Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

29th January 2026

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 7 cm with an angle of 115° between them. Work out the third side, to 1 decimal place.
3
Conditional Probability3 marks
A bag holds 5 red, 6 blue and 5 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 60 < x <= 80 has a frequency density of 1.2. How many values are in that class?
5
Surds3 marks
Simplify sqrt(48) + sqrt(3), giving your answer in the form a sqrt(b).

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