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

Limits, differentiation and integration

64 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 64 questions

Evaluate $lim_{x \to 2} \frac{x ^{2} - 4}{x - 2}$ .
Evaluate $lim_{x \to 3} \frac{x ^{2} - 9}{x - 3}$ .
Evaluate $lim_{x \to 4} \frac{x ^{2} - 16}{x - 4}$ .
Evaluate $lim_{x \to 5} \frac{x ^{2} - 25}{x - 5}$ .
Evaluate $lim_{x \to 6} \frac{x ^{2} - 36}{x - 6}$ .
Evaluate $lim_{x \to 7} \frac{x ^{2} - 49}{x - 7}$ .
Evaluate $lim_{x \to 8} \frac{x ^{2} - 64}{x - 8}$ .
Evaluate $lim_{x \to 9} \frac{x ^{2} - 81}{x - 9}$ .
Evaluate $lim_{x \to 0} \frac{s i n 3 x}{1 x}$ .
Evaluate $lim_{x \to 0} \frac{s i n 5 x}{2 x}$ .
Evaluate $lim_{x \to 0} \frac{s i n 4 x}{1 x}$ .
Evaluate $lim_{x \to 0} \frac{s i n 6 x}{3 x}$ .
Evaluate $lim_{x \to 0} \frac{s i n 7 x}{2 x}$ .
Evaluate $lim_{x \to 0} \frac{s i n 8 x}{4 x}$ .
Evaluate $lim_{x \to \infty} \frac{3 x + 2}{1 x + 5}$ .
Evaluate $lim_{x \to \infty} \frac{4 x + 1}{2 x + 3}$ .
Evaluate $lim_{x \to \infty} \frac{6 x + 5}{3 x + 1}$ .
Evaluate $lim_{x \to \infty} \frac{5 x + 7}{2 x + 4}$ .
Evaluate $lim_{x \to \infty} \frac{8 x + 3}{4 x + 1}$ .
Evaluate $lim_{x \to \infty} \frac{9 x + 2}{3 x + 7}$ .
If $f (x) = 2 x^{3} - 3 x^{2} + 5 x$ , find $f^{'} (2)$ .
If $f (x) = x^{3} + 4 x^{2} - 2 x$ , find $f^{'} (3)$ .
If $f (x) = 3 x^{3} - x^{2} + 6 x$ , find $f^{'} (1)$ .
If $f (x) = 4 x^{3} + 2 x^{2} - 7 x$ , find $f^{'} (2)$ .
If $f (x) = 5 x^{3} - 4 x^{2} + x$ , find $f^{'} (3)$ .
If $f (x) = 2 x^{3} + 6 x^{2} - x$ , find $f^{'} (1)$ .
Find the derivative of $y = (2 x + 1)^{3}$ at $x = 1$ .
Find the derivative of $y = (3 x - 2)^{4}$ at $x = 1$ .
Find the derivative of $y = (5 x + 1)^{2}$ at $x = 0$ .
Find the derivative of $y = (2 x - 1)^{5}$ at $x = 1$ .
Find the derivative of $y = (4 x + 2)^{3}$ at $x = 0$ .
Find the derivative of $y = (3 x - 1)^{2}$ at $x = 1$ .
Find the gradient of $y = \frac{2 x}{x + 1}$ at $x = 2$ .
Find the gradient of $y = \frac{3 x}{x + 2}$ at $x = 2$ .
Find the gradient of $y = \frac{4 x}{x + 1}$ at $x = 3$ .
Find the gradient of $y = \frac{1 x}{x + 5}$ at $x = 2$ .
Find the gradient of $y = \frac{5 x}{x + 3}$ at $x = 1$ .
Find the gradient of $y = \frac{6 x}{x + 2}$ at $x = 2$ .
Find the gradient of $y = sin 2 x$ at $x = 0$ .
Find the gradient of $y = sin 3 x$ at $x = 0$ .
Find the gradient of $y = sin 4 x$ at $x = 0$ .
Find the gradient of $y = sin 5 x$ at $x = 0$ .
Find the gradient of $y = sin 2 x$ at $x = 1$ .
Find the gradient of $y = sin 3 x$ at $x = 1$ .
Find the $x$ -coordinates of the stationary points of $y = 2 x^{3} - 12 x^{2} + 18 x + 1$ .
Find the $x$ -coordinates of the stationary points of $y = 2 x^{3} - 18 x^{2} + 48 x + 1$ .
Find the $x$ -coordinates of the stationary points of $y = 2 x^{3} - 18 x^{2} + 30 x + 1$ .
Find the $x$ -coordinates of the stationary points of $y = 2 x^{3} - 6 x^{2} - 18 x + 1$ .
Find the $x$ -coordinates of the stationary points of $y = 2 x^{3} - 24 x^{2} + 72 x + 1$ .
Find the $x$ -coordinates of the stationary points of $y = 2 x^{3} + 3 x^{2} - 12 x + 1$ .
Evaluate $\int_{0}^{2} (2 x + 3) d x$ .
Evaluate $\int_{0}^{3} (4 x + 1) d x$ .
Evaluate $\int_{0}^{1} (3 x + 5) d x$ .
Evaluate $\int_{0}^{2} (6 x + 2) d x$ .
Evaluate $\int_{0}^{3} (2 x + 7) d x$ .
Evaluate $\int_{0}^{1} (8 x + 1) d x$ .
Evaluate $\int_{0}^{2} (4 x + 4) d x$ .
Evaluate $\int_{0}^{3} (6 x + 3) d x$ .
Find the area bounded by $y = 2 x^{2}$ , the $x$ -axis and the lines $x = 1$ and $x = 3$ .
Find the area bounded by $y = 3 x^{2}$ , the $x$ -axis and the lines $x = 1$ and $x = 2$ .
Find the area bounded by $y = 6 x^{2}$ , the $x$ -axis and the lines $x = 2$ and $x = 3$ .
Find the area bounded by $y = 3 x^{2}$ , the $x$ -axis and the lines $x = 0$ and $x = 2$ .
Find the area bounded by $y = 3 x^{2}$ , the $x$ -axis and the lines $x = 1$ and $x = 4$ .
Find the area bounded by $y = 3 x^{2}$ , the $x$ -axis and the lines $x = 2$ and $x = 4$ .

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