Algebra worksheet — GCSE Foundation

1.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

2.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

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

4.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

5.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

6.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

8.Solve 5(x + 3) = 40

9.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

10.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

11.Which of these is a formula?

12.Which expression means 'y squared, multiplied by 3'?

13.Expand and simplify 2(a + 6) − 2(a − 7)

14.Make b the subject of the formula a = 5b.

15.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.