Test: Indices - Year 8 MCQ

Calculate total seconds: 2⁹ × 3³ × 5⁴ = 512 × 27 × 625 = 8,640,000 seconds.

Convert to days: There are 86,400 seconds in a day (60 × 60 × 24 = 2⁵ × 3² × 5¹).

Divide: 8,640,000 ÷ 86,400 = 100 days.

Calculate days from 17th June to 15th July: June 17–30 = 13 days; July 1–15 = 15 days; Total = 28 days.

Doubling periods: 28 ÷ 4 = 7.

Area after 7 doublings: 20 × 2⁷ = 20 × 128 = 2,560 cm².

Express 0.2 as a fraction: 0.2 = 1/5.

Calculate (0.2)⁴ = (1/5)⁴ = 1⁴/5⁴ = 1/5⁴ = 5^-4.

Use compound interest formula: A = P × (1 + r)ⁿ.

Here, P = 500, r = 0.015, n = 3.

A = 500 × (1.015)³ ≈ 500 × 1.045678625 ≈ 522.8393125.

To nearest 1p: £522.84.

We need 3^x = 6,561.

Calculate powers of 3: 3⁸ = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 6,561.

Thus, the index is 8.

2³ means 2 multiplied by itself 3 times, which equals 8.

Express 8 as 2³, so 8³ = (2³)³ = 2⁹.

Then, 24 × 8³ = 2⁴ × 2⁹ = 2⁴⁺⁹ = 2¹³.

Calculate 2¹³ = 8,192.

Express 25 as 5², so 25^-2 = (5²)^-2 = 5^-4.

Then, 5² × 25^-2 × 5^-2 = 5² × 5^-4 × 5^-2 = 5^2-4-2 = 5^-4.

Calculate 5^-4 = 1/5⁴ = 1/625 = 0.04.

Volume of cube: 25³ = (5²)³ = 5⁶ = 15,625 cm³.

Convert to litres: 15,625 ÷ 1,000 = 15.625 litres (since 1,000 cm³ = 1 litre).

When multiplying powers with the same base, you add the exponents. Therefore,4³ × 4⁵ = 4³⁺⁵ = 4⁸.