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 ac