 12 Solve the simultaneous equations 3a + 5b = 2 2a – 3b = 14 Do not use trial and improvement. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer £............................................................. (4 marks) PP4/43602H 13 13 (a) Simplify fully 17 5 + 2a 2a ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 13 (b) Simplify fully 2x 8 x4 ÷ 5 3 ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 14 36 0.5 6 4 = k where k is an integer. 36 Work out k. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (4 marks) Turn over for the next question 12 Turn over PP4/43602H 14 15 (a) Simplify fully 32 8 ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) 15 (b) Expand and simplify fully (2 – 3 )2 ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (2 marks) PP4/43602H 15 16 Here is an identity. (2x + a)(x + 3) ≡ 2x2 + 4ax + b a and b are numbers. Work out b. ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... ....................................................................................................................................................... Answer ............................................................. (5 marks) END OF QUESTIONS 9 Turn over PP4/43602H 16 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED PP3/43602H
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