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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
The images below show a graphic display calculator screen with different functions displayed as graphs.
a) Which function is trigonometric?
b) Which function is inversely proportional to \(x\)?
c) Which function is exponential?
d) Which function is proportional to \(x^3\)?
2. | GCSE Higher |
Match the equation with the letter of its graph
| Equation | Graph |
|---|---|
| $$y=3-\frac{10}{x}$$ | |
| $$y=2^x$$ | |
| $$y=\sin x$$ | |
| $$y=x^2+7x$$ | |
| $$y=x^2-8$$ | |
| $$y=2-x$$ |
3. | GCSE Higher |
The graph of y = f(x) is drawn accurately on the grid.
(a) Write down the coordinates of the turning point of the graph.
(b) Write down estimates for the roots of f(x) = 0
(c) Use the graph to find an estimate for f(-5.5).
4. | IB Analysis and Approaches |
Part of the function of \(y=f(x)\) is shown in the following diagram.
(a) Write down the value of \(f(1)\).
(b) Write down the value of \(ff(7)\).
(c) Sketch the graph of \(g(x)\) if \(g(x) = -f(x)-1\) on the same set of axes above.
5. | IB Standard |
A function is defined as \(f(x) = 2{(x - 3)^2} - 5\) .
(a) Show that \(f(x) = 2{x^2} - 12x + 13\).
(b) Write down the equation of the axis of symmetry of this graph.
(c) Find the coordinates of the vertex of the graph of \(f(x)\).
(d) Write down the y-intercept.
(e) Make a sketch the graph of \(f(x)\).
Let \(g(x) = {x^2}\). The graph of \(f(x)\) may be obtained from the graph of \(g(x)\) by the two transformations:
(f) Find the values of \(j\), \(k\) and \(s\).
6. | IB Standard |
Let \(f(x) = \frac{9x-3}{bx+9}\) for \(x \neq -\frac9b, b \neq 0\).
(a) The line \(x = 3\) is a vertical asymptote to the graph of \(f\). Find the value of b.
(b) Write down the equation of the horizontal asymptote to the graph of \(f\).
(c) The line \(y = c\) , where \(c\in \mathbb R\) intersects the graph of \( \begin{vmatrix}f(x) \end{vmatrix} \) at exactly one point. Find the possible values of \(c\).
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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
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