Unit 1, Mathematical Methods
Linear and Quadratic Functions Topic Test
Name: ______________________
Instructions



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This test will take part of 1 Period
Technology and Summary notes NOT ALLOWED.
Each correctly answered multiple choice question in Section A is awarded 1 mark. In all
cases, circle the best option but no marks will be awarded if more than a single option is
selected.
Answer questions in Section B using the space provided within this question and answer
booklet
Formulae
𝑥1 +𝑥2 𝑦1 +𝑦2
Midpoint = (
2
,
2
)
Distance = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Gradient (𝑚) =
𝑦2 −𝑦1
𝑥2 −𝑥1
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
𝑥=
Beaconhills College (Pakenham)
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
Unit 1 Mathematical Methods
Page 1 of 7
Unit 1, Mathematical Methods
Section A: Multiple Choice (10 marks)
1
2
3
4
5
In algebraic form, 7 is four times the number that is 5 more than x can be written as
A
7 = 4(x + 5)
B
4x + 5 = 7
C
7 = 5(x + 4)
D
4
x+5=7
E
7–
5
=x
4
For the equation 4𝑥 − 2(3 − 𝑥) = 5𝑥, x equals
A
1
2
B
−6
C
−2
D
6
E
2
If two lines 6x – y + 5 = 0 and ax + 2y – 7 = 0 are parallel then a equals
A
12
B
6
C
0.5
D
3
E
12
The length of the line segment connecting (2, 3) and (6, 6) is
A
25
B
4 5
C
70
D
5
E
7
The equation 4x² + mx + 1 = 0 will have only one solution as a real number when the value(s)
of m is/are
A
m =1
B
m = 1
C
m = 2
D
m=3
E
m=4
Beaconhills College (Pakenham)
Unit 1 Mathematical Methods
Page 2 of 7
Unit 1, Mathematical Methods
6
7
8
9
The expression (4x + 1)2 + 3x  2 is equal to
A
4x2 + 5x 1
B
4x2 +11x  1
C
16x2 + 5x  1
D
16x2 + 5x + 1
E
16x2 + 11x  1
The solution(s) of the equation x2  5x  14 = 0 is/are
A
x = 7 only
B
x = 7, x = 2
C
x = 2, x = 7
D
x = 2, x = 7
E
x = 2 only
The solution(s) of the equation 4x2  1 = 0 is/are
A
x = 1 only
B
x = 1, x = 2
C
1
1
x= 2 ,x=2
D
x = 2, x =
E
x = 2 only
1
2
The equation of the parabola that passes through the point (0, 11) and has its turning point at
(3, 7), is
10
A
y = 2(x + 3)2 + 7
B
y = (x + 3)2 + 7
C
y = (x + 3)2  7
D
y = 2(x – 3)2 – 7
E
y = 2(x – 3)2 + 7
The equation of the axis of symmetry of the graph of y = 2x2 – 12x + 17 is
A
x = 6
B
x=6
C
x = 3
D
x=3
E
x=0
Beaconhills College (Pakenham)
Unit 1 Mathematical Methods
Page 3 of 7
Unit 1, Mathematical Methods
Section B: Short Answer
Instructions
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Answer all questions in Section B in the space provided on this question paper
Do not use decimal approximations unless instructed within the question
Answers awarded more than one mark must show appropriate working to be achieve a
maximum score
Question 1 (3 marks)
David is now 𝑥 years old and his big sister, Carmen is 12 years older than him. Five years ago the
sum of their ages was 28. Find 𝑥.
Question 2 (5 marks)
Find the equation of the line that passes through the point with coordinates (–2, 6) and is:
a.
parallel to the line with equation y = –3x + 4
b.
2 marks
parallel to the x-axis
1 mark
c.
perpendicular to the line with equation y = –3x + 4
Beaconhills College (Pakenham)
Unit 1 Mathematical Methods
2 marks
Page 4 of 7
Unit 1, Mathematical Methods
Question 3 (7 marks)
A line has equation 4𝑥 + 3𝑦 = 12.
a. Express the line in the intercept-form 𝑦 = 𝑚𝑥 + 𝑐 for a suitable choice of the numbers 𝑚 and 𝑐.
2 marks
b.
i.
Hence, state the:
gradient of the line
1 mark
ii.
coordinates of the 𝑦 −axis intercept of the line
1 mark
iii.
coordinates of the x-intercept
1 mark
c.
Hence, plot the graph of 4𝑥 + 3𝑦 = 12 on the axes below, labelling the intercepts.
Beaconhills College (Pakenham)
Unit 1 Mathematical Methods
2 marks
Page 5 of 7
Unit 1, Mathematical Methods
Question 4 (4 marks)
The coordinates of the endpoints of a line segment 𝐴𝐵 are (−2, 𝑎) and (𝑏, −2) respectively.
a. Express the length of the line segment 𝐴𝐵 in terms of 𝑎 and 𝑏.
1 mark
The point with coordinates (2,1) is the midpoint of the line segment 𝐴𝐵.
b. Find the value of the numbers 𝑎 and 𝑏.
c. Hence find the value of the gradient of the line segment 𝐴𝐵.
2 marks
1 mark
Question 5 (5 marks)
The graph with equation 𝑦 = −𝑥 2 + 6𝑥 − 5 is shown below.
a. Express the equation of this graph in the factored form 𝑦 = 𝑎(𝑥 − 𝑒)(𝑥 − 𝑓) .
Beaconhills College (Pakenham)
Unit 1 Mathematical Methods
3 marks
Page 6 of 7
Unit 1, Mathematical Methods
b. Express the equation of this graph in the turning point form = 𝑎(𝑥 − ℎ)2 + 𝑘 .
2 marks
Question 6 (6 marks)
Consider a curve with equation 𝑦 = 2𝑥 2 − 𝑥 − 1 and a straight line of slope 𝑚, crossing the 𝑦 −axis
at the point (0, −3).
a. Show that the 𝑥 −coordinate of any point/s of intersection of the curve and the line must be a
solution of the equation 2𝑥 2 − (𝑚 + 1)𝑥 + 2 = 0.
3 marks
b. The straight line is tangential to the curve 𝑦 = 2𝑥 2 − 𝑥 − 1. Find the value(s) of 𝑚.
3 marks
End of Topic Test
Beaconhills College (Pakenham)
Unit 1 Mathematical Methods
Page 7 of 7