Topic checks
End-of-topic checks using past-paper style questions.
BGE · S3
S3 Leading towards National 5
Finishing the BGE strong and starting National 5 early.
- CfE Fourth Level → SCQF 5
- 3 units
- 8 practice questions
- 5 key dates
Overview
About this course
The S3 Leading towards National 5 course completes Fourth Level and begins the National 5 Mathematics course, giving pupils more time to master the content before the exam in S4. Pupils develop exam technique, learn to communicate their working clearly and build the algebraic fluency that underpins success at Higher.
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 & Formulae6 topics
- Surds and indices
- Scientific notation
- Expanding and factorising – including trinomials
- Completing the square
- Algebraic fractions
- Arcs, sectors and volume of solids
2 Relationships6 topics
- Equation of a straight line
- Simultaneous equations
- Changing the subject
- Quadratic graphs and roots
- Pythagoras – converse and 3D
- Similarity
3 Applications5 topics
- Trigonometry – sine rule, cosine rule, area of triangle
- Vectors – an introduction
- Percentages – appreciation and depreciation
- Fractions – all four operations
- Statistics – standard deviation, quartiles
Assessment
How the course is assessed
Termly assessments
Three reported assessments, each with Paper 1 (non-calculator) and Paper 2 (calculator) sections.
S3 Profile assessment
May assessment covering all National 5 content met so far.
Assessment practice
Practise for forthcoming assessments
8 questions worth 17 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 · December
Expressions & Formulae Assessment
-
Q1
Factorise x² + 2x − 15.
2 marksShow solution
Solution
(x + 5)(x − 3).
-
Q2
Express x² + 6x + 1 in the form (x + p)² + q.
2 marksShow solution
Solution
(x + 3)² − 8.
-
Q3
Simplify 3√12 + √27.
2 marksShow solution
Solution
6√3 + 3√3 = 9√3.
-
Q4
Simplify (a⁴ × a³) ⁄ a².
1 markShow solution
Solution
a⁵.
Set 2 · May
S3 Profile Assessment
-
Q1
Find the equation of the line through (2, 5) with gradient 3.
3 marksShow solution
Solution
y − 5 = 3(x − 2) → y = 3x − 1.
-
Q2
Solve the simultaneous equations 2x + y = 11 and x − y = 1.
3 marksShow solution
Solution
Adding: 3x = 12, x = 4; y = 3.
-
Q3
Change the subject of A = ½bh to h.
2 marksShow solution
Solution
h = 2A ⁄ b.
-
Q4
A triangle has sides 7 cm and 9 cm with an included angle of 50°. Find its area.
2 marksShow solution
Solution
½ × 7 × 9 × sin 50° = 24.1 cm².
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
Progression
Where this course leads
Pupils progress to National 5 Mathematics in S4, with the strongest candidates well placed for Higher in S5.
Useful resources
Go further
More in the BGE
Other courses you might be looking for
S1 Level 2
CfE Second Level
Securing the foundations with confidence.
S1 Level 3
CfE Third Level
Taking the first steps into secondary mathematics.
S2 Level 3
CfE Third Level
Deepening understanding and building independence.
S2 Level 4
CfE Fourth Level
Accelerating towards National 5 and beyond.
Have a question about S3 → National 5?
The department is happy to help — we reply within two working days.