Higher Maths

Straight Line Checklist

This checklist covers every skill required by the SQA Course Specification for the Straight Line unit. Use the examples in the Clelland Maths video to master each technique.

1

Core Gradient Skills

Calculate Gradient from Two Points
Use the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
Parallel Lines
Identify that parallel lines have equal gradients (\( m_1 = m_2 \))
Perpendicular Lines
Use \( m_1 \times m_2 = -1 \) to find or verify perpendicular gradients
Angles and Gradients
Use \( m = \tan \theta \) where \( \theta \) is the angle with the positive direction of the \( x \)-axis
Tip

Remember that a negative gradient corresponds to an obtuse angle.

2

Equations of Straight Lines

Point-Slope Form
Use \( y - b = m(x - a) \) to find equation given point \( (a, b) \) and gradient \( m \)
General Form
Rearrange equations into forms like \( y = mx + c \) or \( ax + by + c = 0 \)
Vertical and Horizontal Lines
Recognise when a gradient is undefined (vertical) or zero (horizontal)
3

Triangle Geometry (The "Big Three")

Medians
Connects a vertex to the midpoint of the opposite side
Altitudes
Passes through a vertex and is perpendicular to the opposite side
Perpendicular Bisectors
Passes through the midpoint of a line segment at a right angle
4

Advanced Reasoning & Proof

Collinearity
Prove collinearity by showing they share a common point and the segments have equal gradients
Simultaneous Equations
Find the point of intersection between two straight lines
Angle with the y-axis
Calculate acute angle with \(y\)-axis by first finding the angle with the \(x\)-axis
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SQA Exam Tips

  • Exact Values: Do not use decimals for gradients unless specified; keep them as simplified fractions or surds.
  • Justification: For collinearity marks, you must state: "Since gradients are equal and there is a common point, the points are collinear".
  • Non-Calculator Fluency: Most straight line questions appear in Paper 1; practice your fraction arithmetic and surd manipulation.