Advanced Higher Mechanics: the 2027 exam, topics and practice questions

The Advanced Higher Mechanics exam in 2027

The date and time are from the 2027 exam timetable, and the paper's structure is from the course specification. The course is worth 32 SCQF credit points at level 7. Unlike the sciences, it wasn't one of the courses that got a shorter exam for 2026 to 2027, so the paper stays at 3 hours.

The specimen paper's formulae list gives Newton's inverse square law of gravitation, the simple harmonic motion equations, centres of mass for a triangle, a semicircle and a lamina under a curve, and some standard derivatives and integrals. The constant acceleration equations aren't on it, so learn them.

What the course covers

The specification splits the paper into three areas, each worth roughly 25% to 45% of the marks:

• Forces, energy and momentum: momentum and impulse, work, power and energy, forces in dynamics and equilibrium, and centre of mass.
• Straight-line, periodic and parabolic motion: motion in a straight line, vectors for motion, projectiles in a vertical plane, motion in a horizontal circle and simple harmonic motion.
• Mathematical techniques for mechanics: partial fractions, differentiation, integration and solving differential equations.

Advanced Higher Mechanics grade boundaries

In 2026, out of 100, an A needed 69, a B 59, a C 49 and a D 39. Of the 486 candidates, 40.1% got an A. The 2026 course report says questions 5(b) and 7(b) were more demanding than intended, which was allowed for when the boundaries were set. Boundaries move every year.

Advanced Higher Mechanics practice questions

We wrote these for this guide. Use g = 9.8 m/s² and show every step: most of the marks are for method.

1. Variable acceleration

Question: a particle starts from rest at the origin with acceleration a = 6t − 4 m/s². Find its velocity and displacement after 3 seconds. Answer: integrate: v = 3t² − 4t + c, and v = 0 when t = 0, so c = 0. At t = 3, v = 27 − 12 = 15 m/s. Integrate again: x = t³ − 2t², so x = 27 − 18 = 9 m. The constant acceleration equations would give the wrong answer here, because the acceleration changes.

2. Projectiles

Question: a ball is struck from level ground at 20 m/s, 30° above the horizontal. Find its time of flight and range. Answer: vertically, it lands when 20 sin 30° × t − 4.9t² = 0, so t = 10 ÷ 4.9 = 2.04 s. Horizontally, the speed stays 20 cos 30° = 17.32 m/s, so the range is 17.32 × 2.04 = 35.3 m. Check it in the Projectile Motion Calculator, then try a projectile question from our Laws of Motion course and press Mark.

3. Friction on a slope

Question: a 2 kg particle sits on a rough plane inclined at 30°, on the point of slipping. Find the coefficient of friction.

Answer: perpendicular to the slope, R = 2 × 9.8 × cos 30° = 16.97 N. Parallel to it, F = 2 × 9.8 × sin 30° = 9.8 N. In limiting friction F = μR, so μ = 9.8 ÷ 16.97 = 0.577, which is tan 30°. The 2026 course report noted candidates leaving forces out when resolving on a slope, so list every force before you start.

4. Simple harmonic motion

Question: a particle moves with simple harmonic motion of amplitude 0.2 m and period π seconds. Find its speed when it is 0.1 m from the centre. Answer: ω = 2π ÷ T = 2 rad/s. From the formulae list, v² = ω²(a² − x²) = 4 × (0.04 − 0.01) = 0.12, so v = 0.346 m/s. See it move in the Pendulum and SHM simulator.

5. Motion in a horizontal circle

Question: a 0.5 kg particle on a light string moves in a horizontal circle of radius 0.8 m on a smooth table at 3 rad/s. Find the tension. Answer: the tension provides the force towards the centre: T = mrω² = 0.5 × 0.8 × 3² = 3.6 N. Try other values in the Circular Motion Calculator.

Common Advanced Higher Mechanics mistakes

These come from the 2026 course report:

• Constant acceleration equations used when the force or acceleration varies. Integrate instead.
• Missing forces on an inclined plane: weight, normal reaction, friction on a rough surface and any applied force.
• Resolving at angles with strings, springs and rods, and slips in elastic potential energy.
• Vertical circles: not using conservation of energy, or leaving out the force towards the centre.
• Displacement and distance mixed up.

Use a daily paper as a short timed prelim

Today's Advanced Higher Mechanics paper is good prelim practice for part of the course. It covers constant and variable acceleration, velocity time graphs, projectiles, forces and Newton's laws, friction and inclined planes, connected particles and moments. It doesn't cover circular motion, simple harmonic motion, centre of mass, work, energy and momentum, or the mathematical techniques, so practise those from your notes and the official past papers. For when prelims happen and how they're used, see our prelims guide.

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