Grade 10 Maths · Paper 1

Functions 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: 41 past paper questions
skills: 29 skills
videos: 29 videos

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Question 5.1 · June 2025 · Paper 1 · Provincial · 2 marks

Given:

f (x) = - x + 1

and

g (x) = \frac{- 2}{x} + 2

, which are not drawn to scale. R and S are points of intersection of the graphs.

DBQ is a line perpendicular to the x-axis with D and B on

g

and

f

respectively. The coordinates of Q are

(- 1; 0)

5.1 Determine the equation of the line of symmetry of

g

with a negative gradient.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

What's in Functions Grade 10

Each skill is one thing a memo gives a tick for. Tap a skill for its own questions, notes and videos.

Graphs2 past paper questions

The Linear Function (Straight Line Graph)3 past paper questions

The Quadratic Function (The Parabola)2 past paper questions

The Hyperbolic Function (The Hyperbola)1 past paper questions

The Exponential Function6 past paper questions

Characteristics of Functions2 past paper questions

Graph Interpretation6 past paper questions

Mathematical Modelling with Functions

Trigonometric Functions21 past paper questions

Interpretation of Trigonometric Functions

More Functions Grade 10 questions and answers

Try each one on paper before you open the memo.

1. Question 6.2 · November 2024 · Paper 1 · Provincial · 2 marks
The graphs of $f (x) = \frac{4}{x} - 2$ and $g (x) = m x + c$ are drawn below. A(4; 4), B, D(0; -4) and E are points on g. B is the x-intercept of both f and g. B and E are the points of intersection of f and g. AC is parallel to the y-axis, with C a point on f.
6.2 Write down the range of f.(2)
Show the memo (1 tick)Memo
1. ✓
  Identify range from horizontal asymptote $y \in R; y \neq = - 2$
  2 marks · State the domain and range
2. Question 5.1 · June 2024 · Paper 1 · Provincial · 2 marks
The graph of $f (x) = 2^{x + 2} + k$ is drawn below.
5.1 Use the laws of indices to show that $2^{x + 2} + k$ is the same as $4. 2^{x} + k$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Split the exponent $2^{x + 2} + k = 2^{x} \cdot 2^{2} + k$
  1 mark · Use the laws of exponents
2. ✓
  Simplify $= 4 \cdot 2^{x} + k$
  1 mark · Use the laws of exponents
3. Question 3.3 · June 2024 · Paper 2 · Provincial · 3 marks
The sketch below shows the graph of $f (x) = cos x$ and $g (x) = 2 sin x$ for the interval $x \in [0^{\circ}; 36 0^{\circ}]$ .
3.3 Determine the range of $m (x)$ if $m (x) = - 4 f (x) + 1$ .(3)
Show the memo (2 ticks)Memo
1. ✓
  Substitute function definition $m (x) = - 4 cos x + 1$
  1 mark · Find trig graph amplitude and range
2. ✓
  Determine rangeRange of $f (x)$ is $[- 1; 1]$
  Min: $- 4 (1) + 1 = - 3$
  Max: $- 4 (- 1) + 1 = 5$
  Range: $y \in [- 3; 5]$
  2 marks · Find trig graph amplitude and range
4. Question 6.1.2 · September 2024 · Provincial · 4 marks
6.1 Given: $f (x) = 2 sin x + 1$ and $g (x) = tan x$ , where $x \in [0^{\circ}; 27 0^{\circ}]$
6.1.2 On the same set of axes provided on the DIAGRAM SHEET, sketch the graphs of f and g. Clearly indicate all intercepts with the axes, as well as turning points and end points of the graphs.(4)
Show the memo (4 ticks)Memo
1. ✓
  Shape of fSine curve for $f (x) = 2 sin x + 1$ from $(0^{\circ}; 1)$ to $(27 0^{\circ}; - 1)$
  1 mark · Sketch a trig graph
2. ✓
  Shape of gTan curve for $g (x) = tan x$ through $(0^{\circ}; 0)$ and $(18 0^{\circ}; 0)$
  1 mark · Sketch a trig graph
3. ✓
  Asymptotes of g $x = 9 0^{\circ}$ and $x = 27 0^{\circ}$
  1 mark · Sketch a trig graph
4. ✓
  Turning point of f $(9 0^{\circ}; 3)$
  1 mark · Sketch a trig graph
5. Question 4.4 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram is a right-angled triangle has sides a, b and c and the $\hat{B} = 9 0^{\circ}$ .
4.4 Solve for x, correct to two decimal places: $3 + sec x = 5$ and $0^{\circ} \leq x \leq 9 0^{\circ}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate sec x $sec x = 2$
  1 mark · Solve a linear equation
2. ✓
  Convert to cos x $cos x = \frac{1}{2}$
  1 mark · Use cosec, sec and cot
3. ✓
  Solve for x $x = 6 0^{\circ}$
  1 mark · Calculate an angle from a ratio

Functions Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Plotting Points on a Coordinate Plane | All 4 QuadrantsMath with Mr. J

Algebra Grade 9: SubstitutionKevinmathscience

HOW to READ and INTERPRET GRAPHS in Mathematics - Grade 8SHFT - Your Learning

Parabola Grade 10: How to drawKevinmathscience

Straight line graphs grade 9: Gradient Part 1Kevinmathscience

Straight line graphs grade 9: DrawKevinmathscience

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