Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
23rd June 2026
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3Histograms2 marks
On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4Surds3 marks
Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 5Completing the Square3 marks
Work out the coordinates of the turning point of y = x^2 + 6x - 15.
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