Algebra worksheet — GCSE Foundation

1.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.

2.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

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

4.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

5.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

6.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

7.Simplify (5x² + 3x − 2) − (2x² − x + 5)

8.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

9.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

10.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

11.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

12.Solve the inequality 2(3x − 1) ≥ 4x + 8.

13.Write down the expression that means the same as (x + 7) ÷ 4.

14.The point B has coordinates (−2, −2). In which quadrant is B?

15.Solve 2x² − 32 = 0.