Worksheets

Practice Worksheets

The following worksheets provide structured practice for each topic in the course.

Worksheet 1: Coordinate Basics

Topic: Plotting points, distance, and midpoint

Exercises:

1. Plot the following points on a coordinate plane:
   • A(4, 3), B(-2, 5), C(-3, -4), D(1, -2), E(0, 6)
2. Calculate the distance between:
   • A(1, 1) and B(4, 5)
   • C(-2, 3) and D(3, -9)
   • E(0, 0) and F(-5, 12)
3. Find the midpoint of:
   • Line segment from (2, 8) to (10, 4)
   • Line segment from (-3, 7) to (5, -1)

Homework: Distance and Perimeter (PDF)

• Single-page A4 homework sheet: Triangle Perimeter
• Teacher-only answer key: Triangle Perimeter Answers
• Consolidation option: Triangle Perimeter (Easy)
• Extension option: Triangle Perimeter (Hard)
• Teacher-only answers (Easy): Triangle Perimeter Easy Answers
• Teacher-only answers (Hard): Triangle Perimeter Hard Answers

Worksheet 2: Gradient and Equations

Topic: Finding gradients and writing equations of lines

Exercises:

1. Find the gradient of the line through:
   • P(1, 3) and Q(5, 11)
   • R(-2, 4) and S(6, -4)
   • T(0, -3) and U(4, 5)
2. Write the equation of the line:
   • With gradient 3 and y-intercept 5
   • With gradient -2 passing through (4, 1)
   • Through points (2, 3) and (6, 11)
3. Convert to slope-intercept form (\(y = mx + c\)):
   • \(3x + y - 6 = 0\)
   • \(2x - 4y + 8 = 0\)
   • \(x + 2y - 10 = 0\)

Worksheet 3: Parallel and Perpendicular Lines

Topic: Working with parallel and perpendicular lines

Exercises:

1. Determine whether each pair of lines is parallel, perpendicular, or neither:
   • \(y = 4x + 1\) and \(y = 4x - 3\)
   • \(y = 2x + 5\) and \(y = -\frac{1}{2}x + 2\)
   • \(y = 3x - 1\) and \(y = 2x + 4\)
2. Find the equation of:
   • The line parallel to \(y = 5x + 2\) through point (2, 3)
   • The line perpendicular to \(y = -3x + 1\) through point (6, 4)
   • The line parallel to \(2x + y - 4 = 0\) through point (-1, 5)
3. Challenge problems:
   • Line \(L\) passes through A(1, 2) and B(7, 8). Find the equation of the line perpendicular to \(L\) that passes through the midpoint of AB.
   • Points P(2, 3), Q(6, 5), and R(x, y) form a right angle at Q. If the line PQ has gradient \(\frac{1}{2}\), find the gradient of QR.

Answer Key

Worksheet 1: 1. (Plot on graph paper) 2. a) 5, b) 13, c) 13 3. a) (6, 6), b) (1, 3)

Worksheet 2: 1. a) 2, b) -1, c) 2 2. a) \(y = 3x + 5\), b) \(y = -2x + 9\), c) \(y = 2x - 1\) 3. a) \(y = -3x + 6\), b) \(y = \frac{1}{2}x + 2\), c) \(y = -\frac{1}{2}x + 5\)

Worksheet 3: 1. a) Parallel, b) Perpendicular, c) Neither 2. a) \(y = 5x - 7\), b) \(y = \frac{1}{3}x + 2\), c) \(y = -2x + 3\) 3. a) \(y = -x + 9\), b) \(m_{QR} = -2\)

Printing Tips

• Print worksheets on A4 paper
• Consider providing graph paper for plotting exercises
• Answer keys can be printed separately for teacher use