Algebra worksheet — GCSE Foundation

1.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

2.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.

3.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.

4.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

5.Solve 3x − 1 = 8

6.a = 2 and b = 5. Work out the value of ab².

7.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

8.Which expression means 'add 3 to n, then multiply the result by 4'?

9.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

10.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

11.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

12.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

13.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

14.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

15.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.