Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
26th September 2025
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 4Surds3 marks
Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 5Inverse and Composite Functions3 marks
f(x) = 3x + 9. Work out the inverse function f^-1(x).
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