Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
25th November 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 5 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 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 4Surds3 marks
Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 5Completing the Square3 marks
Write x^2 + 8x + 13 in the form (x + a)^2 + b.
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