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Broad General Education

Senior Phase

Senior Phase · S6

Advanced Higher Mathematics of Mechanics

Where mathematics meets the physical world.

  • SCQF Level 7
  • 3 units
  • 7 practice questions
  • 6 key dates
Start practising View key dates

Overview

About this course

Advanced Higher Mathematics of Mechanics applies calculus and vectors to the motion of objects – from projectiles and collisions to circular motion and simple harmonic motion. It is an outstanding preparation for engineering, physics and applied mathematics degrees, and pairs naturally with Advanced Higher Mathematics and Physics.

Course structure

What your child will learn

The course is organised into 3 units. Topics are usually taught in the order shown, though teachers may adapt the sequence for their class. Select a unit to see its topics.

1 Linear & Parabolic Motion5 topics
  • Kinematics with calculus
  • Constant acceleration – SUVAT
  • Relative motion and vectors
  • Projectiles – range, time of flight, trajectory
  • Motion graphs
2 Force, Energy & Periodic Motion6 topics
  • Newton's laws and friction
  • Connected particles and pulleys
  • Momentum, impulse and collisions
  • Work, energy and power
  • Circular motion – horizontal and vertical
  • Simple harmonic motion
3 Mathematical Techniques for Mechanics5 topics
  • Differentiation and integration of vectors
  • Differential equations – first and second order
  • Centres of mass
  • Moments and equilibrium
  • Rigid bodies

Assessment

How the course is assessed

01

Question Paper

100 marks · 3 hours. Single externally assessed exam; calculator permitted throughout.

02

Grading

Graded A–D.

Assessment practice

Practise for forthcoming assessments

7 questions worth 21 marks, matched to the assessments on this course. Try each question on paper first, then select it to reveal the worked solution. You can also print a blank set for revision.

Set 1 · November

Linear & Parabolic Motion Assessment

3 questions · 8 marks

Print this set

  1. Q1

    A particle moves with velocity v = 3t² − 4t + 1 m/s. Find its displacement from t = 0 to t = 3 s.

    3 marks
    Show solution

    Solution

    ∫₀³ (3t² − 4t + 1) dt = [t³ − 2t² + t]₀³ = 27 − 18 + 3 = 12 m.

  2. Q2

    A ball is projected at 20 m/s at 30° above the horizontal from ground level. Find its time of flight (g = 9.8).

    3 marks
    Show solution

    Solution

    T = 2u sin θ ⁄ g = 2(20)(0.5)⁄9.8 = 2.04 s.

  3. Q3

    A car accelerates uniformly from 8 m/s to 20 m/s over 96 m. Find the acceleration.

    2 marks
    Show solution

    Solution

    v² = u² + 2as → 400 = 64 + 192a → a = 1.75 m/s².

Set 2 · February

Prelim

4 questions · 13 marks

Print this set

  1. Q1

    A 2 kg block on a rough horizontal plane (μ = 0.3) is pulled by a 10 N horizontal force. Find its acceleration (g = 9.8).

    3 marks
    Show solution

    Solution

    F = 10 − 0.3(19.6) = 4.12 N; a = 4.12⁄2 = 2.06 m/s².

  2. Q2

    A particle of mass 3 kg moving at 4 m/s collides with a 2 kg particle at rest. They coalesce. Find the common velocity and the kinetic energy lost.

    4 marks
    Show solution

    Solution

    v = 12⁄5 = 2.4 m/s. KE before = 24 J; after = ½(5)(2.4²) = 14.4 J; loss 9.6 J.

  3. Q3

    A particle performs SHM with amplitude 0.5 m and period 2 s. Find its maximum speed.

    3 marks
    Show solution

    Solution

    ω = 2π⁄T = π; vₘₐₓ = aω = 0.5π ≈ 1.57 m/s.

  4. Q4

    Solve the differential equation dv/dt = −0.2v, given v = 15 when t = 0.

    3 marks
    Show solution

    Solution

    v = 15e^(−0.2t).

Key dates

Important dates for this course

Session 2025–26. Dates marked * are indicative pending the official SQA timetable; items marked TBC will be updated as soon as they are confirmed. Select “+ cal” on any date to add it to your own calendar.

  • Prelim
  • SQA Exam
  • Parents' Evening
  • Assessment
  • Information

Thu 6 Nov 2025

S5/S6 Parents' Evening

Parents' Evening + cal

w/c 17 Nov 2025

Linear & Parabolic Motion assessment

Assessment + cal

Tue 3 Feb 2026

Advanced Higher Mechanics Prelim

Prelim + cal

Mar 2026

Easter revision school (dates TBC)

Information

May 2026

SQA Exam – Question Paper (date TBC)*

SQA Exam

Tue 4 Aug 2026

SQA results day

Information + cal

Progression

Where this course leads

Degree-level study in engineering, physics, mathematics or related disciplines.

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