Higher exam guide
Higher Mathematics
Course code C847 76 · Specification Version 3.0, May 2023 · valid from 2023–24
Your 2027 exam
- Paper 1 (non-calculator)
- – BST
- Paper 2
- – BST
Published national times, in UK local time. Confirm your personal timetable, room and any assessment arrangements with your school or college. Coursework deadlines are set by your centre.
- Results day
- National contingency day
Qualifications Scotland timetable · Version 02, August 2026 · checked .
How the exam is marked
120 course marks after scaling
Paper 1 (non-calculator)
55 marks
46% of the course result
1 hour 15 minutes
Short-answer and extended-response questions without a calculator.
Paper 2
65 marks
54% of the course result
1 hour 30 minutes
Short-answer and extended-response questions. A calculator may be used.
Course areas and revision checklist
Use this summary alongside the full official specification. ScotSpark practice covers selected skills, not every item below; your teacher can help you fill the gaps.
Algebraic and trigonometric skills
- Factorising cubics and quartics
- Laws of logarithms and exponents
- Addition and double angle formulae
- Wave function: a cos x + b sin x as k cos(x − α) or k sin(x − α)
- Related graphs and transformations, including y = f′(x)
- Inverse of log and exponential functions
- Completing the square (non-unitary x²)
- Composite and inverse functions, domain and range
- Solving cubics and quartics; discriminant to find an unknown
- Quadratic inequalities
- Log and exponential equations and modelling
- Intersections of lines and curves
- Trig equations in degrees or radians
Geometric skills
- Vector pathways in 3D
- Collinearity and internal division
- Scalar product and angle between vectors
- Unit vectors and i, j, k
Calculus skills
- Differentiating powers of x, sin kx and cos kx
- Chain rule
- Tangents, increasing/decreasing functions, stationary points and curve sketching
- Integrating powers of x, (x + q)ⁿ, (px + q)ⁿ and trig functions
- Differential equations dy/dx = f(x)
- Definite integrals
- Optimisation and closed-interval max/min
- Rate of change
- Area under a curve and between curves
Algebraic and geometric skills
- Parallel and perpendicular lines
- m = tan θ
- Medians, altitudes and perpendicular bisectors
- Equation of a circle and tangency
- Intersection of circles or a line and a circle
- Recurrence relations and limits
Reasoning skills
- Interpreting a situation and choosing a strategy
- Explaining why a solution is appropriate in context
Exam technique
- Paper 1 is 55 of the 120 marks, so practise the specified algebra, logarithms and calculus without a calculator.
- Higher differentiation covers powers of x, sin kx, cos kx and the chain rule. Differentiating exponential or logarithmic functions is not a required Higher skill; exponential modelling uses log laws instead.
- State the nature of stationary points with a nature table or another justified method, such as a second derivative.
- For recurrence relations, justify that a limit exists (−1 < a < 1) before finding it.
Version 3.0, May 2023 · checked . Qualifications Scotland replaced SQA in February 2026; official documents may still use the SQA name. Check for later updates and confirm arrangements with your teacher.