Algebra worksheet — GCSE Foundation

1.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

2.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

3.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

4.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

5.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

6.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

7.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

8.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

9.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

10.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

11.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

12.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

13.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

14.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

15.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.