Functions — IGCSE Additional Mathematics 0606 past paper questions

Real questions on functions

The newest 20 of 197 written questions. Open one to see it on the real paper.

0606/11 · May/June 2026 · Q6b[2]
The function $f$ is such that $f (x) = 3 x^{2} + 8 x$ for $x ⩾ k$ , where $k$ is a constant. It is given that $f^{- 1}$ exists. $k$ has the least possible value for which $f^{- 1}$ exists. (b) Find the range of $f .$ See it on the paper →
0606/11 · May/June 2026 · Q6c[3]
The function $f$ is such that $f (x) = 3 x^{2} + 8 x$ for $x ⩾ k$ , where $k$ is a constant. It is given that $f^{- 1}$ exists. $k$ has the least possible value for which $f^{- 1}$ exists. (c) Find an expression for $f^{- 1}$ .See it on the paper →
0606/11 · May/June 2026 · Q6d(i)[1]
The function $f$ is such that $f (x) = 3 x^{2} + 8 x$ for $x \geq k$ , where $k$ is a constant. It is given that $f^{- 1}$ exists. $k$ has the least possible value for which $f^{- 1}$ exists. (d) The function $g$ is such that $g (x) = 3^{x}$ for $x > - 6$ . (i) Write down the domain of $g f$ .See it on the paper →
0606/13 · May/June 2026 · Q8b[1]
A function $f$ is defined by $f (x) = e^{2 x + 1}$ for $x \in R$ . (b) Find the domain of $f^{- 1}$ .See it on the paper →
0606/13 · May/June 2026 · Q8c[2]
A function $f$ is defined by $f (x) = e^{2 x + 1}$ for $x \in R$ . (c) Find an expression for $f^{- 1} (x)$ .See it on the paper →
0606/13 · May/June 2026 · Q8d[4]
4-mark “State” question — its maths and diagrams are best seen on the paper.
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0606/22 · May/June 2026 · Q4a[3]
3-mark “State” question — its maths and diagrams are best seen on the paper.
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0606/22 · May/June 2026 · Q8a[1]
The function $f$ is defined, for $x ⩾ - 1$ , by $f (x) = 1 + 2^{x}$ . (a) Find the range of $f$ .See it on the paper →
0606/22 · May/June 2026 · Q8b(i)[1]
The function $f$ is defined, for $x ⩾ - 1$ , by $f (x) = 1 + 2^{x}$ . (b) (i) Write down the domain of $f^{- 1}$ .See it on the paper →
0606/22 · May/June 2026 · Q8b(ii)[2]
The function $f$ is defined, for $x ⩾ - 1$ , by $f (x) = 1 + 2^{x}$ . (ii) Find an expression for $f^{- 1} (x)$ .See it on the paper →
0606/22 · May/June 2026 · Q8b(iii)[4]
4-mark “State” question — its maths and diagrams are best seen on the paper.
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0606/22 · May/June 2026 · Q8c(i)[1]
8 The function $f$ is defined, for $x ⩾ - 1$ , by $f (x) = 1 + 2^{x}$ . (c) The function $g$ is defined, for $x ⩾ - 1$ , by $g (x) = x (x + k)$ where $k$ is a constant. (i) Explain why $g f$ exists.See it on the paper →
0606/22 · May/June 2026 · Q8c(ii)[1]
The function $f$ is defined, for $x ⩾ - 1$ , by $f (x) = 1 + 2^{x}$ . (c) The function $g$ is defined, for $x ⩾ - 1$ , by $g (x) = x (x + k)$ where $k$ is a constant. (ii) Find an expression for $g f (x)$ .See it on the paper →
0606/22 · May/June 2026 · Q8c(iii)[2]
The function $f$ is defined, for $x ⩾ - 1$ , by $f (x) = 1 + 2^{x}$ . (c) The function $g$ is defined, for $x ⩾ - 1$ , by $g (x) = x (x + k)$ where $k$ is a constant. (iii) It is given that $g f (3) = 126$ . Find the value of $k$ .See it on the paper →
0606/12 · February/March 2026 · Q2b[2]
(b) The function $g$ is defined by $g (x) = 4 e^{x - 2} - 1$ for all real $x$ . Find an expression for $g^{- 1} (x)$ .See it on the paper →
0606/22 · February/March 2026 · Q1c[1]
The function $f$ is defined by $f (x) = 2 x^{2} - 6 x + 4$ for all real values of $x$ . (c) The function $g$ is defined by $g (x) = 2 x^{2} - 6 x + 4$ for $x ⩽ k$ , where $k$ is a constant. Given that $g$ has an inverse, state the largest possible value of $k$ .See it on the paper →
0606/22 · February/March 2026 · Q1d[3]
The function $f$ is defined by $f (x) = 2 x^{2} - 6 x + 4$ for all real values of $x$ . (d) The function $h$ is defined by $h (x) = e^{3 x} - 1$ for $x \leq 0$ . Given that $g h (x)$ exists, find $g h (x)$ , simplifying your answer.See it on the paper →
0606/22 · February/March 2026 · Q5b[5]
The diagram shows a design for a badge. [Diagram: A shape with vertices A, B, C. The inner boundary is a dashed equilateral triangle ABC. The outer boundary consists of three arcs: arc BC, arc CA, and arc AB. The length of side AB is indicated as $x$ cm.] $A B C$ is an equilateral triangle with side $x$ cm. The arcs $B C$ ...See it on the paper →
0606/11 · October/November 2025 · Q4a[1]
[Diagram: A circle in the first quadrant, tangent to the $y$ -axis, with the origin $O$ and axes $x$ and $y$ shown] Explain why this graph does **not** represent a function.See it on the paper →
0606/11 · October/November 2025 · Q4b[4]
(b) The table shows the graphs of four different functions. | | is one-one | is many-one | is its own inverse | |---|---|---|---| | [Diagram: A cubic-like curve with a local minimum and maximum, passing through the origin, with x-axis from 0 to 4 and y-axis up to 4] | | | | | [Diagram: A straight line with negative gr...See it on the paper →

What examiners said

Comprehensive responses • Fewer candidates identified the value of k using their answer from part (a). Limited responses • Errors included the incorrect use of x or k, or not making use of the answer to part (a).
— Examiner report, February/March 2026, 0606/22 Q1(c) (Cambridge)

Comprehensive responses • Most candidates used the correct order of operations to obtain an unsimplified expression. • Most candidates continued to correctly simplify their correct unsimplified expression to obtain an acceptable form of the answer. Limited responses • Some candidates did not simplify (e3x)2 correctly. • Some candidates used the incorrect order of operations.
— Examiner report, February/March 2026, 0606/22 Q1(d) (Cambridge)

Comprehensive responses • Many candidates showed a clear and correct method to find the area of the shape. • Many candidates were able to find the area of a relevant sector, relevant triangle and then a relevant segment. Limited responses • Most errors were due to an incorrect plan. There were several acceptable methods. Some candidates omitted relevant errors or added extra areas,
— Examiner report, February/March 2026, 0606/22 Q5(b) (Cambridge)