N1: NUMBERS AND THEIR OPERATIONS COMMON QUESTIONS by @booksbfrboys on Tiktok

N1: Numbers and Their Operations (Common Questions w/ Real-World Applications) - Primes and Prime Factorisation, HCF, LCM, Sq, Cube, Sq Root, Cube Root (Sec 1) - Calculations with Calculator (Sec 1) - [Negative, Rational, Irrational, Real] numbers, Integers and Their 4 Operations (Sec 1) - Approximation and Estimation (Sec 1) - Standard Form (Sec 3) - Positive, Negative, Zero and Fractional Indices (Sec 3) - Laws of Indices (Sec 3) - Real-World Application of Indices [Compound Interest] (Sec 3) 1. (a) Express in index form with base 11. 5 121 [1] 1. (b) Evaluate without using a calculator. 3 2 3 × 2 4 1 3 [2] 1. (c) Simplify . 𝑎𝑏 ÷ 2 𝑎 ( ) − 2 [1] 2. Simplify , leaving your answer in positive indices. 21 𝑝 2 𝑞 3 𝑟 0 2 𝑟 5 ÷ 7 𝑝𝑞 4 𝑝 2 [2] 3. A group of students line up. If they lined up in 2s or 6s or 9s, there will be one student without a partner. Calculate the least number of students in the contingent. [2] 4. Calculate the highest common factor of 456 and 696. [1] 5. Solve the equation . 2 3 𝑥 × 12 5 𝑥 = 100 [3] 6. Simplify . 24 𝑐 3 𝑑 2 3 𝑑 𝑒 2 ( ) 3 ÷ 5 𝑐 − 2 10 𝑑 𝑓 [2] 7. Calculate . Write your answer correct to 3 significant figures. 11 . 2 7 1 4 30 . 67 − 5 . 23 [1] 8. Without using a calculator, show that is a multiple of 2. 7 103 − 7 101 [1] 9. Use prime factorisation to explain why 72 is not a perfect cube. [2] 10. Simplify . 𝑎𝑏 𝑐 ( ) 3 × 𝑎 𝑏 − 3 𝑐 2 [2]

11. (a) Given , find the value of 𝑥 9 = 9 0 𝑥 . [1] 11. (b) Simplify . 𝑥 2 3 𝑦 ÷ 𝑥 9 𝑦 2 [1] 12. (a) Express 40 and 138 as the product of their prime factors. [2] 12. (b) Hence, find the smallest positive integer such that 138 is divisible by 40. 𝑘 𝑘 [1] 13. A wooden cube with side 8 cm is cut into two-centimetre cubes. All of the two-centimetre cubes are then arranged to form a cuboid of height greater than 8 cm. The perimeter of the cuboid is 36 cm. Find the height of the cuboid. 14. Jas deposited $ into an account that paid a compound interest of 1.85 per 𝑚 % annum. He made no other deposits or withdrawals for three years. At the end of three years, he had $2509.26 in his account. Find the value of , giving your answer correct to the nearest dollar. 𝑚 [2] 15. (a) Solve . 4 9 2 𝑥 + 1 ÷ 3 7 = 1 343 [3] 15. (b) Without using a calculator, show that is divisible by 7. 3 1161 + 3 1158 [2] 16. Alexandar invested some money in a bank after 3 years. The rate of compound interest was fixed at 2 per annum. % At the end of 3 years, Ethan has a total of in his account. $3077 . 50 What was the amount of money that Ethan invested in the beginning? [3] 17. Simplify . 2 𝑝 3 𝑞 ( ) 2 ÷ 𝑞 5 𝑝 [2] 18. Given that , find . 1 343 = 7 𝑘 𝑘 [1] 19. By approximating each number to 2 significant figures, estimate the value of . Show your working and give your answer to a reasonable degree 12 . 1 × 48 . 8 3 27 . 3 of accuracy. [2]

