Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

13th February 2025

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

1
Surds3 marks
Simplify sqrt(48) + sqrt(27), giving your answer in the form a sqrt(b).
2
Proof3 marks
Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
3
Direct and Inverse Proportion Depth3 marks
y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
4
The Cosine Rule3 marks
A triangle has sides of 12 cm and 9 cm with an angle of 65° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 6 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

You are looking at an earlier sheet. Today's sheet is the one that adds a day.

Your run is kept in this browser only, and there is no account.

Every sheet is deterministic: the same date always regenerates the same five questions. All of February 2025, including the monthly compilation PDF.