Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
25th December 2025
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 4 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3Histograms2 marks
On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4Surds3 marks
Simplify sqrt(32) + sqrt(2), giving your answer in the form a sqrt(b).
- 5Algebraic Fractions3 marks
Write 4/(x + 2) + 2/(x - 4) as a single fraction.
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