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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
A motorbike moves from rest along a straight road. The graph below shows the speed, \(v\) in metres per second of the motorbike \(t\) seconds after it started to move.
(a) What is the maximum speed achieved by the motorbike.
(b) Calculate an estimate of the gradient of the graph at t = 10.
(c) Describe what your answer to part (b) represents.
(d) Work out an estimate for the distance the motorbike travels in the first 25 seconds of its journey by dividing the area under the graph into five strips of equal width.
2. | A-Level |
(a) Use the trapezium rule with 4 ordinates to estimate to 2 decimal places the value of
$$ \int^{\frac{2\pi}{3}}_0 \sin{x} \; \text{dx} $$(b) State whether this estimate is an overestimate or underestimate of the area.
[Note: If knowing about radians is not part of your course then \( \frac{2\pi}{3} \) can be replaced with 120°.]
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