Page 4 - 新思维数学活动用书8 样章

How to use this book

How to use this book

1 Integers
This workbook provides questions for you to practise what you have learned in class. There is a unit

to match each unit in your Learner’s Book. Each exercise is divided into three parts:

• Focus: these questions help you to master the basics
• Practice: these questions help you to become more confident in using what you

have learned
1.1 Factors, multiples and primes 2.5 Constructing and solving equations
• Challenge: these questions will make you think very hard.
You will also find these features:
2.5 Constructing and solving equations

Exercise 1.1 Words you need Exercise 2.5 Key words
Key words

to know. Focus factor tree solve
Focus 1 Write if each of the following is a formula, an expression or variable
highest common
an equation.
1 a Draw a factor tree for 250 that starts with 2 × 125. factor (HCF) b m = 2b − 3g 2
a ab + 7c
b Can you draw a different factor tree for 250 that starts with c 8(x − 8) d 2x + 5 = 13
lowest common
Remember that: Examples
2 × 125? Give a reason for your answer. A formula is a rule that shows the relationship between two F = ma
multiple (LCM)
or more quantities (variables). It must have an equals sign. v = u + 10t
c Draw a factor tree for 250 that starts with 25 × 10. An expression is a statement that involves one or more 3x − 7
prime factor
2
d Write 250 as a product of its prime factors. variables, but does not have an equals sign. a + 2b
An equation contains an unknown number, it must have
2 a Draw a factor tree for 300. an equals sign, and it can be solved to find the value of the 3x − 7 = 14
4 = 6y + 22
unknown number.
b Draw a different factor tree for 300. Worked example 2.1
Step-by-step examples
c Write 300 as a product of prime numbers. You can use a flow chart like this to solve an equation.
showing how to solve
3 a Write as a product of prime numbers Solve 3x + 5 = 17
i 6 ii 30 iii 210 Answer x ×3 +5 17 Reverse the flow chart to work out
a problem.
3x + 5 = 17
b What is the next number in this sequence? Why? 12 the value of x.
So x = 4 4 ÷3 –5 17
4 Work out
a 2 × 3 × 7 b 2 × 3 × 7 2 c 2 × 3 × 7 3 2.2 Using expressions and formulae
3
3
2
2
5 a Draw a factor tree for 8712. Challenge
Questions marked with this
b Write 8712 as a product of prime numbers. 13 When x = −4, all of these expressions except one have the
same value.
symbol help you to practise
6 Write each of these numbers as a product of its prime factors. Which is the odd one out?
c 98
a 96 b 97 thinking and working d 99 x − 7 (x +1 ) 2 − 36 x x −5 2x + 17 5 − x
2
14 Write any values of x that make each pair of expressions equal.
mathematically. a 3x + 1 and 3x + 1 b 4 − x and x − 4 27
2
Practice 5x 2x
c
5
2 + 5 and + 5 d 3(x + 2) and 2(x + 3)
7 Write as a product of prime numbers 15 a Use the formula D = wp + 4 to work out the value of D when w = 2.5
02-新思��学 活动用�8_c02(p12-37)-3校_P.indd 27 2022/7/19 上午 10:45:49
and p = 6.
a 70 b 70 2 c 70 3 b Rearrange the formula D = wp + 4 to make p the subject.
8 a Write each square number as a product of its prime factors. c Use your formula to work out the value of p when D = 100 and
w = 12.
i 9 ii 36 iii 81 16 The formula below is used to calculate the distance travelled Tip 3
by an object.
iv 144 v 225 vi 576 s ut + 1 2 at where: s = distance 2 1 at means
2
=
2
u = starting speed 1
vii 625 viii 2401 a = acceleration 2 ××at 2
t = time
Work out the distance travelled by an object when
a u = 0, a = 6 and t = 5 b u = 30, a = −4 and t = 10
5

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19
19

02-新思��学 活动用�8_c02(p12-37)-3校_P.indd 19 2022/7/19 上午 10:45:37