Grade 10 Pure Mathematics Practice Pack
Grade 10 Pure Mathematics Practice Pack
Oct 14, 2026 · @Babalwa
This pack has 27 exam-style questions worth 147 marks, covering every Grade 10 pure
mathematics topic across terms 1 to 4, with full answers at the end.
How to Use This Pack
The questions are original and written in the style of Grade 10 end-of-term exams (ages 15
to 16). They are not reproductions of real papers. Attempt each section without the
answers, then mark yourself using the worked solutions on the last pages.
Show all working. Method marks (M) are given for a correct approach, accuracy marks
(A) for correct answers, and B marks for independent facts.
Give exact answers unless asked to round. Otherwise give answers to 3 significant
figures, or 1 decimal place for angles.
Calculators are allowed. Set your calculator to degrees for trigonometry.
Marks for each part are shown in square brackets, e.g. [3].
Every question is tagged Foundation, Core or Stretch. Start with the Foundation questions
(Q1, Q4, Q5, Q6, Q7, Q10, Q12, Q15, Q17, Q22, Q23, Q24, Q26). Move to Core when you are
scoring about 75% on those. Stretch questions are Q11 and Q16.
Term-by-Term Map
Term Topics Questions Marks
Term 1 Number, indices and surds; algebraic manipulation; Q1 to Q7 39
linear and simultaneous equations; forming
equations
Term 2 Quadratic equations and graphs; inequalities; Q8 to Q16 49
straight lines; sequences
Term 3 Angles and circle theorems; similar shapes; Q17 to Q23 36
Pythagoras and trigonometry; sine and cosine rules
Term 4 Functions; area, volume and sectors; vectors; Q24 to Q27 23
proportion; full-pack revision
Sit each term's questions as a short paper at the end of that term, then the whole pack as
a mock exam.
Page 1 of 11
, Grade 10 Pure Mathematics Practice Pack
Section A: Number, Indices and Surds (Term 1)
Question 1 [5 marks] · Foundation
(a) Write 360 as a product of its prime factors. [2]
(b) Find the highest common factor (HCF) and the lowest common multiple (LCM) of 360
and 84. [3]
Question 2 [6 marks] · Core
(a) Simplify (2x³y)⁴ ÷ (8x⁵y²). [3]
(b) Evaluate 8^(2/3) and 16^(−1/2). [2]
(c) Work out (3.6 × 10⁵) × (2 × 10⁻²), giving your answer in standard form. [1]
Question 3 [6 marks] · Core
(a) Simplify √48 − √27. [2]
(b) Expand and simplify (3 + √2)(3 − √2). [2]
(c) Rationalise the denominator of 10/√5. [2]
Section B: Algebra and Equations (Term 1)
Question 4 [6 marks] · Foundation
(a) Expand and simplify (x + 3)(x − 5). [2]
(b) Factorise fully 3x² − 12. [2]
(c) Factorise 2x² + 5x − 3. [2]
Question 5 [6 marks] · Foundation
(a) Solve 3(2x − 1) = 5x + 4. [2]
(b) Solve (x + 1)/2 − (x − 2)/3 = 2. [3]
(c) Make t the subject of v = u + at. [1]
Question 6 [6 marks] · Foundation
(a) Solve the simultaneous equations 2x + 3y = 12 and 5x − 3y = 9. [3]
(b) Solve the simultaneous equations 3x + 2y = 7 and x − y = 4. [3]
Page 2 of 11
Grade 10 Pure Mathematics Practice Pack
Oct 14, 2026 · @Babalwa
This pack has 27 exam-style questions worth 147 marks, covering every Grade 10 pure
mathematics topic across terms 1 to 4, with full answers at the end.
How to Use This Pack
The questions are original and written in the style of Grade 10 end-of-term exams (ages 15
to 16). They are not reproductions of real papers. Attempt each section without the
answers, then mark yourself using the worked solutions on the last pages.
Show all working. Method marks (M) are given for a correct approach, accuracy marks
(A) for correct answers, and B marks for independent facts.
Give exact answers unless asked to round. Otherwise give answers to 3 significant
figures, or 1 decimal place for angles.
Calculators are allowed. Set your calculator to degrees for trigonometry.
Marks for each part are shown in square brackets, e.g. [3].
Every question is tagged Foundation, Core or Stretch. Start with the Foundation questions
(Q1, Q4, Q5, Q6, Q7, Q10, Q12, Q15, Q17, Q22, Q23, Q24, Q26). Move to Core when you are
scoring about 75% on those. Stretch questions are Q11 and Q16.
Term-by-Term Map
Term Topics Questions Marks
Term 1 Number, indices and surds; algebraic manipulation; Q1 to Q7 39
linear and simultaneous equations; forming
equations
Term 2 Quadratic equations and graphs; inequalities; Q8 to Q16 49
straight lines; sequences
Term 3 Angles and circle theorems; similar shapes; Q17 to Q23 36
Pythagoras and trigonometry; sine and cosine rules
Term 4 Functions; area, volume and sectors; vectors; Q24 to Q27 23
proportion; full-pack revision
Sit each term's questions as a short paper at the end of that term, then the whole pack as
a mock exam.
Page 1 of 11
, Grade 10 Pure Mathematics Practice Pack
Section A: Number, Indices and Surds (Term 1)
Question 1 [5 marks] · Foundation
(a) Write 360 as a product of its prime factors. [2]
(b) Find the highest common factor (HCF) and the lowest common multiple (LCM) of 360
and 84. [3]
Question 2 [6 marks] · Core
(a) Simplify (2x³y)⁴ ÷ (8x⁵y²). [3]
(b) Evaluate 8^(2/3) and 16^(−1/2). [2]
(c) Work out (3.6 × 10⁵) × (2 × 10⁻²), giving your answer in standard form. [1]
Question 3 [6 marks] · Core
(a) Simplify √48 − √27. [2]
(b) Expand and simplify (3 + √2)(3 − √2). [2]
(c) Rationalise the denominator of 10/√5. [2]
Section B: Algebra and Equations (Term 1)
Question 4 [6 marks] · Foundation
(a) Expand and simplify (x + 3)(x − 5). [2]
(b) Factorise fully 3x² − 12. [2]
(c) Factorise 2x² + 5x − 3. [2]
Question 5 [6 marks] · Foundation
(a) Solve 3(2x − 1) = 5x + 4. [2]
(b) Solve (x + 1)/2 − (x − 2)/3 = 2. [3]
(c) Make t the subject of v = u + at. [1]
Question 6 [6 marks] · Foundation
(a) Solve the simultaneous equations 2x + 3y = 12 and 5x − 3y = 9. [3]
(b) Solve the simultaneous equations 3x + 2y = 7 and x − y = 4. [3]
Page 2 of 11
