Chapter 10: Equations
Test A (40 marks)
Name: ___________________________________
Part A – Multiple-choice questions
1
2
3
(10 marks)
The sum of 5 and x is 9. An equation that represents this is:
A
x=5+9
B
5+x=9
D
x=59
E
5–x=9
C
5x = 9
Claire is c years old. In 6 years’ time she will be 18. An equation that represents
this situation is:
A
c + 6 = 18
B
6c = 18
D
c – 6 = 18
E
c
= 18
6
C
6 – c = 18
The value of the missing number that would make this equation true is:
30 − _____ = 12
4
A
6
B
8
D
18
E
28
C
16
When solving 4x = 36, using backtracking, we:
A
add 4 to both sides
B
subtract 4 from both sides
C
divide both sides by 4
D
multiply both sides by 4
E
cannot solve this equation
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5
6
7
8
The balance method of solving equations tells us:
A
to do the same thing to both sides of the equation
B
to use flow charts to solve an equation
C
to apply opposite operations to solve an equation
D
whether an equation is true or false
E
how to solve equations with fractions
When solving the equation 5a − 7 = 19, which step is performed first?
A
Subtract 7 from both sides
B
Add 7 to both sides
C
Divide both sides by 5
D
Multiply both sides by 5
E
Subtract 19 from both sides
Which value of x makes the equation 3x + 4 = 19 true?
A
3
B
4
D
6
E
5
C
19
C
18
Consider the rule a = 3b − 7. The value of b, if a = 26, is:
A
5
B
9
D
11
E
71
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2
Questions 9 and 10 refer to the following statement.
A number is doubled, and then 7 is added. This gives a final result of 31.
9
10
An equation that represents this statement is:
A
2(n + 7) = 31
B
n
+ 7 = 31
2
D
2n – 7 = 31
E
n+ 7
= 31
2
C
2n + 7 = 31
C
10
The number is:
A
8
B
9
D
11
E
12
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Part B – Short-answer questions
(20
marks)
1
For each of the following equations, state whether it is true or false.
a
12 − 4 = 32  4
b
35=7+9
_____________________________
____________________________
_____________________________
____________________________
(1 + 1 = 2 marks)
2
If k is 6, are the following equations true or false?
a
k  8 = 54
b
9 + k = 2k + 3
_____________________________
_____________________________
_____________________________
_____________________________
(1 + 1 = 2 marks)
3
Solve each of the following equations.
a
c
e
a + 6 = 14
b
b−3=5
_____________________________
_____________________________
_____________________________
_____________________________
c  4 = 28
d
9d = 27
_____________________________
_____________________________
_____________________________
_____________________________
18  e = 3
f
f  5 = 10
_____________________________
_____________________________
_____________________________
_____________________________
(6  1 = 6 marks)
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4
Solve each of the following equations.
a
c
2a + 9 = 17
b
4b − 12 = 24
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
c+ 5
=3
4
d
d
-2= 6
3
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
(4  2 = 8 marks)
5
Consider the rule y = 2x − 9. Find the value of:
a
y if x = 8
b
x if y = 5
_____________________________
_____________________________
_____________________________
_____________________________
(2  1 = 2 marks)
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Part C – Extended-response questions
1
(10 marks)
Jim the electrician charges a $40 call-out fee and $60 per hour.
a
Define a variable for the number of hours Jim worked.
________________________________________________________________
b
Write an equation to show how the total cost C, of a job is calculated.
C =______________________
c
If a job costs $460 substitute this into your equation. Then algebraically
solve the equation.
________________________________________________________________
________________________________________________________________
d
How many hours did Jim work to earn $460?
________________________________________________________________
(1 + 1 + 2 + 1 = 5 marks)
2
In Australian Rules football a goal is worth 6 points and a ‘behind’ is worth 1
point. This can be represented by S = 6g + b where S is the total score when g
goals and b behinds are scored.
a
What is the score for a team that has scored 9 goals and 8 behinds?
_______________________________________________________________
_______________________________________________________________
b
How many behinds (b) did a team make if they scored 4 goals (g) and had a
total Score (S) of 37 points?
_______________________________________________________________
_______________________________________________________________
c
How many goals did a team make if they scored 10 behinds and had a total
of 52 points?
_______________________________________________________________
(1 + 2 + 2 = 5 marks)
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