Grade 12 Maths · Functions · Paper 1

Function Types Grade 12

Real Function Types 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: 73 past paper questions
skills: 14 skills
videos: 14 videos

Try a Function Types exam question

No sign-up. Takes 3 minutes.

Question 4.1 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

The graph of

f (x) = \frac{4}{x - 3} + 4

is drawn below. M is the point where the asymptotes of

f

intersect. C and D are the x- and y-intercepts respectively of

f

. A is the point on

f

that is closest to M. Diagram for this question

4.1 Write down the coordinates of M.(2)

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

Function Types skills

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

More Function Types Grade 12 questions and answers

Try each one on paper before you open the memo.

4. Question 4.1 · May/June 2024 · Paper 1 · National (DBE) · 2 marks
Given: $g (x) = \frac{1}{x - 1} + 2$
4.1 Write down the equations of the asymptotes of $g$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Vertical asymptote $x = 1$
  1 mark · State the asymptotes
2. ✓
  Horizontal asymptote $y = 2$
  1 mark · State the asymptotes
5. Question 6.2 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
The graphs of $f (x) = x^{2} - 2 x - 3$ and $g (x) = m x + c$ are drawn below. D and E are the $x$ -intercepts and P is the $y$ -intercept of $f$ . The turning point of $f$ is T $(1; - 4)$ . The graphs of $f$ and $g$ intersect at P and E.
6.2 Calculate the coordinates of D and E.(3)
Show the memo (3 ticks)Memo
1. ✓
  Equate equation to zero $x^{2} - 2 x - 3 = 0$
  1 mark · Find the x-intercepts
2. ✓
  Both x-values $(x - 3) (x + 1) = 0$
  $x = 3$ or $x = - 1$
  1 mark · Solve a quadratic by factorising
3. ✓
  Final coordinates $D (- 1; 0), E (3; 0)$
  1 mark · Find the x-intercepts
6. Question 3.1.1 · March 2025 · Provincial · 2 marks
Given: $f (x) = (x - 1)^{2} - 9$
3.1 Properties of $f (x)$ .
3.1.1 Determine the turning point of $f$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify x-coordinate $x = 1$
  1 mark · Find turning point of a parabola
2. ✓
  Identify y-coordinate $y = - 9$
  Turning Point: $(1; - 9)$
  1 mark · Find turning point of a parabola
7. Question 3.1.2 · March 2025 · Provincial · 3 marks
3.1 Given: $f (x) = \frac{2 x + 3}{- x - 3}$

Given: $f (x) = \frac{2 x + 3}{- x - 3}$
3.1.2 Hence, determine the coordinates of the intercepts of $f$ with the axes.(3)
Show the memo (3 ticks)Memo
1. ✓
  Calculate y-intercept (x=0) $y = \frac{3}{0 + 3} - 2 = 1 - 2 = - 1$
  y-intercept: $(0; - 1)$
  1 mark · Find the y-intercept
2. ✓
  Let $y = 0$ $\frac{3}{x + 3} - 2 = 0$
  1 mark · Find the x-intercepts
3. ✓
  x-intercept $\frac{3}{x + 3} = 2$
  $x = - \frac{3}{2}$ , so the x-intercept is $(- \frac{3}{2}; 0)$
  1 mark · Find the x-intercepts
8. Question 4.2.3 · March 2025 · Provincial · 2 marks
4.2 Consider $g (x) = (\frac{1}{3})^{x}$ .
4.2.3 The graph of $h (x) = a (\frac{1}{3})^{x} + 7$ passes through the point $(- 2; 10)$ . Calculate the value of $a$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute point $10 = a (\frac{1}{3})^{- 2} + 7$
  $10 = a (3^{2}) + 7 = 9 a + 7$
  1 mark · Find equation of exponential graph
2. ✓
  Solve for a $3 = 9 a \to a = \frac{1}{3}$
  1 mark · Find equation of exponential graph
9. Question 3.1 · March 2024 · Paper 1 · Provincial · 2 marks
The diagram shows the graph of $f (x) = \frac{3}{x + 2} + 1$
3.1 Write down the equations of the asymptotes of $f$ .(2)
Show the memo (1 tick)Memo
1. ✓
  Identify vertical and horizontal asymptotes $x = - 2$
  $y = 1$
  2 marks · State the asymptotes
10. Question 4.2 · March 2024 · Paper 1 · Provincial · 3 marks
The sketch below shows the graphs of $h (x) = - x^{2} + 2 x + p$ and $t (x) = m x + 5$ . $D$ is the $x$ -intercept, and $B$ the $y$ -intercept of $t$ . $A$ is the $y$ -intercept of $h$ . $C$ is the $x$ -intercept of $h$ . $F$ is the turning point of $h$ . $E$ is a point on $t$ , such that $EC$ is parallel to the $y$ -axis. $A B$ is 2 units and $C D$ is 7 units.
4.2 Determine the coordinates of $F$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution into $x = \frac{- b}{2 a}$ $x = \frac{- b}{2 a} = \frac{- 2}{2 ( - 1 )}$
  1 mark · Find turning point of a parabola
2. ✓
  Value of x $x = 1$
  1 mark · Find turning point of a parabola
3. ✓
  Value of y $y = - (1)^{2} + 2 (1) + 3 = 4$ | $F (1; 4)$
  1 mark · Find turning point of a parabola

Function Types Grade 12 videos

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

Grade 9 Mathematics - Calculating the x and y intercepts of a straight lineMrs Townsend Mathematics - South Africa

1) Vertical line test gr 12Kevinmathscience

Draw Parabola Grade 11 | Part 1 | Grade 11 FunctionsKevinmathscience

Grade 12 Functions Student Question Find equation of p(x) if f(x) is shifted 2 units left | NTENTE \ New Technological Education

Functions : Horizontal Translations - Horizontal Shift - y = f(x - c) Examples and ExplanationRadford Mathematics

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