Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
5th September 2025
- 1Surds3 marks
Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 2Proof3 marks
Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 3Direct and Inverse Proportion Depth3 marks
y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 25.
- 4The Sine Rule3 marks
In triangle ABC, angle A is 55°, side a is 12 cm and side b is 8 cm. Work out the acute angle B, to 1 decimal place.
- 5Conditional Probability3 marks
A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
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