Functions and Graphs
Intercepts; completing the square; domains and ranges; composite and inverse functions; graph transformations; exponential and logarithmic graphs.
18 questions · 69 marks
Higher Maths · Free Practice
Higher Maths Worksheets
10 topic worksheets with 180 original, exam-style questions. Every question is newly written by Excel in MathSci to match the Higher Maths course, and each worksheet builds from core skills to full exam-style problems.
All topics student workbook
Every worksheet in one printable PDF: 10 topics, 180 questions, with space for working under each question.
Choose a topic
Open a worksheet to practise on screen, or download the PDF to print it.
Vectors
Two- and three-dimensional vectors; position vectors; magnitude; scalar product; collinearity; internal division; three-dimensional angles.
18 questions · 62 marks
Quadratics and Polynomials
Factorising; quadratic roots and the expression b-squared minus four ac; tangency; factor and remainder theorems; cubic intersections.
18 questions · 68 marks
Trigonometric Equations
Sine, cosine and tangent equations; degrees and radians; multiple angles; double-angle formulae; equations reducible to tangent; harmonic form.
18 questions · 70 marks
Differentiation
Indices and surds; differentiating algebraic and trigonometric functions; chain rule; tangents; stationary points and their nature; rates of change.
18 questions · 74 marks
Integration
Indefinite integrals; fractional and negative powers; standard composite-function integrals; trigonometric integrals; definite integrals; initial conditions.
18 questions · 61 marks
Straight Line
Gradients and equations; parallel and perpendicular lines; angle of inclination; midpoints and distances; medians, altitudes and perpendicular bisectors.
18 questions · 69 marks
Circle
Circle equations; completing the square; diameter; point location; equations with no real circle; line–circle intersections; tangent equations; circle geometry.
18 questions · 74 marks
Recurrence Relations
Percentage change; linear recurrence formulae; computing terms; fixed limiting values; finding coefficients; financial and population models.
18 questions · 72 marks
Optimisation and Area Between Curves
Maximum and minimum values; optimisation in geometric and practical contexts; definite integrals for area; signed regions and areas between curves.
18 questions · 83 marks
How to get the most from these worksheets
Every worksheet follows the same three-part structure. Section A covers the prerequisite skills; if you lose marks here, the topic itself will not stick, so fix these first. Section B practises each technique on its own. Section C is exam-style and mixes skills the way Paper 1 and Paper 2 questions do.
The worked answers are not published online. That is deliberate: checking every line against a solution sheet teaches less than finding out where your method went wrong. If you get stuck, our Higher Maths tutors in Glasgow will go through it with you. When you are ready for the real thing, move on to the Higher Maths past papers.
Frequently asked questions
Which Higher Maths topics do the worksheets cover?
There are 10 worksheets: Functions and Graphs, Vectors, Quadratics and Polynomials, Trigonometric Equations, Differentiation, Integration, Straight Line, Circle, Recurrence Relations, Optimisation and Area Between Curves. Each one has 18 questions split into prerequisite skills, topic practice and exam-style challenge sections.
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.
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