Madras Mathematics Department Find my course

Explore

Broad General Education

Senior Phase

Senior Phase · S4

National 5 Mathematics

The gateway qualification for Higher and beyond.

  • SCQF Level 5
  • 3 units
  • 10 practice questions
  • 7 key dates
Start practising View key dates

Overview

About this course

National 5 Mathematics is a rigorous course that develops algebraic, geometric, trigonometric and statistical skills. It is assessed by two external SQA exam papers in May. A good pass at National 5 is required for Higher Mathematics and is valued by colleges, universities and employers across the UK.

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 Expressions & Formulae7 topics
  • Surds and indices
  • Scientific notation
  • Brackets and factorising
  • Completing the square
  • Algebraic fractions
  • Gradient
  • Arcs, sectors, volumes of solids
2 Relationships9 topics
  • Straight line – y − b = m(x − a)
  • Simultaneous equations
  • Changing the subject
  • Quadratic functions, graphs and formula
  • Discriminant
  • Pythagoras & converse
  • Similar shapes
  • Trig graphs and equations
  • Trig identities
3 Applications7 topics
  • Sine & cosine rules, area of a triangle
  • Bearings
  • Vectors – 2D and 3D, magnitude
  • Percentages – compound
  • Fractions – mixed operations
  • Statistics – standard deviation, quartiles, interquartile range
  • Scatter graphs & line of best fit

Assessment

How the course is assessed

01

Paper 1 (Non-calculator)

50 marks · 1 hour 15 minutes. Tests fluency with surds, fractions, algebra and exact-value trigonometry.

02

Paper 2 (Calculator)

60 marks · 1 hour 50 minutes. Longer, context-based problems.

03

Grading

Graded A–D on the combined total of 110 marks. Typically ~70% for an A, ~50% for a C.

Assessment practice

Practise for forthcoming assessments

10 questions worth 26 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 · January

Prelim – Paper 1 (Non-calculator)

5 questions · 11 marks

Print this set

  1. Q1

    Evaluate 2⅓ − 1⅘.

    2 marks
    Show solution

    Solution

    7⁄3 − 9⁄5 = 35⁄15 − 27⁄15 = 8⁄15.

  2. Q2

    Express 4⁄√8 with a rational denominator.

    2 marks
    Show solution

    Solution

    4⁄√8 × √8⁄√8 = 4√8⁄8 = √8⁄2 = √2.

  3. Q3

    Factorise fully 2x² − 18.

    2 marks
    Show solution

    Solution

    2(x² − 9) = 2(x − 3)(x + 3).

  4. Q4

    Solve x² − 5x − 14 = 0.

    2 marks
    Show solution

    Solution

    (x − 7)(x + 2) = 0 → x = 7 or x = −2.

  5. Q5

    Find the equation of the line through (−2, 7) and (4, −5).

    3 marks
    Show solution

    Solution

    m = (−5 − 7)⁄(4 + 2) = −2; y − 7 = −2(x + 2) → y = −2x + 3.

Set 2 · January

Prelim – Paper 2 (Calculator)

5 questions · 15 marks

Print this set

  1. Q1

    A car bought for £18 500 depreciates by 12% per year. Find its value after 3 years, to the nearest pound.

    3 marks
    Show solution

    Solution

    18 500 × 0.88³ = £12 606.

  2. Q2

    In triangle PQR, PQ = 8 cm, QR = 11 cm and angle PQR = 64°. Find PR.

    3 marks
    Show solution

    Solution

    PR² = 8² + 11² − 2(8)(11)cos 64° = 107.84; PR = 10.4 cm.

  3. Q3

    Find the standard deviation of 4, 7, 8, 10, 11.

    4 marks
    Show solution

    Solution

    Mean = 8; Σ(x − x̄)² = 16 + 1 + 0 + 4 + 9 = 30; s = √(30⁄4) = 2.74.

  4. Q4

    Find the discriminant of 3x² − 2x + 5 and state the nature of the roots.

    2 marks
    Show solution

    Solution

    b² − 4ac = 4 − 60 = −56 < 0, so no real roots.

  5. Q5

    Vectors u = (2, −1, 3) and v = (−4, 0, 5). Find |u + v|.

    3 marks
    Show solution

    Solution

    u + v = (−2, −1, 8); |u + v| = √(4 + 1 + 64) = √69 ≈ 8.31.

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

w/c 6 Oct 2025

Unit 1 class assessment

Assessment + cal

Thu 27 Nov 2025

S4 Parents' Evening

Parents' Evening + cal

w/c 8 Dec 2025

Unit 2 class assessment

Assessment + cal

Wed 21 Jan 2026

National 5 Prelim (Papers 1 & 2)

Prelim + cal

Mar 2026

Easter revision school (dates TBC)

Information

Fri 1 May 2026

SQA Exam – Paper 1 (9:00) & Paper 2 (10:45)*

SQA Exam + cal

Tue 4 Aug 2026

SQA results day

Information + cal

Progression

Where this course leads

Higher Mathematics in S5 (an A or B pass is strongly recommended), or Higher Applications of Mathematics.

More in the Senior Phase

Other courses you might be looking for

Have a question about National 5 Mathematics?

The department is happy to help — we reply within two working days.

Email the department