Very much a work in progress. Over time I hope to compile some quality tasks for use at SQA Higher Maths. This stuff is arranged in the old (proper) order for Higher. None of that crazy SQA unit order here!

Model Paper for Special 2021 Arrangements

Straight Line

• Drawing Altitudes, Medians and Perpendicular Bisectors
• Everything!
• Identifying Information Requires: Altitudes, Medians and Perpendicular Bisectors
• m = Tan&
• Medians and Altitudes
• Median – Working Backwards

Functions

• Composite Functions Matching Task
• Composite Functions Scaffolded
• Domain and Range
• Function Composition – Graphical Explanation
• Function Pyramids
• Graphing Inverse Functions
• Odd One Out
• Transformations of Functions – 2 Steps
• Transformations of Functions – 3 Steps

Trigonometry (Unit One)

• Deciding Which Quadrants to Select
• Evaluating Trig Expressions
• Exact Values Match Up
• Fractions involving Pi (Pre-radians worksheet)
• ‘Quadratic’ Trig Equations – Scaffolded Intro
• Radian Measure Intro
• Related Exact Values

Logs and Exponentials (Unit One)

• Creating Equivalent Log Expressions
• Evaluating Logs
• Intro to Exponentials
• Log Relationships

Differentiation (Unit One)

• Preparing for Differentiation – Negative and Fraction Indices
• Preparing for Differentiation – Quotients
• Equation of a Tangent to a Curve
• Optimisation
• Scaffolded Differentiation Practice
• Scaffolded Differentiation Practice (Harder!): Quotients, Brackets etc
• Sketching the graph of the Derived Function
• Stationary Points

Recurrence Relations

• Introductory tasks and an investigation of the limit

Polynomials

A note: I don’t use synthetic division, so you won’t get resources which specifically focus on that technique. However, you might like my article: https://startingpointsmaths.wordpress.com/2019/05/10/a-progression-from-long-multiplication-to-algebraic-long-division/ This gives a deep dive on the rationale for using grid model instead.

• Cubic Polynomials – Factorising and Sketching
• Grid Multiplication and Division (Algebra)
• Polynomials – Finding Missing Coefficients

Quadratics

• Basic Quadratic Understanding
• Increasingly Difficult Quadratics and Polynomials
• Quadratic Inequalities Pre-Requisite Task
• Scaffolded Quadratic Inequalities. – Susan Whitehouse Task
• Quadratic Inequalities – Hidden in another context

Integration (Unit Two)

• Areas – Isolating the key ideas
• Area Between Two Curves – Scaffolded
• Increasingly Difficult Integration

Trigonometry (Unit Two)

• Addition and Double Angle Formulae

Circle

• Increasingly Difficult Circle Equations

Further Calculus

• Chain Rule Challenge
• Chain Rule – Scaffolded
• Increasingly Difficult Differentiation of Trig Terms

Vectors

• Angle Between Two Vectors
• Dividing a line in a Given Ratio
• Properties of the scalar product