Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

1st October 2025

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

1
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
2
The Cosine Rule3 marks
A triangle has sides of 11 cm and 15 cm with an angle of 72° between them. Work out the third side, to 1 decimal place.
3
Conditional Probability3 marks
A bag holds 3 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
4
Histograms3 marks
On a histogram the bar for 30 < x <= 50 has a frequency density of 1.5. How many values are in that class?
5
Bounds3 marks
A rectangle is 4 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.

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