Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

15th March 2025

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

1
Bounds3 marks
A car covers 560 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
2
Completing the Square3 marks
Write x^2 + 14x + 1 in the form (x + a)^2 + b.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
4
The Cosine Rule3 marks
A triangle has sides of 15 cm and 12 cm with an angle of 27° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 6 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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