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Aberdare Community School Mathematics Department WJEC GCSE Higher – Non Calculator Number Product of prime factors Name: ............................................................. Set: ............................................................. Date: ............................................................. Teacher: ............................................................. 12 9. (a) Examiner only Arholwr yn unig Express 360 as a product of prime numbers in index form. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (b) Explain why 2 5 × 3 4 is not a perfect square. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] 10. (a) The diagram below shows two straight lines AB and AC. Find and shade the region which satisfies both of the following conditions. (i) All points in the region are nearer to AC than to AB. (ii) All points in the region are less than 6 cm from B. A C (185-04) B [3] 12 8. (a) Examiner only Express 480 as a product of prime numbers in index form. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (b) Explain why 36 × 54 is a perfect square. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] (185-09) 10 9. Examiner only Express 500 as a product of prime numbers in index form. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (185-04) 10 5. (a) Examiner only Express 792 as a product of prime numbers in index form. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (b) Write down the least positive whole number that 792 must be multiplied by to make the result a perfect square. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] (c) Explain why 25 × 36 × 132 is not a perfect square. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] (185-09) 9 (b) Examiner only Another pupil sat Paper 1 and was given a mark of 78, but was absent for Paper 2. Use your line of best fit to estimate the mark on Paper 2 for this pupil. .................................................................................................................................................................................................................................... [1] 9. (a) Express 1323 as a product of prime numbers in index form. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (b) Write down the least whole number by which 1323 should be multiplied to make the result a perfect square. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] (185-04) Turn over. 8 5. (a) Examiner only Estimate the value of 58 × 21 . 98 .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [2] (b) Given that 34 × 670 = 22 780, find the value of 22 780 . 67 .................................................................................................................................................................................................................................... [1] (c) Estimate the value of 8·037 × 2·976. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] (d) Write down the value of a half of 3 . 4 .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] (e) Express 225 as a product of prime factors using index notation. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (f) Find the value of the reciprocal of 0·7. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [2] (185-13) 9 Examiner only 7. (a) Solve x + 5 = 14. 3 .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [2] (b) Simplify 5 (2y + 3) – 2 (4y – 7). .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [2] .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [2] 8. (a) Share £600 in the ratio 3 : 2. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [2] (b) Express 126 as a product of prime numbers using index notation. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (185-09) Turn over. 9 Make g the subject of the formula t = 5g – 8. A09-185-09 (c) 12 8. (a) Examiner only Arholwr yn unig Express 360 as a product of prime numbers in index form. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (b) Explain why 2 5 × 3 4 is not a perfect square. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] 9. (a) The diagram below shows two straight lines AB and AC. Find and shade the region which satisfies both of the following conditions. (i) All points in the region are nearer to AC than to AB. (ii) All points in the region are less than 6 cm from B. A C (185-04) B [3] 12 6. (a) Examiner only Express 792 as a product of prime numbers in index form. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (b) Explain why 18 is not a perfect square. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [1] (185-09) 13 9. (a) Examiner only Express 756 as a product of prime numbers in index form. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [3] (b) Evaluate the following. Express your answer in standard form. 2 ×5 2 2 8 2 ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [3] (185-09) Turn over. 9 7. (a) Examiner only Express 1764 as a product of prime factors using index notation. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [3] (b) Write down the nth term of the sequence 13, 19, 25, 31, . . . . . . . . . ........................................................................................................................................................................................................................ 4363 020009 ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [2] (c) Write down the nth term of the sequence 2, 5, 10, 17, 26, 37, . . . . . . . . . ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [2] (4363-02) Turn over. 15 10. (a) (i) Examiner only Express 324 as a product of prime numbers in index form. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... (ii) Is 648 a square number? You must explain your answer. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... [5] (b) Simplify each of the following. (i) 5 x 4 y6 × 4 x 5 y ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... (ii) 50 a6b 10 a3b3 ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... [4] (0185-13) Turn over. 6 4. (a) Find the highest common factor of 30 and 45. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [1] (b) Find the lowest common multiple of 18 and 24. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [2] (d) Express 525 as a product of prime numbers using index notation. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [3] (4363-02) Examiner only 10 8. (i) Express 360 as a product of prime factors using index notation. (d) (ii) What is the least number that you must multiply 360 by to make a perfect square? [4] (0185-13) Examiner only 12 7. (a) Explain how you know that 24 is not a square number. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [1] (b) Express 112 as a product of prime numbers in index form. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [3] (0185-09) Examiner only 8 Examiner only 6. (c) Express 112 as a product of prime numbers in index form. [3] (d) Explain how you know that 32 is not a square number. [1] 4352-02 11 Examiner only (i) Express 106 as a product of prime factors in index form. (b) [2] (ii) Explain how you know that one million is a square number. [1] (4363-02) Turn over. 8 6. (a) Find the highest common factor of 30 and 75. [1] (b) Find the lowest common multiple of 6 and 21. [2] (4363-02) Examiner only 3 Examiner only 1.(a)Find the highest common factor of 48 and 64. [1] (b) Find the lowest common multiple of 36 and 90. [1] 4363 020 0 03 (c) Write down all the prime numbers between 70 and 80. [1] © WJEC CBAC Ltd. (4363-02) 7 Examiner only 5. (i) Write 1200 as a product of prime factors using index notation. (b) 4363 020007 [3] (ii) Write down the smallest possible number by which 1200 has to be multiplied to create a perfect square. [1] (4363-02) 11 Examiner only (d) Express 240 as a product of prime factors using index notation. (e) Evaluate the reciprocal of 0.9 and state whether this is greater or less than 0.9. [2] © WJEC CBAC Ltd. (4370-05) Turn over. 4370 0 5 0 011 [3] 5 3. Examiner only (a) Write 3600 as a product of prime factors using index notation. 4363 020 0 05 [3] © WJEC CBAC Ltd. (4363-02) Turn over. 12 8. (a) Find the highest common factor of 90 and 105. [2] (b) Find the lowest common multiple of 90 and 105. [2] (c) Express 936 as a product of prime numbers in index form. [3] © WJEC CBAC Ltd. (4370-05) Examiner only 11 4363 0 2 0 011 Examiner only 9. Jack makes the following statements. • 36 and 60 are both common factors of 180. • The highest common factor of 36 and 60 is not a factor of 180. Decide whether each of Jack’s statements is correct. You must show your working and give a reason for your answer. [3] © WJEC CBAC Ltd. (4363-02) Turn over. 7 4. Examiner only (i) Express 3969 as a product of prime numbers in index form. (a) [3] (ii) Explain how you know that 3969 is a perfect square. 4 35 2 020007 [1] © WJEC CBAC Ltd. (4352-02) Turn over. 7 (a) Express 396 as a product of prime numbers in index form. 5. [3] Examiner only (b) Write down the smallest positive integer which should be divided into 396 to produce a perfect square. [1] 4 35 2 020007 © WJEC CBAC Ltd. (4352-02) Turn over. 12 (a) Find the highest common factor of 36 and 54. 8. © WJEC CBAC Ltd. (4363-02) [1] Examiner only 11 (a) Write down the smallest possible number by which 24 has to be multiplied to create a perfect square. [2] 9. Examiner only 4363 0 2 0 0 11 © WJEC CBAC Ltd. (4363-02) Turn over. 8 5. Express 126 as a product of prime numbers in index form. © WJEC CBAC Ltd. (4352-02) [3] Examiner only 7 (b) Express the highest common factor of 24 and 40 as a product of prime numbers in index form.[3] Examiner only 4370 050 0 07 © WJEC CBAC Ltd. (4370-05) Turn over.
