Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
10th November 2025
- 1Bounds3 marks
A block has mass 660 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2Factorising Harder Quadratics3 marks
Solve 12x^2 - 11x + 2 = 0.
- 3Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 4The Cosine Rule3 marks
A triangle has sides of 5 cm and 13 cm with an angle of 43° between them. Work out the third side, to 1 decimal place.
- 5Conditional Probability3 marks
A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
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