Algebra worksheet — GCSE Foundation

1.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

2.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

3.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

4.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.

5.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

6.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

7.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.

8.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.

9.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

10.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

11.Write down the expression that means the same as m² × m × 3.

12.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

13.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

14.Simplify 2a + 3b − a + 2b − b

15.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.