Grade 10 Maths · Functions · Paper 1

Graphs Grade 10

Real Graphs 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: 17 past paper questions
skills: 4 skills
videos: 4 videos

Try a Graphs exam question

No sign-up. Takes 3 minutes.

Question 5.3 · June 2025 · Paper 1 · Provincial · 3 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)

5.3 Determine the length of DB.(3)

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

Graphs skills

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

More Graphs Grade 10 questions and answers

Try each one on paper before you open the memo.

4. Question 4.1.1 · June 2025 · Paper 1 · Provincial · 3 marks
4.1 Given: $f (x) = - x^{2} + 4$
4.1.1 Sketch the graph of $f$ . Clearly indicate all the intercepts with the axes on the graph.(3)
Show the memo (1 tick)Memo
1. ✓
  Describe the correct sketch of the graphThe graph must be a parabola showing:
  1. A concave down shape (opening downwards)
  2. A y-intercept and turning point at $(0; 4)$
  3. Two x-intercepts at $(- 2; 0)$ and $(2; 0)$
  3 marks · Sketch a graph from its equation
5. Question WE23.3 · Siyavula Grade 8 Mathematics, 23 Graphs, The Cartesian plane, Worked example 23.3 · 2 marks
$Diagram for this question$
WE23.3 The graph below shows the Cartesian plane and four points. The points are labelled $A$ , $B$ , $C$ and $D$ . Which point has the coordinates $(5; 1)$ ?(2)
Show the memo (2 ticks)Memo
1. ✓
  Use the coordinatesIn $(5; 1)$ , $x = 5$ and $y = 1$ .
  From the origin, move $5$ units to the right (the $x$ -coordinate is positive), then $1$ unit upwards (the $y$ -coordinate is positive).
  1 mark · Plot and read points
2. ✓
  AnswerThe point that has the coordinates $(5; 1)$ is point $D$ .
  1 mark · Plot and read points
6. Question WE23.4 · Siyavula Grade 8 Mathematics, 23 Graphs, The Cartesian plane, Worked example 23.4 · 2 marks
$Diagram for this question$
WE23.4 The diagram shows the Cartesian plane and two points. The points are labelled $A$ and $B$ . Write down the coordinates of $A$ and $B$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Coordinates of B $B$ is $6$ units to the right of the origin and $5$ units above it.
  $B (6; 5)$
  1 mark · Plot and read points
2. ✓
  Coordinates of A $A$ lies on the $y$ -axis, so its $x$ -coordinate is $0$ . It is $6$ units below the origin.
  $A (0; - 6)$
  1 mark · Plot and read points
7. Question d · Siyavula Grade 8 Mathematics, 23 Graphs, Analysing and interpreting global graphs, Worked example 23.1 · 3 marks
Aliwal Shoal in KwaZulu-Natal is one of the best scuba-diving spots in South Africa. The graph shows the depths that a scuba diver reached during a $30$ minute dive.
Use the graph to answer the questions. $Diagram for this question$
d Complete each sentence by filling in the missing words:
(i) Between $0$ and $10$ minutes the depth of the scuba diver is ______ .
(ii) Between $10$ and $16$ minutes the depth of the scuba diver remains ______ .
(iii) Between $16$ and $30$ minutes the depth of the scuba diver is ______ .(3)
Show the memo (3 ticks)Memo
1. ✓
  0 to 10 minutesBetween $0$ and $10$ minutes the depth of the scuba diver is increasing.
  1 mark · Interpret or draw a global graph
2. ✓
  10 to 16 minutesBetween $10$ and $16$ minutes the depth of the scuba diver remains constant.
  1 mark · Interpret or draw a global graph
3. ✓
  16 to 30 minutesBetween $16$ and $30$ minutes the depth of the scuba diver is decreasing.
  1 mark · Interpret or draw a global graph
8. Question b · Siyavula Grade 8 Mathematics, 23 Graphs, Drawing global graphs, Worked example 23.2 · 2 marks
Forty learners completed a physical fitness test consisting of different exercises. $5$ learners completed the test in $10$ minutes, $7$ learners completed the test in $15$ minutes, $8$ learners completed the test in $20$ minutes, $11$ learners completed the test in $25$ minutes, $6$ learners completed the test in $30$ minutes and $3$ learners completed the test in $35$ minutes.
Use the information provided to answer the questions.
b Use the information provided to draw a suitable graph.(2)
Show the memo (2 ticks)Memo
1. ✓
  Plot the pointsPlot the points $(10; 5)$ , $(15; 7)$ , $(20; 8)$ , $(25; 11)$ , $(30; 6)$ and $(35; 3)$ with time (minutes) on the horizontal axis and number of learners on the vertical axis.
  1 mark · Plot and read points
2. ✓
  Points not joinedThe data is discrete, so the points are not joined by a line (see the graph). $Memo diagram$
  1 mark · Interpret or draw a global graph
9. Question 5.4 · November 2025 · Paper 2 · Provincial · 1 mark
Given: $f (x) = a sin (\frac{x}{2}) - 1$ and $g (x) = cos x + q$ , $x \in [- 90°; 270°]$

The graphs of $f$ and $g$ are drawn below.

Use the graphs to answer the following questions where $x \in [- 90°; 270°]$ : $Diagram for this question$
5.4 Write down the value(s) of $x$ where $f (x) - g (x) = - 2$ (1)
Show the memo (1 tick)Memo
1. ✓
  Answer $x = 0°$
  1 mark · Plot and read points
10. Question 6.5.1 · November 2024 · Paper 2 · Provincial · 1 mark
The graph of $f (x) = cos (x + 30°)$ in the interval of $x \in [- 120°; 150°]$ has been drawn in the diagram below. $Diagram for this question$
6.5 Use the graph to answer the following questions in the interval $x \in [- 120°; 150°]$ .

For which values of $x$ is:
6.5.1 $f$ having a minimum value?(1)
Show the memo (1 tick)Memo
1. ✓
  Answer $x = 150°$
  1 mark · Plot and read points

Graphs 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

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.

The NavyBlue app showing a learner's weak skills