Grade 11 Maths · Functions · Paper 1

Interpretation of Trigonometric Functions Grade 11

Real Interpretation of Trigonometric Functions past paper questions and answers from 2023 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: 22 past paper questions
skills: 6 skills
videos: 6 videos

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Question 5.5 · November 2025 · Paper 1 · Provincial · 2 marks

The graphs of

f (x) = \frac{a}{x + p} + q

and

g (x) = \frac{x}{3} + c

are drawn below. C

(3; - 1)

is the point of intersection between the asymptotes of

f

. A and B are

x

- and

y

-intercepts of

f

and

g

respectively. E

(4; 2)

is a point on

f

in the first quadrant. $Diagram for this question$

5.5 Determine the value of

x

, for which

f (x) \cdot g (x) < 0

(2)

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

Interpretation of Trigonometric Functions skills

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

More Interpretation of Trigonometric Functions Grade 11 questions and answers

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4. Question 6.4.2 · November 2025 · Paper 1 · Provincial · 3 marks
The graphs of $f (x) = - x^{2} - 6 x$ and $g (x) = a x^{2} + b x$ are drawn below. $g$ is the reflection of $f$ along the $x$ -axis. A and B $(- 5; n)$ are symmetrical on $f$ along $x = - p$ , i.e. the axes of symmetry. $Diagram for this question$
6.4 Determine the value(s) of $k$ for which:
6.4.2 $f (x + k)$ will have two real roots that have different signs.(3)
Show the memo (2 ticks)Memo
1. ✓
  $x$ -values $- x^{2} - 6 x = 0$
  $x^{2} + 6 x = 0$
  $x (x + 6) = 0$
  $x = 0$ or $x = - 6$
  1 mark · Find the x-intercepts
2. ✓
  Answer $∴ - 6 < k < 0$
  2 marks · Shift a graph
5. Question 6.2 · November 2024 · Paper 2 · Provincial · 2 marks
The graph of $f (x) = cos (x + 30°)$ in the interval of $x \in [- 120°; 150°]$ has been drawn in the diagram below. $Diagram for this question$
6.2 Write down the range of $h (x) = f (x + 60°) + 1$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Correct interval $0$ to $2$
  1 mark · Find trig graph amplitude and range
2. ✓
  Correct notation $y \in [0; 2]$ or $0 \leq y \leq 2$
  1 mark · Find trig graph amplitude and range
6. Question 5.6 · November 2024 · Paper 1 · Provincial · 3 marks
The lines $y = - x + 4$ and $y = x - 2$ are the axes of symmetry of the function $f (x) = \frac{- 3}{x + p} + q$ .
5.6 For which values of $x$ will $x . f (x) \leq 0$ ?(3)
Show the memo (2 ticks)Memo
1. ✓
  $x \leq 0$ $x \leq 0$
  1 mark · Solve product inequality from graphs
2. ✓
  $3 < x \leq 6$ $3 < x \leq 6$
  2 marks · Solve product inequality from graphs
7. Question 6.4 · November 2024 · Paper 1 · Provincial · 3 marks
Sketched below is the graph of $f (x) = x^{2} - 4 x - 5$ for $x \in (- \infty; 6]$ .

A and B are the $x$ -intercepts and C the $y$ -intercept of $f$ . $Diagram for this question$
6.4 Write down the equation of $g$ in the form $g (x) = a x^{2} + b x + c$ , if it is given that $g (x)$ is obtained by shifting $f (x)$ two units to the right and five units up.(3)
Show the memo (3 ticks)Memo
1. ✓
  $(x - 2)$ $g (x) = (x - 2)^{2} - 4 (x - 2) - 5 + 5$
  1 mark · Shift a graph
2. ✓
  $+ 5$ $... + 5$
  1 mark · Shift a graph
3. ✓
  Answer $= x^{2} - 4 x + 4 - 4 x + 8 - 5 + 5$
  $= x^{2} - 8 x + 12$
  1 mark · Collect like terms
8. Question 6.3 · November 2024 · Paper 2 · Provincial · 2 marks
6.3 For which values of $x$ would $f (x) - g (x) \leq 0$ ; $x \in [0°; 180°]$ ?(2)
Show the memo (2 ticks)Memo
1. ✓
  Interval $f (x) \leq g (x)$
  $60° \leq x \leq 180°$
  1 mark · Solve an inequality from a graph
2. ✓
  NotationOR $x \in [60°; 180°]$
  1 mark · Solve an inequality from a graph
9. Question 5.6 · November 2023 · Paper 1 · Provincial · 2 marks
The diagram below shows the graph of $f (x) = \frac{a}{x + p} + q$ . The asymptotes of $f$ intersect at $(- 3; - 1)$ and $f$ cuts the $x$ -axis at $x = - 5$ . $Diagram for this question$
5.6 For which values of $x$ is $f (x) \geq 0$ ?(2)
Show the memo (1 tick)Memo
1. ✓
  Answer $- 5 \leq x < - 3$
  2 marks · Solve an inequality from a graph
10. Question 7.7 · November 2023 · Paper 1 · Provincial · 2 marks
The diagram below shows the graphs of $f (x) = a x^{2} + b x + c$ and $g (x) = m x + q$ . D $(- 1; 4)$ and F $(1; 6)$ are points of intersection of $f$ and $g$ . T and U are the $x$ -intercepts of $f$ , E $(0; 6)$ the $y$ -intercept of $f$ and S is the $x$ -intercept of $g$ . VW is a straight line drawn parallel to the $y$ -axis. $Diagram for this question$
7.7 Determine the values of $x$ for which $f (x) - g (x) \leq 0$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  $x \leq - 1$ $x \leq - 1$
  1 mark · Solve an inequality from a graph
2. ✓
  $x \geq 1$ or $x \geq 1$
  1 mark · Solve an inequality from a graph

Interpretation of Trigonometric Functions Grade 11 videos

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

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

f(x) bigger than 0 | Grade 11 FunctionsKevinmathscience

Hyperbola Increasing Decreasing | Grade 11 FunctionsKevinmathscience

for which values of x is f(x).g(x)≥0. functions grade 12Benit mathematics

Trig functions grade 11 and 12: Determine EquationKevinmathscience

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