Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
26th October 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 5 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3Histograms2 marks
On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4Bounds3 marks
x = 91 and y = 42, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5Proof3 marks
Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
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