Printable · GCSE Higher · ages 14-16
Algebra worksheet — GCSE Higher
Fifteen questions across the algebra statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
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Algebra worksheet — GCSE Higher
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- 1.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.
- 2.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.
- 3.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
- 4.Which of these equations is equivalent to 5x − 2 = 3x + 8?
- 5.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.
- 6.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.y = x² + 1
- 7.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.
- 8.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.
- 9.Solve x² − 5x + 6 = 0 by factorising.
- 10.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.y = 3x − 2
- 11.Make x the subject of the formula y = x/2 − 5.y = x
- 12.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?
- 13.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.y = x² + 12x + 40
- 14.Work out the period of the graph of y = cos x, in degrees.y = cos(x)
- 15.Expand and simplify 2(a + 6) − 2(a − 7)
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