Number: Integers and Powers - Worksheets, Questions and Revision

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KS3 · Number

KS3.M-N1 Number: Integers and Powers

AQA AQA KS3 Maths progression framework - Number · Calculator allowed · about 75 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write these integers in order, starting with the smallest.
-8, 3, -1, 0, -5, 6
(2)
2
Work out the value of each calculation.
(a)-3 + 7(1)
(b)-6 - 5(1)
(c)8 - 12(1)
(d)-9 + (-4)(1)
3
Work out the value of each calculation.
(a)-4 x 6(1)
(b)-3 x -7(1)
(c)-36 / 4(1)
(d)-45 / -9(1)
4
Work out the value of each power.
(a)52(1)
(b)33(1)
(c)25(1)
5
Index notation links a power to repeated multiplication.
(a)Write 7 x 7 x 7 as a single power of 7, and work out its value.(2)
(b)Write 63 as repeated multiplication, and work out its value.(2)
6
Use the correct order of operations (BIDMAS) to work out each expression.
(a)3 + 23 x 4(2)
(b)(7 - 2)2 - 10(2)
(c)40 / 23 + 1(2)
7
On a winter morning in Sheffield, the temperature at 6am was -4C. By midday it had risen by 9C. By 9pm it had fallen by 15C from the midday temperature.
(a)What was the temperature at midday?(1)
(b)What was the temperature at 9pm?(2)
(c)Work out the difference between the temperature at 6am and the temperature at 9pm.(2)
8
Priya's bank balance is -45 pounds (she is overdrawn by 45 pounds). She deposits 120 pounds and then pays a bill of 85 pounds.
(a)Work out her balance after the deposit.(2)
(b)Work out her balance after paying the bill.(2)
(c)A second bill of 30 pounds arrives. Priya's bank will not let her go more than 50 pounds overdrawn. Show working to determine whether she can pay this bill.(2)
9
From the list 21, 23, 27, 29, 33, 37, write down all the prime numbers.
(2)
10
Factors of a number divide into it exactly.
(a)List all the factors of 84.(2)
(b)Using your list, or otherwise, find the highest common factor of 84 and 60.(2)
11
Multiples of a number are found by multiplying it by 1, 2, 3, and so on.
(a)List the first six multiples of 9.(2)
(b)Find the lowest common multiple of 6 and 8 by listing multiples of each number.(2)
12
Write 360 as a product of its prime factors, giving your answer in index form.
(3)
13
Prime factors can be used to find the highest common factor (HCF) of two numbers.
(a)Write 84 as a product of its prime factors, giving your answer in index form.(2)
(b)Write 126 as a product of its prime factors, giving your answer in index form.(2)
(c)Use your answers to parts a and b to find the highest common factor of 84 and 126.(2)
14
Prime factors can also be used to find the lowest common multiple (LCM) of two numbers.
(a)Write 45 and 60 each as a product of prime factors, in index form.(2)
(b)Hence find the lowest common multiple of 45 and 60.(2)
15
Simplify each expression, writing your answer as a single power. Do not evaluate.
(a)32 x 34(1)
(b)53 x 51(1)
(c)25 x 22(1)
16
Simplify or work out the value of each expression.
(a)Simplify 78 / 73, giving your answer as a single power of 7.(2)
(b)Simplify (42)3, giving your answer as a single power of 4.(2)
(c)Work out the value of 65 / 63.(2)
17
Work out the value of each root.
(a)√81(1)
(b)√144(1)
(c)cube root of 27(1)
(d)cube root of 125(1)
18
In a quiz of 10 questions, each correct answer scores +4 points and each incorrect answer scores -2 points.
(a)Tom gets 7 questions correct and 3 incorrect. Work out his total score.(2)
(b)Aisha's total score on the same 10 questions is -2. Work out how many questions Aisha answered correctly.(3)
19
Two lighthouses flash together at exactly 9:00pm. Lighthouse A flashes every 8 seconds and lighthouse B flashes every 12 seconds.
(a)Work out how many seconds it will be until the two lighthouses next flash together.(3)
(b)State the time when the two lighthouses will next flash together.(1)
20
A market trader has 90 apples and 126 oranges. She wants to make identical fruit bags, each with the same number of apples and the same number of oranges, using all the fruit with none left over.
(a)Write 90 and 126 as products of their prime factors.(2)
(b)Work out the greatest number of identical bags she can make.(2)
(c)For this greatest number of bags, work out how many apples and how many oranges go in each bag.(2)
21
Powers of 10 are used to write very large numbers in a compact form.
(a)Write 4,500,000 in the form A x 10n, where 1 ≤ A < 10.(2)
(b)Work out the value of 3 x 104 x 2 x 102, giving your answer as an ordinary number.(2)
Mark scheme · KS3.M-N1 Number: Integers and Powers

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Question 21