Browse Integers, powers & roots

45 questions at your level

DifficultyAllLevel 1Level 2Level 3Level 4Level 5

Negatives and the order of operations

13 questions

LessonNot started
Work out −4×(−3)2+5×(−2)-4 \times (-3)^2 + 5 \times (-2) (2 marks)
●●●●●Level 12 marksStart
Use your calculator to work out 5.42−2.76.25\dfrac{5.4^2 - 2.7}{\sqrt{6.25}}

Write down all the figures on your calculator display. [2]
●●●●●Level 12 marksStart
Work out 3.6×0.243.6 \times 0.24 [2]
●●●●●Level 12 marksStart
Work out

(a) −7+12-7 + 12

(b) −3−8-3 - 8

(c) (−4)×(−6)(-4) \times (-6)
●●●●●Level 23 marksStart
Work out

(a) 3+4×223 + 4 \times 2^2

(b) 18−12÷3+118 - 12 \div 3 + 1
●●●●●Level 34 marksStart
(a) Work out (−12)÷(−3)+(−2)×5(-12) \div (-3) + (-2) \times 5

(b) At midnight the temperature in Oslo is −8°C. By noon the temperature has risen by 13°C. By the next midnight it has fallen 9°C from its noon value.

Work out the temperature at the next midnight.
●●●●●Level 34 marksStart
Add one pair of brackets to each statement to make it true.

(a) 3+4×2−1=133 + 4 \times 2 - 1 = 13

(b) 20÷4+1−3=120 \div 4 + 1 - 3 = 1
●●●●●Level 32 marksStart
Work out 2+3×614−4\dfrac{2 + 3 \times 6}{14 - 4}
●●●●●Level 32 marksStart
One night in Aberdeen the temperature fell to −8°-8°C.

The next afternoon it rose to 5°5°C.

(a) Work out the rise in temperature.

The following night the temperature fell 99 degrees from 5°5°C.

(b) Work out the temperature that night.
●●●●●Level 32 marksStart
p=−2p = -2 and q=−3q = -3

Work out the value of 3p2−q33p^2 - q^3
●●●●●Level 43 marksStart
(a) Priya says that −62=36-6^2 = 36.

Explain why Priya is wrong.

(b) Work out (−1)100−(−1)99(-1)^{100} - (-1)^{99}

(c) Work out 5−2×(4−7)25 - 2 \times (4 - 7)^2
●●●●●Level 45 marksStart
a=−5a = -5

Work out the value of 2a2+3a2a^2 + 3a
●●●●●Level 42 marksStart
Work out 5−2×(3−7)2÷85 - 2 \times (3 - 7)^2 \div 8
●●●●●Level 43 marksStart

Prime factorisation

17 questions

LessonNot started
Write down all the prime numbers between 1010 and 2020.
●●●●●Level 11 markStart
Write 2424 as a product of its prime factors.
●●●●●Level 12 marksStart
x=2×3×5x = 2 \times 3 \times 5. Write down the value of xx.
●●●●●Level 11 markStart
Write 9090 as a product of its prime factors. Give your answer in index form. [2]
●●●●●Level 12 marksStart
Write 6060 as a product of its prime factors. Give your answer in index form.
●●●●●Level 22 marksStart
(a) Write 360360 as a product of its prime factors. (2 marks)
(b) You are given that 84=22×3×784 = 2^2 \times 3 \times 7

Write down the highest common factor (HCF) of 360360 and 8484. (1 mark)
●●●●●Level 23 marksStart
Write 504 as a product of its prime factors.

Give your answer in index form.
●●●●●Level 33 marksStart
Write 396396 as a product of its prime factors. Give your answer in index form.
●●●●●Level 32 marksStart
(a) Write 168168 as a product of its prime factors.

(2 marks)

A=34×5A = 3^4 \times 5

B=32×53B = 3^2 \times 5^3
(b) Write down the lowest common multiple (LCM) of AA and BB.

(1 mark)
●●●●●Level 33 marksStart
2520=23×32×5×72520 = 2^3 \times 3^2 \times 5 \times 7

(a) Write 5040 as a product of prime factors in index form.

(b) Write 252 as a product of prime factors in index form.
●●●●●Level 42 marksStart
k=23×3×52k = 2^3 \times 3 \times 5^2

(a) Explain why kk is not a square number.

(b) Find the smallest whole number nn such that knkn is a square number.
●●●●●Level 43 marksStart
p=24×3×53p = 2^4 \times 3 \times 5^3

(a) Explain how you can tell that 12 is a factor of pp.

