Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
23rd August 2025
- 1Histograms2 marks
On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2Bounds3 marks
A car covers 640 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3Inverse and Composite Functions3 marks
f(x) = 5x + 11. Work out the inverse function f^-1(x).
- 4Velocity Time Graphs3 marks
A cyclist speeds up steadily from 5 m/s to 19 m/s over 4 seconds. Use the area under the velocity-time graph to find the distance travelled.
- 5Proof of the Circle Theorems2 marks
In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
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