Algebra worksheet — GCSE Foundation

1.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

2.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

3.Which expression is equivalent to 4(x − 2) + 10?

4.Work out the value of 3n − 2 when n = 1

5.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

6.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

7.Solve the inequality 5x − 3 > 2x + 9.

8.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

9.A point lies on the y-axis. What can be said about the x-coordinate of that point?

10.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

11.Write down the y-intercept of the line with equation y = 3x + 8.

12.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

13.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

14.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

15.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?