Tawjihi (Palestinian General Secondary Examination), Scientific Stream · Mathematics

Further calculus and probability

18 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 18 questions

Find the area enclosed between the curve $y = x^{2}$ and the line $y = 2 x$ .
Find the area enclosed between the curve $y = x^{2}$ and the line $y = 3 x$ .
Find the area enclosed between the curve $y = x^{2}$ and the line $y = 4 x$ .
Find the area enclosed between the curve $y = x^{2}$ and the line $y = 6 x$ .
Find the area enclosed between the curve $y = x^{2}$ and the line $y = 5 x$ .
Find the area enclosed between the curve $y = x^{2}$ and the line $y = 7 x$ .
The curve $y = 2 x^{3} - 12 x^{2} + 18 x + 4$ has a maximum and a minimum point. Find the difference between the $y$ -coordinates of the maximum and the minimum point.
The curve $y = 2 x^{3} - 21 x^{2} + 60 x + 1$ has a maximum and a minimum point. Find the difference between the $y$ -coordinates of the maximum and the minimum point.
The curve $y = 2 x^{3} - 15 x^{2} + 24 x + 6$ has a maximum and a minimum point. Find the difference between the $y$ -coordinates of the maximum and the minimum point.
The curve $y = 2 x^{3} - 3 x^{2} - 12 x + 3$ has a maximum and a minimum point. Find the difference between the $y$ -coordinates of the maximum and the minimum point.
The curve $y = 2 x^{3} - 24 x^{2} + 72 x + 5$ has a maximum and a minimum point. Find the difference between the $y$ -coordinates of the maximum and the minimum point.
The curve $y = 2 x^{3} - 18 x^{2} + 30 x + 2$ has a maximum and a minimum point. Find the difference between the $y$ -coordinates of the maximum and the minimum point.
A bag contains 3 red, 4 blue and 5 white balls. Three balls are taken at random without replacement. Find the probability that one of each colour is taken.
A bag contains 4 red, 5 blue and 3 white balls. Three balls are taken at random without replacement. Find the probability that one of each colour is taken.
A bag contains 2 red, 6 blue and 4 white balls. Three balls are taken at random without replacement. Find the probability that one of each colour is taken.
A bag contains 5 red, 5 blue and 5 white balls. Three balls are taken at random without replacement. Find the probability that one of each colour is taken.
A bag contains 3 red, 7 blue and 2 white balls. Three balls are taken at random without replacement. Find the probability that one of each colour is taken.
A bag contains 6 red, 3 blue and 4 white balls. Three balls are taken at random without replacement. Find the probability that one of each colour is taken.

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