Graphs of Functions (OCR GCSE Maths: Higher): Exam Questions

Complete the table of values for $y=2^x$

On the grid, draw the graph of $y=2^x$ for values of $x$ from $—2\mathrm{to}3$

Complete this table for $y=x^2-4$.

Draw the graph of $y=x^2-4$ for values of $x$ from $-3$ to $3$.

Use the graph to solve the equation $x^2-4=1$.

Give your answers to $1$ decimal place.

Complete the table of values for $y=x^2—x—6$

On the grid, draw the graph of $y=x^2—x—6$ for values of $x$ from $—3\mathrm{to}3$

Use your graph to find estimates of the solutions to the equation $x^2-x-6=—2$

The diagram shows part of a sketch of the curve $y=\sin x^{\circ }.$

Write down the coordinates of the point $P$.

Write down the coordinates of the point $Q$.

Here are some graphs.

In the table below, match each equation with the letter of its graph.

On the grid below, sketch the graph of $y=\text{sin} x+2$ for $0°\le x\le 720°$.

Complete the table of values for $y=x^2-3x+2$

On the grid, draw the graph of $y=x^2—3x+2$ for values of $x$ from $—1\mathrm{to}5$

Find estimates for the solutions of the equation $x^2-3x+2=4$

The diagram shows the graph of $y=x^2+8x-9$.

The graph crosses the $x$-axis at $x=-9$ and $x=1$.

Write down the coordinates of the point where the graph crosses the $y$-axis.

Write down the equation of the line of symmetry of the graph.

Complete the table of values for $y=x^2-3x+1$

On the grid, draw the graph of $y=x^2—3x+1$ for values of $x$from $—2\mathrm{to}4$

By drawing a suitable straight line on the grid, find estimates for the solutions of

$x^2-3x+1=3$

On the grid, draw the graph of $x^2+y^2=4$

On the grid, sketch the graph of $y=\cos x\mathrm{for}{0}^{°}⩽x⩽{360}^{°}$

Sketch the graph of $y=\cos x^{°}\mathrm{for}0⩽x⩽360$

Sketch the graph of $y=\sin x$ for $0°<x<360°$

The number of gannets on an island is assumed to follow this exponential growth model.

N = 0.45 × 1.07^x

N is the number of gannets, in thousands.
x is the number of years after 1st January 2010.

Complete the table for N = 0.45 × 1.07^x.

Draw the graph of $\mathrm{N}=0.45\times 1.{07}^{\mathrm{x}}$

Use the graph to find the year when the gannet population is predicted to reach 1000.

Part of the graph of$y=2x^2-4x-1$ is shown on the grid.

Use the graph to find estimates for the solutions of the equation $2x^2-4x-1=0$

Give your solutions correct to one decimal place.

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation $x^2-x-1=0$

Show your working clearly.

Give your solutions correct to one decimal place.

Complete the table of values for $y=x^2–5x+6$

On the grid, draw the graph of $y=x^2–5x+6\mathrm{for}0⩽x⩽5$

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation

$x^2–5x=x–7$

Write $3x^2-12x+7$ in the form $a{(x+b)}^2+c$

The line $\mathbf{L}$ is the line of symmetry of the curve with equation $y=3x^2-12x+7$

Using your answer to part (a) or otherwise, write down an equation of $\mathbf{L}$.

Circle the point that lies on the curve  $y=x^2–4x+1$

Here is a sketch of $y=\cos x$for values of $x$ from 0° to 360°

$\alpha °$ is an acute angle.
$\cos \alpha °=k$

Circle the value of $\cos (180°–\alpha °)$

Circle the value of $\cos$$(360°+\alpha °)$

Write $x^2+6x-11$ in the form $(x+a{)}^2-b$, where $a$ and $b$ are integers.

Use your answer to part (a) to find the coordinates of the turning point of the graph of $y=x^2+6x-11$.

On the grid, construct the graph of $x^2+y^2=16$

Find estimates for the solutions of the simultaneous equations

$\begin{array}{rcl}{x}^2+y^2& =& 16\\ y& =& 2x+1\end{array}$

On the grid, draw the graph of $x^2+y^2=12.25$

Hence find estimates for the solutions of the simultaneous equations

$\begin{array}{rcl}{x}^2+y^2& =& 12.25\\ 2x+y& =& 1\end{array}$

Complete the table of values for $y=x^2—2x$

On the grid, draw the graph of $y=x^2—2x$for values of $x$ from $—2\mathrm{to}4$

Solve  $x^2-2x-2=1$

Complete the table of values for $y=x^2—2x—1$

On the grid, draw the graph of  $y=x^2—2x—1$ for values of $x$ from $—2\mathrm{to}4$

Solve   $x^2-2x-1=x+3$

The diagram shows the graph of $y=x^2—4x—2$

Use the graph to find estimates for the solutions of

i) $x^2-4x-2=0$

[1]

ii) $x^2-4x-6=0$

[2]

Use the graph to find estimates for the values of $x$ that satisfy the simultaneous equations

$\begin{array}{rcl}y& =& x^2—4x—2\\ & & \\ x+y& =& 6\end{array}$

Construct the graph of $x^2+y^2=9$

By drawing the line $x+y=1$ on the grid, solve the equations $$\begin{gathered} x^2+y^2=9 \\ x+y=1 \end{gathered}$$

The graph of $y=k^x$, where $k$ is a positive constant, is shown above.

Find the value of $k$.

The graph of $y=\sin x°$ for values of $x$ from $—270\mathrm{to}+270$ is shown above.

On the same axes, draw the graph of $y=1—\sin x°$ for values of $x$ from $—270\mathrm{to}+270$

Write  $x^2-10x+22$  in the form  ${\left(x-a\right)}^2-b$.

Sketch the graph of $y=x^2-10x+22$ .

Show clearly the coordinates of any turning points and the value of the $y$-intercept.

The graph of $y=2x^2+3x-9$ is drawn below.

Use the graph to solve $2x^2+3x-9=0$.

$$\begin{gathered} x=............................\mathrm{or} \\ x=............................ \end{gathered}$$

The equation 2x² + x − 4 = 0 can be solved by finding the intersection of the graph of y = 2x² + 3x − 9  and the line y = ax + b.

i) Find the value of a and the value of b.

$\begin{array}{rcl}a& =& .............................\\ b& =& ..............................\left[2\right]\end{array}$