Exam-Style Questions.

1.	GCSE Higher

Sketch the graph of \(y=0.5^x +1\) for \(0 \le x \le 5\) labeling the y intercept.

Worked Solution

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2.	GCSE Higher

(a) Use the red graphs to solve the simultaneous equations:

$$4x-7y=-47$$ $$3y=-5x$$

(b) Use the blue graph to find estimates for the solutions of the quadratic equation:

$$x^2-5x+3=0$$

Worked Solution

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3.	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 \(x^3\)?

Worked Solution

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4.	GCSE Higher

Match the equation with the letter of its graph

Equation	Graph
$$y=3-\frac{10}{x}$$
$$y=2^x$$
$$y=\sin x$$
$$y=x^2+7x$$
$$y=x^2-8$$
$$y=2-x$$

Worked Solution

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5.	IGCSE Extended

The table shows some values (rounded to one decimal place) for the function \(y=\frac{2}{x^2}-x, x\neq 0\).

\(x\)	-3	-2	-1	-0.5	0.5	1	2	3	4
\(y\)	3.2	2.5		8.5	7.5	1.0		-2.8

(a) Complete the table of values.

(b) Draw the graph of \(y=\frac{2}{x^2}-x\) for \(-3\le x \le -0.5\) and \(0.5\le x\le 4\).

(c) Use your graph to solve the equation \(\frac{2}{x^2}-x-3=0\)

(d) Use your graph to solve the equation \(\frac{2}{x^2}-x=1-2x\)

(e) By drawing a suitable tangent, find an estimate of the gradient of the curve at the point where x = 1.

(f) Using algebra, show that you can use the graph at \(y=0\) to find \(\sqrt[3]2\)

Worked Solution

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6.	GCSE Higher

(a) Solve the simultaneous equations.

$$4p + 2q = 1$$

$$p - q = 1$$

(b) Hence, for \(0^\circ \leq u \leq 360^\circ\) and \(0^\circ \leq v \leq 360^\circ\), solve the simultaneous equations.

$$4\sin u + 2\cos v = 1$$

$$\sin u - \cos v = 1$$

Worked Solution

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7.	GCSE Higher

(a) Find the coordinates of the point at which the curve \(y = k^x\) intersects the y-axis.

The equation of circle \(A\) is \(x^2+y^2=25\). This circle is translated by the vector \( \begin{pmatrix} 0 \\ 4 \\ \end{pmatrix} \) to give circle \(B\).

(b) Draw a sketch of circle \(B\) clearly labelling the points of intersection with the y-axis.

Worked Solution

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