Grade 10 Maths · Paper 1
Algebra Grade 10
Real past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.
- past paper questions
- 269 past paper questions
- skills
- 38 skills
- videos
- 38 videos
Try a real exam question
No sign-up. Takes 3 minutes.
Question 2.2 · March 2025 · Provincial · 4 marks
2.2 Simplify: (4)
Work it out on paper first. Then mark yourself with the official memo, one tick at a time.
What's in Algebra Grade 10
Each skill is one thing a memo gives a tick for. Tap a skill for its own questions, notes and videos.
The Number System39 past paper questions
- Calculate with integersAdd, subtract, multiply and divide positive and negative whole numbers in the right order (for example −3 × −4 = 12, and (7 − 4)³ = 27).6 past paper questions · 2 videos
- Calculate with common fractionsAdd, subtract, multiply and divide fractions and mixed numbers, and write them in simplest form (for example 1/2 + 1/3 = 5/6, and 3/4 ÷ 1/2 = 3/2).3 past paper questions · 4 videos
- Classify a real numberDecide whether a number is rational or irrational, natural, whole or an integer (for example √9 = 3 is rational but √2 is irrational).20 past paper questions · 4 videos
- Find undefined or non-real valuesFind values that make an expression undefined or non-real (for example 1/(x − 2) is undefined when x = 2, and √−4 is non-real).14 past paper questions · 3 videos
- Place a surd between two integersFind the two whole numbers a square root lies between by using nearby perfect squares (for example √20 is between √16 = 4 and √25 = 5).11 past paper questions · 3 videos
Rounding Off1 past paper questions
Rewriting Rational Numbers2 past paper questions
- Convert fractions, decimals and percentagesChange a number between fraction, decimal and percentage form (for example 1/4 = 0,25 = 25%).3 past paper questions · 4 videos
- Convert recurring decimals to fractionsChange a recurring decimal into a fraction by multiplying by a power of 10 and subtracting (for example 0,333… = 1/3).2 past paper questions · 3 videos
Algebraic Expressions20 past paper questions
- Collect like termsAdd and subtract terms with the same letters and powers to simplify an expression (for example 3x + 2y − x + 4y = 2x + 6y).38 past paper questions · 4 videos
- Multiply out a single bracketMultiply every term inside a bracket by the term outside it, watching the signs (for example −2x(x − 3) = −2x² + 6x).13 past paper questions · 3 videos
- Multiply two binomialsMultiply two brackets by multiplying each term in the first by each term in the second (for example (x + 2)(x + 3) = x² + 5x + 6).11 past paper questions · 3 videos
- Take out a common factorFactorise by taking out the biggest common factor and putting the rest in a bracket (for example 6x² + 9x = 3x(2x + 3)).37 past paper questions · 4 videos
- Square a binomialSquare a bracket with two terms, remembering the middle term (for example (x + 3)² = x² + 6x + 9, not x² + 9).18 past paper questions · 3 videos
- Factorise a difference of squaresFactorise one square minus another square into two brackets (for example x² − 9 = (x − 3)(x + 3)).21 past paper questions · 4 videos
- Factorise a trinomialFactorise x² + bx + c using two numbers that multiply to c and add to b (for example x² + 5x + 6 = (x + 2)(x + 3)).43 past paper questions · 3 videos
- Multiply out larger bracketsMultiply out bigger brackets, multiplying every term by every other term (for example (x + 1)(x² − x + 1) = x³ + 1).15 past paper questions · 4 videos
- Factorise by grouping in pairsFactorise four terms by grouping them in pairs and taking out the common bracket (for example ax + ay + bx + by = (a + b)(x + y)).13 past paper questions · 4 videos
- Factorise trinomials with a leading coefficientFactorise a trinomial where the number in front of x² is not 1 (for example 2x² + 7x + 3 = (2x + 1)(x + 3)).24 past paper questions · 3 videos
- Factorise sum or difference of cubesFactorise a sum or difference of two cubes into a bracket and a trinomial (for example x³ − 8 = (x − 2)(x² + 2x + 4)).12 past paper questions · 4 videos
