Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 2(x + 6)?

2.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

3.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

4.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

5.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

6.Which of these equations describes a vertical line?

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

8.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

9.Which of these is an identity?

10.Make x the subject of the formula y = 3(x + 2).

11.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

12.Write down the first four terms of the sequence with nth term 6n − 5.

13.Which expression is equivalent to 4(x − 2) + 10?

14.Make x the subject of the formula y = (x − 4)/5.

15.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.