Write these integers in order, starting with the smallest. -6, 4, -9, 0, -3, 7
(1)
2
Work out -8 + 15.
(1)
3
Work out -12 - 5.
(1)
4
Work out the value of each calculation. (a) -6 x 7 (b) -48 / 8
(2)
5
Work out the value of 34.
(1)
6
Work out the value of each power. (a) 25 (b) 103
(2)
7
Simplify 53 x 52, giving your answer as a single power.
(1)
8
Use the correct order of operations to work out 6 + 4 x (9 - 5).
(2)
9
From the list 41, 42, 43, 44, 45, write down all the prime numbers.
(2)
10
Write down all the factors of 24.
(2)
11
List the first five multiples of 9.
(2)
12
Write 84 as a product of its prime factors, giving your answer in index form.
(2)
13
Work out the value of each root. (a) √64 (b) cube root of 125
(2)
14
On a winter morning in York, the temperature at 7am was -5C. By 1pm it had risen by 11C. By 10pm it had fallen by 9C from the 1pm value. Work out the temperature at 10pm.
(3)
15
Amir's bank balance is -60 pounds (he is overdrawn by 60 pounds). He deposits 95 pounds and then pays a bill of 48 pounds. Work out his new balance.
(3)
16
Prime factors can be used to find the highest common factor (HCF) of two numbers. Write 60 and 84 as products of their prime factors, and hence find the HCF of 60 and 84.
(3)
17
Prime factors can also be used to find the lowest common multiple (LCM) of two numbers. Given that 18 = 2 x 32 and 24 = 23 x 3, find the LCM of 18 and 24.
(3)
18
In a quiz of 12 questions, each correct answer scores +5 points and each incorrect answer scores -3 points. A player answers all 12 questions and gets 8 correct. Work out the player's total score.
(3)
19
Stretch question. Two beacons flash together at exactly 8:00pm. Beacon A flashes every 12 seconds and beacon B flashes every 18 seconds. Work out the next time the two beacons flash together again, stated as a number of seconds after 8:00pm.
(4)
Mark scheme · KS3.M-N1D Number: Integers and Powers: Fluency and Exam Drill
Question 1
B1 -9, -6, -3, 0, 4, 7 cao
Answer: -9, -6, -3, 0, 4, 7
Question 2
B1 7 cao
Answer: 7
Question 3
B1 -17 cao
Answer: -17
Question 4
B1 (a) -42 cao
B1 (b) -6 cao
Answer: (a) -42 (b) -6
Question 5
B1 81 cao
Answer: 81
Question 6
B1 (a) 32 cao
B1 (b) 1000 cao
Answer: (a) 32 (b) 1000
Question 7
B1 55 cao
Answer: 55
Question 8
M1 works out the bracket first: 9 - 5 = 4, and multiplies by 4 before adding
A1 22 cao
Answer: 22
Question 9
B2 41 and 43 (B1 for one correct with no incorrect values)
Answer: 41 and 43
Question 10
B2 1, 2, 3, 4, 6, 8, 12, 24 (B1 for at least 6 correct with no incorrect values)
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Question 11
B2 9, 18, 27, 36, 45 (B1 for at least three correct in order)
Answer: 9, 18, 27, 36, 45
Question 12
M1 correct prime factor tree or division method shown
A1 22 x 3 x 7 cao
Answer: 22 x 3 x 7
Question 13
B1 (a) 8 cao
B1 (b) 5 cao
Answer: (a) 8 (b) 5
Question 14
M1 finds the 1pm temperature: -5 + 11 = 6C
M1 finds the 10pm temperature: 6 - 9
A1 -3C cao
Answer: -3C
Question 15
M1 -60 + 95 = 35
M1 35 - 48
A1 -13 pounds (overdrawn by 13 pounds) cao
Answer: -13 pounds
Question 16
M1 60 = 22 x 3 x 5
M1 84 = 22 x 3 x 7
A1 HCF = 22 x 3 = 12 cao
Answer: 12
Question 17
M1 takes the highest power of each prime: 23 and 32