Sec 3 E-Math Numbers & Their Operations topical questions

Express 180 as a product of its prime factors.

Given that 48 = 2⁴ × 3 and 90 = 2 × 3² × 5, find (a) the HCF and (b) the LCM of 48 and 90.

1. (a)Find the HCF.[2]
2. (b)Find the LCM.[2]

Evaluate (5/4)⁻².

(a) Write 0.0000519 in standard form. (b) Write 7.3 × 10⁴ as an ordinary number.

1. (a)Write 0.0000519 in standard form.[1]
2. (b)Write 7.3 × 10⁴ as an ordinary number.[1]

Write 0.03749 correct to (a) 2 significant figures and (b) 3 significant figures.

1. (a)2 significant figures.[1]
2. (b)3 significant figures.[1]

A carpenter saws two planks, one 96 cm long and one 160 cm long, into pieces all of the same length, with no wood wasted. Find the greatest possible length of a piece.

Without a calculator, evaluate (16/25)^(−1/2).

Two shuttle buses leave the same car park at 09 00. The blue bus leaves every 12 minutes and the orange bus leaves every 18 minutes. Using prime factorisations, find the time when the two buses next leave together.

Simplify (27a⁶)^(2/3).

Work out (8.4 × 10⁻⁷) ÷ (6 × 10⁻³), giving your answer in standard form.

Without using a calculator, estimate the value of 0.4098 × 50.4², showing the numbers you use.

The mass of the Earth is about 5.97 × 10²⁴ kg and the mass of the Moon is about 7.35 × 10²² kg. Find how many times heavier the Earth is than the Moon, giving your answer correct to 3 significant figures.

A graphics processor can carry out 4.5 × 10⁸ calculations each second. Working continuously for 2 minutes, how many calculations does it carry out? Give your answer in standard form.

Without a calculator, estimate the value of (61.8 − 5.02) ÷ 0.481, showing the rounded numbers you use.

Solve the equation 3^(2x+1) = 81^(x−1).

The number 945 is written as 3³ × 5 × 7. Find the smallest positive integer n such that 945n is a perfect square, and state that perfect square.

Light travels at approximately 3 × 10⁸ metres per second. A year is approximately 3.15 × 10⁷ seconds. Find, in standard form, the distance light travels in one year (a light-year).

Singapore has a population of about 5.92 × 10⁶ living on a land area of about 7.28 × 10² km². Calculate the population density per km², giving your answer in standard form correct to 3 significant figures.

Given that 45 360 = 2⁴ × 3⁴ × 5 × 7, find the smallest positive integer n such that 45 360n is a perfect square, and state √(45 360n).

Solve the equation 2^(x+1) × 4^(x−2) = 8.