Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
29th March 2026
- 1The Nth Term of a Quadratic Sequence2 marks
A quadratic sequence starts 1, 7, 15, 25. Work out the second difference, and the coefficient of n^2.
- 2Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 5, y = 125. Work out the positive value of x when y = 125.
- 33d Pythagoras and Trigonometry3 marks
A cuboid measures 10 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4Conditional Probability3 marks
A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5Histograms3 marks
A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
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