Simplifying Algebraic Expressions71 past paper questions
- Collect like termsAdd and subtract terms with the same letters and powers to simplify an expression (for example 3x + 2y − x + 4y = 2x + 6y).38 past paper questions · 4 videos
- Take out a common factorFactorise by taking out the biggest common factor and putting the rest in a bracket (for example 6x² + 9x = 3x(2x + 3)).37 past paper questions · 4 videos
- Square a binomialSquare a bracket with two terms, remembering the middle term (for example (x + 3)² = x² + 6x + 9, not x² + 9).18 past paper questions · 3 videos
- Factorise a difference of squaresFactorise one square minus another square into two brackets (for example x² − 9 = (x − 3)(x + 3)).21 past paper questions · 4 videos
- Simplify an algebraic fractionSimplify a fraction with letters by factorising the top and bottom and cancelling common factors (for example (x² − 4)/(x − 2) = x + 2).57 past paper questions · 4 videos
- Multiply out larger bracketsMultiply out bigger brackets, multiplying every term by every other term (for example (x + 1)(x² − x + 1) = x³ + 1).15 past paper questions · 4 videos
- Factorise by grouping in pairsFactorise four terms by grouping them in pairs and taking out the common bracket (for example ax + ay + bx + by = (a + b)(x + y)).13 past paper questions · 4 videos
- Factorise sum or difference of cubesFactorise a sum or difference of two cubes into a bracket and a trinomial (for example x³ − 8 = (x − 2)(x² + 2x + 4)).12 past paper questions · 4 videos
- Add or subtract algebraic fractionsAdd or subtract fractions with letters by writing them over the lowest common denominator (for example 1/x + 1/2 = (2 + x)/(2x)).15 past paper questions · 4 videos
Exponents40 past paper questions
- Use the laws of exponentsUse the laws of powers, like adding the powers when you multiply the same base (2³ × 2² = 2⁵) and knowing that x⁰ = 1.61 past paper questions · 4 videos
- Change the base of a powerWrite a number as a power of a smaller base so the powers can be compared or combined (for example 8ˣ = (2³)ˣ = 2³ˣ).59 past paper questions · 3 videos
- Take out a common powerSplit powers with the same base and take out the common power (for example 2ˣ⁺¹ + 2ˣ = 2ˣ(2 + 1) = 3 × 2ˣ).24 past paper questions · 3 videos
- Write a root as a powerChange a root into a power with a fraction exponent, or back again (for example ∛(x²) = x^(2/3), and √x = x^(1/2)).10 past paper questions · 3 videos
Exponential Equations12 past paper questions
- Change the base of a powerWrite a number as a power of a smaller base so the powers can be compared or combined (for example 8ˣ = (2³)ˣ = 2³ˣ).59 past paper questions · 3 videos
- Solve an exponential equationSolve an equation with the unknown in the power by making the bases the same and equating the powers (for example 2ˣ = 2³, so x = 3).51 past paper questions · 3 videos
- Take out a common powerSplit powers with the same base and take out the common power (for example 2ˣ⁺¹ + 2ˣ = 2ˣ(2 + 1) = 3 × 2ˣ).24 past paper questions · 3 videos
- Solve an equation with rational exponentsSolve an equation with a fraction power by raising both sides to the flipped power (for example x^(2/3) = 4 gives x = 4^(3/2) = 8).17 past paper questions · 3 videos
Linear Equations12 past paper questions
- Solve a linear equationSolve an equation by doing the same inverse operation on both sides until the unknown stands alone (for example 3x + 4 = 19 gives x = 5).70 past paper questions · 3 videos
- Clear fractions in an equationGet rid of fractions in an equation by multiplying every term by the lowest common denominator (for example x/2 + x/3 = 5 becomes 3x + 2x = 30).8 past paper questions · 3 videos
Quadratic Equations17 past paper questions
- Reject solutions that do not fitCheck each answer against the situation and throw out any that make no sense (for example a length cannot be negative, so reject x = −4).7 past paper questions · 3 videos
