Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

22nd October 2023

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

1
Bounds3 marks
x = 108 and y = 52, each correct to the nearest whole number. Work out the upper bound of x - y.
2
Completing the Square3 marks
Write x^2 - 10x - 4 in the form (x + a)^2 + b.
3
Direct and Inverse Proportion Depth3 marks
y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
4
The Cosine Rule3 marks
A triangle has sides of 5 cm and 7 cm with an angle of 122° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 4 red, 3 blue and 4 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 October 2023, including the monthly compilation PDF.