Algebra worksheet — GCSE Foundation

1.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

2.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?

3.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

4.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

5.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

6.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.

7.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.

8.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.

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

10.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

11.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

12.Work out the value of m² + 3m when m = −2

13.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

14.Which of these is an expression?

15.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.