Powers & roots

18A cube has a volume of 512 cm³ Work out the surface area of the cube.

Jason says, “The cube root of 27 is 9 because 27 divided by 3 is 9” Is Jason correct? You must give a reason for your answer.

Junaid says that 20 is a square number because 10² = 20

Is Junaid correct? Give a reason for your answer.

Chloe says, “ When you divide an even number by an even number the answer is always an even number.”

Write down an example to show that Chloe is wrong.

The diagram shows a solid cylinder with base radius 3 cm and height 8 cm. It also shows a solid cube with side length hcm.

The cylinder is made from steel with a density of 7.86 g/cm³ The cube is made from brass with a density of 8.5 g/cm³ The mass of the cylinder is equal to the mass of the cube. Work out the value of h. Give your answer correct to 1 decimal place.

Find the square root of 64

Work out –12 ÷ –4

Find the value of 2⁵

Write one pair of brackets in this calculation so that the answer is correct. 30 ÷ 3 + 2 − 4 = 2

Write down a square number that is between 10 and 50

Zia has to set a 4‑digit security passcode on her phone. Each digit of the passcode is a number from 1 to 9 She can use each number more than once. Zia tells her friend Amber that the first digit is a cube number the second digit is a prime number the third digit is greater than 6 the fourth digit is an odd number. The diagram shows one possible 4‑digit passcode.

Amber is going to have one attempt at guessing Zia’s passcode. Work out the probability that Amber guesses Zia’s passcode on the first attempt.

22A cube has a total surface area of 150 cm² Work out the volume of the cube.

A cube has a total surface area of 150 cm² Work out the volume of the cube.

Work out 3²

Write down the value of 7²

The diagram shows a shape made from 6 identical squares.

The total area of the shape is 5406 cm²

Find an estimate for the length of one side of each square. Give your answer correct to the nearest whole number.

Is your answer to part (a) an underestimate or an overestimate? You must give a reason for your answer.

Here is a list of whole numbers from 21 to 30 21 22 23 24 25 26 27 28 29 30

From the list, write down a square number.

From the list, write down a multiple of 8

Write down all the figures on your calculator display.

Give your answer to part (a) correct to 2 decimal places.

Here is a list of numbers. 3 4 9 18 27 30 36 From the numbers in the list, write down a cube number.

Work out 2.5²

Work out the probability of getting 4 tails when the coin is thrown 4 times.

Work out the value of 5³

Here is a list of numbers. 4 6 9 10 15 27 30 40 From the list, write down all the numbers that are powers of 3

Work out 3 5 + 7

Work out 2³

Write brackets () in this statement to make it correct.

Write down a square number that is also an odd number.

Work out the cube root of 64

A square has an area of 81 cm²

Find the perimeter of the square.

The diagram shows a right-angled triangle and a parallelogram.

The area of the parallelogram is 5 times the area of the triangle. The perpendicular height of the parallelogram is h cm.

Find the value of h.

Write down the value of 36

Work out the value of 3⁵

The total surface area of a cube is 294 cm².

Work out the volume of the cube.

Work out the value of 2⁴