Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

28th October 2025

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

1
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
2
Surds3 marks
Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).
3
Completing the Square3 marks
Work out the coordinates of the turning point of y = x^2 + 8x + 12.
4
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 3, y = 81. Work out the positive value of x when y = 576.
5
Vectors Proof Questions3 marks
In a vector proof you find that vector PQ = 4a + 2b and vector RS = 12a + 6b. What does this show about PQ and RS?

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