20. Express 0.00952 nanoseconds in megaseconds, giving your answer in standard form. [1] 21. Without using a calculator, show that is divisible by 7. 2 17 − 2 14 [2] 22. Simplify the expression . 3 𝑦 𝑥 2 × 𝑦 𝑥 ÷ 𝑥 3 9 𝑦 − 2 [2] 23. Write the following in order of size, largest first. − 7 8 , − 8 × 1 0 − 1 , − 0 . 81 [1] 24. (a) Calculate . 4 . 73− 3 . 28 3 99 . 7× 1 . 25 Write down the first four digits on your calculator display. [1] 24. (b) The number 102 999 corrected to n significant figures is 103 000. Write down the largest possible value of n . [1] 25. One hundred identical drops of oil have a total mass of 4550 milligrams. 1 milligram = grams. 1 × 1 0 − 3 It is given that 1 of oil weighs 0.91 grams. 𝑐 𝑚 3 Calculate the volume of one drop, in , giving your answer in standard form. 𝑚 3 [2] 26. The numbers 98, 784 and 1176, written as a product of their prime factors are and . 98 = 2 × 7 2 , 784 = 2 4 × 7 2 1184 = 2 3 × 3 × 7 2 (a) Find the largest possible integer, , which divides 98, 784 and 1176. 𝑤 [1] (b) Find the smallest integer, , such that is a whole number. 𝑝 3 784 × 1176 𝑝 [1] 27. Solve the equation . 1 4 𝑦 = 2 − 6 [2] 28. Given that , find the value of . 2 𝑥 + 1 + 2 𝑥 = 24 𝑥 [2] 29. Simplify , leaving your answer in positive indices. 2 𝑥𝑦 ( ) 2 35 𝑥 𝑦 7 ÷ 𝑥 − 1 𝑦 − 2 4 ( ) − 2 [2]

30. Ms Chew invested $ in a bank that pays compound interest at the rate of 𝑃 4 per annum compounded half-yearly. If she received $6341.21 from the % Bank after 6 years, find the value of , giving your answer to the nearest 𝑃 whole number. [2] 31. (a) Express 315 as a product of prime factors. [1] 31. (b) Find the smallest whole number by which 315 must be multiplied to obtain a perfect square. [1] 32. Given that , find the value of . 4 1 2 𝑛 ( ) ÷ 6 4 − 2 = 2 5 𝑛 [2] 33. $10 000 was invested in an account which pays per annum compound 𝑟 % interest. At the end of 3 years, the interest earned $1910.16. Find the value of . 𝑟 [2] 34. (a) Expressed as the products of their prime factors, 196 = 2 2 × 7 2 252 = 2 2 × 3 2 × 7 Write down the highest common factor of 196 and 252. [1] 34. (b) The lowest common multiple of 252 and an even number is 756. (i) Express 756 as the product of its prime factors. [1] (ii) Find the smallest possible value of the even number. [1] 35. (a) Simplify . 𝑎 7 𝑏 2 × 𝑎 3 𝑏 ( ) − 2 [1] 35. (b) Solve . 2 × 3 𝑥 3 = 162 [2] 36. (a) Express 540 as the product of its prime factors. [1] 36. (b) Find two numbers, both smaller than 100, that have a lowest common multiple of 540 and a highest common factor of 6. [2] 37. Kelly has 300 one-centimetre cubes. She arranges all of the cubes into a cuboid. The perimeter of the top of the cuboid is 18 cm. Each side of the cuboid has a length greater than 3 cm. Find the height of the cuboid. [2]

38. (a) Express 462 as a product of its prime factors. [1] 38. (b) Written as a product of its prime factors, . 1512 = 2 3 × 3 3 × 7 (i) Find the smallest whole number for which is a multiple of 1512. 𝑛 462 𝑛 [1] (ii) Explain why 1512 is not a perfect cube. [[1] 39. (a) Calculate . 3 + − 4 2 + 2 × 115 Write down the first 6 digits on your calculator display. [1] 39. (b) Write your answer to part (a) correct to 3 decimal places. [1] 40. (a) Given that , find the value of . 6 𝑚 ÷ 6 − 3 = 6 2 𝑚 [1] 40. (b) Arrange the following numbers in increasing value. Show your working clearly. 0 . 0037 × 1 0 6 3 . 7 × 1 0 5 370 × 1 0 − 3 37 [2] 40. (c) Simplify . Leave your answer in positive index form. 3 8 𝑥 6 × 1 3 𝑦 − 5 [2] 41. Kyran invested $12 000 into a fund w