AQA GCSE (9–1) Maths Grade 4–5 Booster Workbook
Easy to use and revise with a write-in format Answers supplied as a tear-out section
Assess your understanding and test problem solving skills with more in-depth questions
AQA GCSE
AQA GCSE
Maths
Maths
Higher Student Book
Higher Practice Book Use and apply standard techniques
Higher Skills Book Reason, interpret and communicate mathematically and solve problems
4th Edition
Kevin Evans Keith Gordon Brian Speed Michael Kent
AQ AQA QA GCSE M Maths th Higher Student Book 978-0-00-759734-5
Rob Ellis
AQA G GCSE CSE M Maths th Higher Practice Book 978-0-00-811383-4
Grade 4–5 Booster Workbook
AQA GCSE
Maths
AQA GCSE (9–1) Maths
in GCSE Mathematics, providing extra support where it is most needed. Written by a trusted maths teacher and author, the range of questions will help you focus on the key topics and skills required to succeed.
Sandra Wharton
AQA GCS GCSE SE M Maths th Higher Skills Book 978-0-00-811385-8
AQA GCSE (9–1)
Maths Grade 4–5 Booster Workbook
Greg Byrd AQA GCSE
Maths 4th Edition
Foundation Student Book
AQA GCSE
AQA GCSE
Maths
Maths
Foundation Practice Book
Foundation Skills Book
Use and apply standard techniques
Reason, interpret and communicate mathematically and slove problems
Kevin Evans Keith Gordon Brain Speed Michael Kent
Rob Ellis
Sandra Wharton
ISBN 978-0-00-811419-0
AQ AQA QA GCSE M Maths th Foundation Student Book 978-0-00-759743-7
AQA GCSE Maths Foundation Practice Book 978-0-00-811384-1
AQA GCSE Maths Foundation Skills Book 978-0-00-811386-5
9 780008 114190
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1 Number 1.1 Rounding / Giving an approximate answer 1
Round each number to one significant figure. a 5.7 =
b 0.0626 =
c 751.3 =
Remember: Significant figures and decimal places are not the same.
2
Round each number to two significant figures. a 22.475 =
3
c 57 392.1 =
Round each number to three significant figures. a 91.042 =
4
b 0.868 =
b 0.037 885 =
c 7896.4833 =
Round each of these to the number of significant figures (sf) indicated. a 3750 (1 sf) =
b 7.3861 (2 sf) =
c 0.005 555 (3 sf) =
d 99.8933 (3 sf) =
e 99.8933 (2 sf) =
f 99.8933 (1 sf) =
5
Use your calculator to work these out. Give your answers correct to three significant figures. 2 599 209 989 × 0.618 a 185 = = b = c + 0.41 0.51 320 × 0.053 0.47
6
Use approximations to estimate an answer to each calculation. Start by rounding each number to 1 sf. You must show your working clearly. a 72.3 × 18.4
b 193.42 ÷ 38.09
c 31.9 × 13.9 1.18 – 0.52
d
2 e 185 0.47
f
g 989 × 0.618 320 × 0.053
h
8.77 × 5.08 19.3 – 4.9
21.93 × 3.84
599 209 + 0.41 0.51
Remember: When approximating with square roots, round the number under the root to a square number.
6
1 Number
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7
It took me 3 hours and 45 minutes to drive from Birmingham to Pembroke, a distance of 206 miles. My car travels 48 miles per gallon of diesel. The diesel cost £5.54 per gallon. a Approximately how many miles did I travel each hour? b What was the approximate cost of the diesel for my journey to Pembroke and back again?
1.2 Prime factors / Lowest common multiples / Highest common factors 1
a Write 28 as the product of its prime factors. Give your answer in index form. b Write 72 as the product of its prime factors. Give your answer in index form.
2
Write down the lowest common multiple (LCM) of each pair of numbers. a 5 and 7
3
b 28 and 72
Write down the highest common factor (HCF) of each pair of numbers. a 12 and 20
4
b 28 and 72
Tariq coughs every two minutes. Henry sneezes every five minutes. Paul moans every eight minutes. Tariq, Henry and Paul cough, sneeze and moan at the same time. In how many minutes will they next cough, sneeze and moan together at the same time?
5
Given that A = 24 × 33 × 52 and B = 24 × 3 × 53 write down, as a product of powers of prime factors: a the highest common factor (HCF) of A and B
6
11 × 23 = 253
2532 = 64 009
b the lowest common multiple (LCM) of A and B.
2533 = 16 194 277
a Write 64 009 as a product of prime factors in index form. b Write 16 194 277 as a product of prime factors in index form. c Write 2537 as a product of prime factors in index form. 1.2 Prime factors / Lowest common multiples / Highest common factors
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1.3 Indices 1
Write each expression in power notation. a 3×3×3×3×3= b 10 × 10 × 10 = c 2×2×2×2×2×2=
2
Write each expression in power notation. a a×a×a×a= b b×b= c x×x×x×x×x×x=
3
4
Simplify each expression. Write each answer as a number or letter to a single power. a 52 × 52 =
b 73 × 75 =
c 217 × 23 =
d 39 ÷ 33 =
e 65 ÷ 64 =
f 820 ÷ 815 =
g y2 × y2 =
h b3 × b5 =
i j17 × j3 =
j m6 ÷ m2 =
k a9 ÷ a8 = 6 m 74 = 7 x2 o 5 = x
l t4 ÷ t4 = x5 n 2 = x
Simplify each expression fully. a 2a2 × 2a3 × a4 = x 3 × 3x 2 c = x 4t 3 × 3t 5 e = 6t 4 × t
5
p d2 × d3 × d4 =
b h4 × h5 ÷ h3 = b2 × 6b3 d = 2b 4 4 a 4 × 3a 3 ÷ 2a 2 f = 6 × a2
Given that 34 = x2 work out the value of x.
1.4 Fractions 1
8
Work these out. Give each answer in its simplest form and as a mixed number where appropriate. 2 4 3 1 + = + = a b 5 9 4 7 5 3 8 3 c d – = – = 6 5 9 4
1 Number
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2
Work these out. Give each answer in its simplest form and as a mixed number where appropriate. a 3 31 + 1 35 = b 3+ 3 + 4 = 8 10 5 c 4 41 + 2 23 = d 2 23 + 1 43 = 8 3 e 3× 1= f × = 9 4 4 2 g 1 43 × 2 21 = h 21 × 31 = i 4×
2 85
=
2 8 25
5
×4 = 1 1 l ÷ = 3 4 3 n 1 5 ÷ 6 25 =
j
1 1 k = ÷ 4 3 m 6 25 × 1 35 =
3
A patio is 3 41 m long and 2 51 m wide. What is the area of the patio?
4
Amy’s stride is four-fifths of a metre long. How many strides does she take to walk the length of a bus that is 12 m long?
5
Work these out. Give each answer in its simplest form and as a mixed number where appropriate. a 5 21 −
6
5 8
+ 1 35 =
b 8 − 1 43 − 78 =
Work these out. Give each answer as a mixed number where possible. 2 a 2 51 × 1 33 b 4 × 4 × 5 × 5 ÷ 3 × 3 × 75 5 8 8 8 8 5
1.5 Percentage increase and decrease 1
Increase £250 by 12%.
2
Increase £2.50 by 12%.
3
Decrease 45 m by 12%.
4
Decrease 4.5 m by 12%.
5
Last year Xavier’s salary was €21 550. This year it is €22 412. What is the percentage increase of Xavier’s salary?
6
Hassan bought a van for £12 500. A year later he sold it for £8995. Work out the percentage decrease in the value of the van.
1.5 Percentage increase and decrease
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