Algebra worksheet — GCSE Foundation

1.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.

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

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

4.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

5.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

6.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

7.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

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

9.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

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

11.Which of these equations gives a straight-line graph when plotted?

12.Make x the subject of the formula y = x/2 − 5.

13.Which of these equations is equivalent to 5x − 2 = 3x + 8?

14.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

15.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.