Daily Practice · Higher Plus

Daily Practice - Higher Plus

Grades 8-9 - exam-stretch algebra, geometry and reasoning.

23rd July 2026

5 questions · 15 marks · Grades 8-9 · 51 question types in this band

1
Perpendicular Lines and the equation of a tangent3 marks
The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
2
Conditional Probability3 marks
A bag holds 5 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
3
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
4
Surds3 marks
Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
5
Factorising Harder Quadratics3 marks
Solve 12x^2 - 13x + 3 = 0.

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