Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
22nd December 2025
- 1Bounds3 marks
A block has mass 410 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2Inverse and Composite Functions3 marks
f(x) = 3x - 7 and g(x) = 6x - 8. Work out fg(-2).
- 3Direct and Inverse Proportion Depth3 marks
y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 4Vectors Proof Questions3 marks
OACB is a parallelogram with vector OA = a and vector OB = q. P is the point dividing AB in the ratio 1 : 3. Write vector OP in terms of a and q.
- 5Probability Equation Questions3 marks
The probability of winning a game is 1/5. A player expects 14 wins. How many games did they play?
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