Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Product of prime factors - Mathematics
Document related concepts
Transcript
Aberdare Community School Mathematics Department WJEC GCSE Foundation – Non Calculator Number Product of prime factors Name: ............................................................. Set: ............................................................. Date: ............................................................. Teacher: ............................................................. 22 17. (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] 18. (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 (185-01) B [3] 24 18. (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] (185-07) 21 (c) Examiner only The mean mark for the pupils on Paper 1 is 61 and the mean mark on Paper 2 is 59. Draw a line of best fit on your scatter diagram. [2] (d) 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] 18. (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] 185-01 Turn over. 22 18. (a) Examiner only Share £600 in the ratio 3 : 2. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [2] (b) Express 126 as a product of prime numbers using index notation. .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................... [3] (185-07) 24 18. (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] 19. (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 (185-01) B [3] 21 17. (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] (185-07) Turn over. 15 Examiner only 10. Express 525 as a product of prime numbers using index notation. ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ ........................................................................................................................................................................................................................ [3] (4363-01) Turn over. 20 Examiner only [2] 18. (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] (185-07) 15 Examiner only [3] 11. (a) Express 112 as a product of prime numbers in index form. [3] (b) Explain how you know that 32 is not a square number. [1] 4352-01 17 15. (a) Find the highest common factor of 30 and 75. [1] (b) Find the lowest common multiple of 6 and 21. [2] (4363-01) Examiner only 18 Examiner only 13. (a) Express 140 as a product of prime numbers in index form. [3] (b) The number 126 can be expressed as 2 × 32 × 7. Using this fact and your answer to (a), write down the Highest Common Factor (HCF) of the numbers 140 and 126. [1] © WJEC CBAC Ltd. (4370-03) 16 (b) Write 1200 as a product of prime factors using index notation. [3] © WJEC CBAC Ltd. (4363-01) Examiner only 14 13. (a) Write 3600 as a product of prime factors using index notation. [3] © WJEC CBAC Ltd. (4363-01) Examiner only 21 Examiner only 16. (a) Express 936 as a product of prime numbers in index form. [3] (b) Explain why 50 is not a perfect square number. [1] © WJEC CBAC Ltd. (4370-03) Turn over. 17 Examiner only 13. (a) Express 150 as a product of prime numbers in index form. [3] (b) What is the smallest positive whole number that 150 can be multiplied by to make a perfect square? [1] © WJEC CBAC Ltd. (4370-03) Turn over. 14 Examiner only (c) Express 396 as a product of prime numbers in index form. END OF PAPER © WJEC CBAC Ltd. (4352-01) [3]
