Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

12th August 2023

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

1
Quadratic Simultaneous Equations3 marks
Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 4, y = 112. Work out the positive value of x when y = 63.
3
3d Pythagoras and Trigonometry3 marks
A cuboid measures 12 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
4
Conditional Probability3 marks
A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
5
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?

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