- Solve a quadratic by factorisingSolve a quadratic equation by factorising and setting each bracket equal to zero (for example (x − 2)(x + 5) = 0 gives x = 2 or x = −5).124 past paper questions · 3 videos
- Write a quadratic in standard formExpand and rearrange an equation into the form ax² + bx + c = 0 (for example x(x + 3) = 10 becomes x² + 3x − 10 = 0).82 past paper questions · 4 videos
- Factorise trinomials with a leading coefficientFactorise a trinomial where the number in front of x² is not 1 (for example 2x² + 7x + 3 = (2x + 1)(x + 3)).24 past paper questions · 3 videos
Literal Equations8 past paper questions
Number Line6 past paper questions
Linear Inequalities19 past paper questions
- Solve a linear inequalitySolve an inequality like an equation, but flip the sign when you multiply or divide by a negative (for example −2x > 6 gives x < −3).26 past paper questions · 3 videos
- Write or draw a solution setShow a solution set on a number line with open or closed dots, or write it in interval notation (for example −2 ≤ x < 3 is [−2; 3)).15 past paper questions · 4 videos
Simultaneous Equations17 past paper questions
- Change the subject of a formulaRearrange a formula to make a different letter the subject (for example from A = πr², make r the subject: r = √(A ÷ π)).42 past paper questions · 4 videos
- Solve simultaneous equations by eliminationSolve two equations together by adding or subtracting them so one unknown cancels (for example x + y = 7 plus x − y = 1 gives 2x = 8).10 past paper questions · 4 videos
- Solve simultaneous equations by substitutionSolve two equations together by substituting one into the other (for example putting y = 2x into x + y = 9 gives 3x = 9, so x = 3).26 past paper questions · 4 videos
Mathematical Modelling6 past paper questions
- Set up an expression or equationTurn a word problem or diagram into an equation by choosing a letter for the unknown (for example 'a number plus 5 is 12' gives x + 5 = 12).18 past paper questions · 3 videos
- Reject solutions that do not fitCheck each answer against the situation and throw out any that make no sense (for example a length cannot be negative, so reject x = −4).7 past paper questions · 3 videos
More Algebra Grade 10 questions and answers
Try each one on paper before you open the memo.
1. Question 1.3.1 · March 2025 · Provincial · 2 marks
1.3 Factorise the following expressions fully.1.3.1 (2)Show the memo (1 tick)Memo
- ✓Find factors of -10 that add to -3
2 marks · Factorise a trinomial
- ✓
2. Question 2.1.1 · March 2025 · Provincial · 2 marks
2.1 Solve for x:2.1.1 (2)Show the memo (1 tick)Memo
- ✓Solve or
2 marks · Solve a quadratic by factorising
- ✓
3. Question 3.1.2 · June 2025 · Paper 1 · Provincial · 3 marks
3.1 Solve for if:3.1.2 , where and represent your answer on a number line.(3)Show the memo (3 ticks)Memo
- ✓Isolate the x term
1 mark · Solve a linear inequality
- ✓Solve for x
Therefore:1 mark · Solve a linear inequality
- ✓Represent on a number lineThe correct representation is a number line showing an open circle at and a closed (shaded) circle at , with a solid line connecting the two values.
1 mark · Write or draw a solution set
- ✓
4. Question 2.1.2 · March 2024 · Provincial · 3 marks
2.1 Solve for :2.1.2 (3)Show the memo (2 ticks)Memo
- ✓Factorise
- ✓Solve or
2 marks · Solve a quadratic by factorising
- ✓
5. Question 2.1.2 · June 2025 · Paper 1 · Provincial · 3 marks
2.1 Simplify the following expressions fully:2.1.2 (3)Show the memo (3 ticks)Memo
- ✓Expand the binomials (Option 1)
1 mark · Multiply two binomials
- ✓Simplify the terms inside the bracket (Option 1)
1 mark · Collect like terms
- ✓Multiply by the constant outside (Option 1)
1 mark · Multiply out a single bracket
- ✓
Algebra Grade 10 videos
Short lessons from South African teachers first. Videos load only when you tap play, to save your data.
Free on Android
Know exactly which skill is costing you marks.
Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.
Get NavyBlue free on Google Play
