1.8 Squares, cubes and roots
9 exam questions worth 19 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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Which of these is a cube number?
Choose one answer.
Correct Not quite: the answer is 64
Mark scheme
B: 64
Model answer
64 (B). 4 × 4 × 4 = 64.
Write down the value of (a) 12^2 (b) 5^3.
Mark scheme
B1: 144; B1: 125
Model answer
(a) 12 × 12 = 144. (b) 5 × 5 × 5 = 125.
Work out 3^3 + 4^2.
Mark scheme
M1: 27 and 16; A1: 43
Model answer
3³ = 27 and 4² = 16, so the total is 43.
Write down the value of (a) \sqrt{169} (b) \sqrt[3]{216}.
Mark scheme
B1: 13; B1: 6
Model answer
(a) 13 because 13 × 13 = 169. (b) 6 because 6 × 6 × 6 = 216.
Write down the two consecutive integers between which \sqrt{60} lies.
Mark scheme
M1: 49 < 60 < 64 (or 7² and 8²); A1: 7 and 8
Model answer
7² = 49 and 8² = 64, and 49 < 60 < 64, so √60 is between 7 and 8.
Work out 2^5 \times 3^2.
Mark scheme
M1: 32 and 9; A1: 288
Model answer
2⁵ = 32 and 3² = 9, so 32 × 9 = 288.
Solve x^2 = 81.
Mark scheme
B1: x = 9; B1: x = -9 (accept ±9)
Model answer
x = 9 or x = -9, because both 9 × 9 and (-9) × (-9) equal 81.
A square has an area of 196 cm². Work out the perimeter of the square.
Mark scheme
M1: √196; A1: side 14 cm; A1: 56 cm
Model answer
The side is √196 = 14 cm, so the perimeter is 4 × 14 = 56 cm.
Pete says that 4^3 = 12 and that \sqrt{100} = 50. Explain Pete's mistakes and write down the correct values.
Mark scheme
B1: 4³ means 4 × 4 × 4, not 4 × 3; B1: 64; B1: √100 = 10 because 10 × 10 = 100 (not half of 100)
Model answer
4³ = 4 × 4 × 4 = 64; Pete multiplied 4 by 3. √100 = 10 because 10 × 10 = 100; Pete halved 100 instead of finding the number that multiplies by itself to give 100.
Found a mistake?