Straight Line Past Papers Unit 1 Outcome 1 - Mathsrevision.com

Higher Mathematics
PSfrag replacements
O
x
y
Straight Line Past Papers Unit 1 Outcome 1
Multiple Choice Questions
Each correct answer in this section is worth two marks.
1. The line with equation y = ax + 4 is
perpendicular to the line with
equation 3x + y + 1 = 0.
What is the value of a?
A. −3
B. − 1 3
C.
1
3
D. 3
[END OF MULTIPLE CHOICE QUESTIONS]
Written Questions
[SQA]
2.
Find the equation of the perpendicular bisector of the line joining A(2, −1) and
B(8, 3). 4
[SQA]
3.
Find the equation of the straight line which is parallel to the line with equation
2x + 3y = 5 and which passes through the point (2, −1). 3
[SQA]
4.
Find the equation of the line through the point (3, −5) which is parallel to the line
with equation 3x + 2y − 5 = 0. 2
[SQA]
5.
rag replacements
O
x
y
replacements
O
x
y hsn.uk.net
Page 1
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA] 6. Find the size of the angle a ◦ PSfrag replacements
that the line
joining the points A(0, −1) and B(3 √ 3, 2)
y
B(3 √ 3, 2)
makes with the positive direction of the
x-axis. a ◦
3
O
x
A(0, −1)
[SQA]
7.
rag replacements
O
x
y
[SQA]
8.
rag replacements
O
x
y
[SQA]
9.
rag replacements
O
replacements x
y
O
x
y hsn.uk.net
Page 2
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
10.
rag replacements
O
x
y
[SQA]
11.
rag replacements
O
x
y
[SQA]
12.
rag replacements
O
x
y
[SQA]
13.
rag replacements
O
x
y
replacements
O
x
y hsn.uk.net
Page 3
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA]
14.
rag replacements
O
x
y
[SQA]
15.
rag replacements
O
x
y
replacements
O
x
y hsn.uk.net
Page 4
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes

Higher Mathematics
PSfrag replacements
O
x
y
[SQA] 16. Triangle ABC has vertices A(−1, 6),
B(−3, −2) and C(5, 2).
A(−1, 6)
Find
(a) the equation of the line PSfrag p, replacements
the
median from C of triangle ABC. C(5, 2) 3
(b) the equation of the line q, the
O
perpendicular bisector of BC. x 4
(c) the coordinates of the point of
B(−3, −2)
intersection of the lines p and q. 1
y
[SQA] 17. Triangle ABC has vertices A(2, 2), y
B(12, 2) and C(8, 6). PSfrag replacements
C(8, 6)
(a) Write down the equation of l 1 ,
the perpendicular bisector of
AB. 1
A(2, 2) B(12, 2)
(b) Find the equation of l 2 , the
perpendicular bisector of AC. O
x 4
(c) Find the point of intersection of
lines l 1 and l 2 . 1
(d) Hence find the equation of the
circle passing through A, B and
C. 2
[SQA]
18.
The vertices of a triangle are P(−1, 1), Q(2, 1) and R(−6, 2). Find the equation of
the altitude of triangle PQR, drawn from P. 3
[SQA] 19. Find the equation of the median AD of triangle ABC where the coordinates of A,
B and C are (−2, 3), (−3, −4) and (5, 2) respectively. 3
[END OF WRITTEN QUESTIONS]
replacements
O
x
y hsn.uk.net
Page 5
Questions marked ‘[SQA]’ c○ SQA
All others c○ Higher Still Notes