AQA GCSE · Mathematics 8300

Graphs: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Graphs.

10 questions23 marksFree, no account

Question 1

1 mark

A point is plotted on a coordinate grid in the second quadrant.
Which of the following coordinates could represent this point?

Question 2

1 mark

A quadratic function is given by the equation \( y = x^2 - 4x + 3 \).
By factorising the expression or otherwise, identify the roots of the function where the graph crosses the \( x \)-axis.

Question 3

1 mark

The straight line \(y = x + 2\) intersects the curve \(y = x^2 - 4\) at two points.
Find the positive \(x\)-coordinate of the point of intersection.

Question 4

1 mark

Which of the following is the correct equation for a straight line that is parallel to the line \( y = 2x + 7 \) and passes through the origin \( (0,0) \)?

Question 5

1 mark

A straight line passes through the point \( (0, 4) \) and the point \( (3, 10) \).
Find the equation of the line in the form \( y = mx + c \).

Question 6

2 marks

A straight line has the equation \( y = 5x + 9 \).
Write down the gradient and the coordinates of the y-intercept of this line.

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

A line passes through the points \(A(0, 5)\) and \(B(4, 13)\).
Find the equation of the line in the form \(y = mx + c\).

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

A circle has the equation \( x^2 + y^2 = 20 \).
Find the equation of the tangent to the circle at the point \( (2, 4) \).
Give your answer in the form \( y = mx + c \).

Write your answer out first, then check it against the worked solution.

Question 9

3 marks

Consider the linear function \(y = 3x + 4\).

a) Complete the following table of values for this function:

\(\begin{array}{|c|c|c|c|c|} \hline x & -1 & 0 & 1 & 2 \\ \hline y & & & & \\ \hline \end{array}\)

b) Use your table to state the coordinates of the point where the graph crosses the \(y\)-axis.

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

Line \(L\) passes through the points \(A(2, 5)\) and \(B(4, 13)\).

a) Calculate the gradient of line \(L\).

b) Find the equation of line \(L\) in the form \(y = mx + c\).

c) A second line, \(M\), is parallel to line \(L\) and passes through the origin. Write down the equation of line \(M\).

Write your answer out first, then check it against the worked solution.

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