Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

2.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

3.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

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

5.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

6.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

7.How many turning points does the graph of y = x² − 7x + 10 have?

8.Solve 3x − 5 = 4.

9.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.

10.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

11.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

12.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

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

14.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

15.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.