Algebra worksheet — GCSE Foundation

1.y = x + 4. Work out the value of y when x = 3.

2.Write down the gradient of the line with equation y = 7x − 2.

3.Work out the value of 5m² + 3m when m = −2.4

4.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

5.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

6.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

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

8.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

11.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

12.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

13.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

14.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

15.Solve 3x − 5 = 4.