(b) Find the largest square number that is a factor of pp.
●●●●●Level 43 marksStart
780=22×3×5×13780 = 2^2 \times 3 \times 5 \times 13

Use this fact to write each of the following as a product of prime factors in index form.

(a) 15601560

(b) 390390
●●●●●Level 42 marksStart
n=23×35×52n = 2^3 \times 3^5 \times 5^2

Find the smallest whole number that nn must be multiplied by to give a square number.
●●●●●Level 43 marksStart
12=22×312 = 2^2 \times 3

Find the smallest whole number that 1212 must be multiplied by to give a cube number.
●●●●●Level 43 marksStart
360=23×32×5360 = 2^3 \times 3^2 \times 5

Find the smallest whole number that 360 must be multiplied by to give a cube number.
●●●●●Level 53 marksStart
N=23×52N = 2^3 \times 5^2

(a) Write down the value of NN.

(b) Work out how many factors NN has in total.

Hint: every factor of NN has the form 2a×5b2^a \times 5^b.
●●●●●Level 53 marksStart

HCF and LCM

17 questions

LessonNot started
Write down all the factors of 1818.
●●●●●Level 11 markStart
Find the highest common factor (HCF) of 1212 and 1818.
●●●●●Level 12 marksStart
Find the lowest common multiple (LCM) of 66 and 88.
●●●●●Level 12 marksStart
(a) Find the highest common factor (HCF) of 1212 and 1818.

(b) Find the lowest common multiple (LCM) of 1212 and 1818.
●●●●●Level 22 marksStart
(a) Find the highest common factor (HCF) of 2424 and 3636 (1 mark)

(b) Find the lowest common multiple (LCM) of 2424 and 3636 (1 mark)
●●●●●Level 22 marksStart
(a) Write 360360 as a product of its prime factors. (2 marks)
(b) You are given that 84=22×3×784 = 2^2 \times 3 \times 7

Write down the highest common factor (HCF) of 360360 and 8484. (1 mark)
●●●●●Level 23 marksStart
(a) Write 84 and 120 as products of their prime factors.

(b) Find the highest common factor (HCF) of 84 and 120.

(c) Find the lowest common multiple (LCM) of 84 and 120.
●●●●●Level 34 marksStart
Two buses leave the station together at 9:00 am.

Bus A leaves every 2020 minutes. Bus B leaves every 2525 minutes.

At what time will they next leave together?
●●●●●Level 33 marksStart
(a) Write 168168 as a product of its prime factors.

(2 marks)

A=34×5A = 3^4 \times 5

B=32×53B = 3^2 \times 5^3
(b) Write down the lowest common multiple (LCM) of AA and BB.

(1 mark)
●●●●●Level 33 marksStart
AA and BB are numbers such that

A=23×52×11A = 2^3 \times 5^2 \times 11

B=5×112B = 5 \times 11^2
(a) Find the highest common factor (HCF) of AA and BB.

(1 mark)
(b) Find the lowest common multiple (LCM) of AA and BB.

(2 marks)
●●●●●Level 33 marksStart
Two lighthouses flash together at 8 pm.

One lighthouse flashes every 36 seconds. The other flashes every 60 seconds.

How many seconds after 8 pm do they next flash together?
●●●●●Level 43 marksStart
A florist has 72 roses and 90 tulips.

She makes identical bunches, using every flower.

(a) What is the greatest number of bunches she can make?

(b) How many roses and how many tulips are in each bunch?
●●●●●Level 44 marksStart
A=23×32×5A = 2^3 \times 3^2 \times 5 and B=22×34×7B = 2^2 \times 3^4 \times 7

(a) Find the highest common factor (HCF) of AA and BB.

(b) Find the lowest common multiple (LCM) of AA and BB.

Give each answer as a product of prime factors in index form.
●●●●●Level 44 marksStart
(a) Write 6060 and 126126 as products of their prime factors.

(b) Find the highest common factor (HCF) of 6060 and 126126.

(c) Find the lowest common multiple (LCM) of 6060 and 126126.
●●●●●Level 44 marksStart
Hot dog sausages are sold in packs of 1010. Bread rolls are sold in packs of 88.

Dev wants to buy exactly the same number of sausages as rolls.

(a) What is the smallest number of sausages he can buy?

(b) How many packs of each does he buy?
●●●●●Level 43 marksStart
Two whole numbers are each greater than 6.

The highest common factor of the two numbers is 6.

The lowest common multiple of the two numbers is 90.

Find the two numbers.
●●●●●Level 53 marksStart
The highest common factor of two numbers is 44.

The lowest common multiple of the same two numbers is 4848.

One of the numbers is 1212.

Find the other number.
●●●●●Level 53 marksStart