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Year 10 Linear Relationships Test A (Standard) Name: __________________________
Class: ______
Multiple choice section – choose the correct answer
Question 1
Choose the correct answer.
4.1
A 3y = 2x + 15
5x
= -3 is:
6
D 12
2
x
3
D 2x + 3y = 15
By+5=-
The solution to the equation 7 –
C 3y + 15x = -2
A5
Question 7
The line which is parallel to the line with the
equation y  2 x  1 is:
A 2 x  y  2
B y  2 x  12
C x  2y  4
D 2x  y  6
B -6
C -4.8
Question 2
The solution to the equation
5(a – 2) = 3(a + 2) is:
A2
B8
C6
4.1
D -2
Question 3
Choose the correct answer.
The gradient of the line joining the points
(3, -2) and (-3, 7) is:
2
3
2
A
BC0
D3
2
3
4.2
Question 4
The gradient of the equation
4x – 2y = 8 is:
4.2
A4
B8
C2
D
4.2
Question 6
Choose the correct answer.
The equation of a linear graph with
a y-intercept of 5 and a gradient
2
of - is:
3
4.3
Question
number
Answer
1
2
3
Question 8
4.4
The gradient of a line which is perpendicular
to the line with equation y  2 x  4 is:
1
1
A2
B -2
C
D
2
2
Question 9
4.5
The solution to the inequation 3x  5  10 is:
A x = 5 B x < 5 C x > 5 D x5
Question 10
Choose the correct answer.
Which of the following is not a solution of
2  5x
< 1?
8
A x = 0 B x = -1.5 C x = -0.9 D x = 2.1
1
2
Question 5
Choose the correct answer.
The gradient of the line with equation
x = 7 is:
A undefined
B7
C1 D0
4
5
4.4
4.5
Question 11
4.6
Choose the correct answer.
The simultaneous equations y = -2x + 10 and
2y + 3x = 14 have the solution:
A x = -6, y = 22
B x = 0, y = 10
C x = 2, y = 6
D x = 6, y = -2
6
7
8
9
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
10
11
Total
1
Year 10 Linear Equations Test A (Standard)
Name: __________________________
Class: ______
Short answer section
Question 12
Use words from the list below to complete the following sentences.
linear relationship y  mx  c
perpendicular
linear equation
inequation
inverse operations
gradient
parallel
rise over run
y-intercept
11
one
(a) A ________________________________________ exists between two variables when the
graph of the relationship is a straight line.
(b) A linear relationship is described by a ______________________________ .
(c) Linear equations can be solved by applying _______________________________________ to
both sides of the equation.
(d) The ______________________of a line is a measure of its steepness which can be evaluated by
evaluating the fraction ______________________________.
(e) The general equation of a straight line is _____________________ where m is the gradient of
the line and c is the ________________________ of the line.
(f) Lines which are ___________________ have the same gradients.
(g) Lines which are _______________________________ meet each other at an angle of 90 .
(h) A linear equation has _____ solution and a linear _______________________ has a range of
solutions according to the inequality.
Question 13
The line with equation y  2 x  3 is shown on the graph.
4
4.3
4.4
3
4.1
State an equation of a line which is (a) parallel (b) perpendicular to the line y  2 x  3 and sketch
them on the graph above.
Question 14
Solve the following equation.
4x  5
5
7
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
2
Year 10 Linear Equations Test A (Standard)
Name: __________________________
Class: ______
Question 15
Solve the following equation.
4x  2 2x 1

2
3
5
4
4.1
Question 16
Find the gradient of the line joining the points (1, 3) and (4, 9).
2
4.2
Question 17
Find the gradient of the line shown below.
2
4.2
2
4.3
(1, –1)
Question 18
Sketch the graph of y = -3x + 2.
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
3
Year 10 Linear Equations Test A (Standard)
Name: __________________________
Question 19
Class: ______
4
4.4
4
4.5
3
4.5
1
(a) Show that the line with equation x  3 y  1 is parallel to the line with equation y   x  11 .
3
(b) Show that the line with equation x  2 y  6 is perpendicular to the line with equation
y  2x  3  0 .
Question 20
Give the set of positive whole-number values that will solve the following inequations.
(a) 3x + 1 16
(b) 5x – 3 < 7
Question 21
Solve to find the set of x values that satisfy 2(3x + 2)  2x – 8
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
4
Year 10 Linear Equations Test A (Standard)
Name: __________________________
Class: ______
Question 22
Solve this pair of simultaneous equations.
y = 3x – 10
2x – 3y = 16
4
4.6
Question 23
Solve this pair of simultaneous equations.
2x + 3y = 16
5x – 2y = 2
4
4.6
Short answer total:_________/47
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10 Linear Equations Test A (Standard)
Name: __________________________
Class: ______
Extended answer section
Question 24
An elevator is descending towards the basement of a building at a steady rate. It descends 4 metres
every 3 seconds and it reaches the basement (h = 0) after 33 seconds.
(a) Sketch a graph that describes the relationship between the height, h, of the elevator and the
time, t.
7
4.2
4.3
4.4
(b) Find the gradient of the graph and hence, the rate of descent of the elevator.
(c) Write down an equation that describes the relationship between the height, h, of the elevator
and the time, t.
(d) How high is the elevator in the building when t = 0?
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
6
Year 10 Linear Equations Test A (Standard)
Name: __________________________
Class: ______
Question 25
(a) Sketch the line with equation y  2 x  4 on the set of axes below.
10
4.2
4.3
4.4
(b) (i) Draw the line AB that passes through the points A(1, 0) and B (4, 6) and find the equation
of the line AB .
(ii) Prove that the line with equation y  2 x  4 is parallel to the line AB .
(c) (i) Draw the line CD that passes through the points C (2, 7) and D(6,5) and find the equation
of the line CD .
(ii) Prove that the line with equation y  2 x  4 is perpendicular to the line CD .
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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Year 10 Linear Equations Test A (Standard)
Name: __________________________
Question 26
A baker uses dried fruit in the fruit buns she makes. She has already used half the contents of the
last 5 kg bag she has and wants to know how many more buns could possibly be made before she
gets the new supply. Each bun uses 12 g of dried fruit ingredients.
Class: ______
4
4.5
5
4.6
3
4.6
(a) Write down an inequation that describes the baker’s situation.
(b) Solve the inequation to find out how many buns could be made.
Question 27
Colin bought 2 apples and 3 bananas for 80 cents, Sally bought 1 apple and
5 bananas for 75 cents. How much did each piece of fruit cost?
Question 28
The sum of three consecutive even numbers is 372.
Find the three numbers.
Extended answer total:_________/29
Copyright © Pearson Australia 2011 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4425 4580 9
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