Skills covered: Gradients and equations; parallel and perpendicular lines; angle of inclination; midpoints and distances; medians, altitudes and perpendicular bisectors.
Instructions: Attempt all questions. Show sufficient working to justify your answers. Give exact values unless a degree of accuracy is stated. Each section is separate, so you can target the part you need.
These are the same worksheets our pupils use at the Pollokshields tuition centre. Start with Section A if straight line still feels shaky; if you are confident, go straight to Section C and time yourself.
Section A
Prerequisite core skills
Revise earlier learning
Question 1
[2 marks]
Find the gradient of the line passing through A(−2,5) and B(4,−1).
Question 2
[3 marks]
Find the equation of the line with gradient 23 passing through (2,−1). Give your answer in the form ax+by=c.
Question 3
[3 marks]
Find the equation of the line through (−3,4) parallel to 2x+3y=12.
Question 4
[3 marks]
Find the equation of the line through (4,1) perpendicular to y=−4x+5.
Question 5
[2 marks]
Find the coordinates of the midpoint of the line segment joining (−3,2) and (5,−4).
Question 6
[2 marks]
Calculate the distance between (1,2) and (7,10).
Section B
Topic practice
Build individual techniques
Question 7
[4 marks]
A line has an angle of inclination of 135∘ and passes through (2,5). Find its equation in the form ax+by=c.
Question 8
[4 marks]
Find the coordinates of the point of intersection of 3x+2y=11 and x−y=2.
Question 9
[4 marks]
Find the equation of the line through P(3,−2), perpendicular to 5x−2y=8.
Question 10
[5 marks]
Triangle ABC has vertices A(−2,0), B(4,0) and C(0,4). Find the equation of the median from C to AB.
Question 11
[5 marks]
Find the equation of the perpendicular bisector of the line segment joining A(−4,1) to B(2,7).
Question 12
[3 marks]
Calculate the angle of inclination of the line 2x−3y=6, giving your answer to one decimal place.
Question 13
[4 marks]
Find the perpendicular distance between the parallel lines y=2x−3 and y=2x+7.
Question 14
[5 marks]
A(2,−1), B(−4,3) and C(6,5) are the vertices of a triangle. Find the equation of the median from A.
Section C
Exam-style and challenge
Combine skills, exam-style
Question 15
[6 marks]
Triangle ABC has vertices A(1,1), B(7,3) and C(3,9). Find the equations of the altitude and median from C.
Question 16
[3 marks]
A line has equation 3x−2y=12. Find its angle of inclination, to one decimal place.
Question 17
[5 marks]
The lines y=(k−1)x+2 and 2x+(k+3)y=5 are perpendicular. Find k.
Question 18
[6 marks]
ABCD is a parallelogram with A(0,0), B(6,2) and D(−2,6). Show that ∠BAD=90∘, find C, and determine the equation of diagonal BD.
Looking for the answers?
We do not publish the worked answers online. If you get stuck, bring the worksheet to a session and one of our Higher Maths tutors will go through the method with you, line by line, the way the SQA marking instructions award it.
Are the answers to these worksheets available online?
No. We keep the worked answers off the website on purpose. Pupils learn far more by attempting every question, checking against their notes and then going over the method with a tutor. Our students work through the full worked solutions in class, and if you are stuck on a particular question you can book a session and we will go through it with you step by step.
Are these official SQA or Qualifications Scotland papers?
No. Every question is newly written by Excel in MathSci to match the Higher Maths course specification. They are original practice resources, not official Qualifications Scotland papers, so use them alongside the real past papers rather than instead of them.
How should I use the three sections?
Section A checks the prerequisite skills you need before the topic makes sense, so start there if the topic feels shaky. Section B builds each technique on its own. Section C is exam-style and combines several skills, so treat it as a timed test once Sections A and B feel comfortable.
Can I print the worksheet?
Yes. Download the free PDF, which has space to write your working under every question, or print this page directly. The worksheet is free for personal study; please ask before reproducing it for a class or a commercial service.
