Algebra worksheet — GCSE Higher

1.Which of these is an identity?

2.y = 5 − 2x. Work out the value of x when y = 11.

3.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.

4.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

5.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

6.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

7.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

8.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?

9.The point A(−6, 8) lies on the circle x² + y² = 100, whose centre is the origin O. The tangent to the circle at A crosses the y-axis at the point B. Work out the length of OB.

10.The point (5, −12) lies on the circle x² + y² = 169, which has centre (0, 0). Work out the equation of the tangent to the circle at (5, −12), giving your answer in the form y = mx + c.

11.Factorise x² − 3x − 10.

12.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

13.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

14.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.

15.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.