Question 1

Find the slope of the line joining points $(2,5)$ and $(-3,-4)$

Accepted Answer

$\frac{9}{5}$

Answer

$\frac{5}{9}$

Answer

$\frac{4}{9}$

Answer

$-\frac{9}{5}$

Question 2

The equation of line passing through $(2,-3)$ and perpendicular to $2x - 3y + 7 = 0$ is

Accepted Answer

$3x + 2y = 0$

Answer

$3x - 2y = 0$

Answer

$2x - 3y = 0$

Answer

$2x + 3y = 0$

Question 3

Find the coordinates where line $2x + y - 5 = 0$ meets the x-axis

Accepted Answer

$(2.5,0)$

Answer

$(0,-5)$

Answer

$(0,5)$

Answer

$(5,0)$

Question 4

The distance between lines $3x - 4y + 2 = 0$ and $3x - 4y - 6 = 0$ is

Accepted Answer

$\frac{8}{5}$

Answer

$\frac{5}{8}$

Answer

$2$

Answer

$1$

Question 5

The point of intersection of lines $x + 2y = 7$ and $2x - y = 4$ is

Accepted Answer

$(3,2)$

Answer

$(1,4)$

Answer

$(2,3)$

Answer

$(4,1)$

Question 6

Equation of the line through $(1,2)$ and parallel to $x - 3y + 7 = 0$ is

Accepted Answer

$x - 3y + 5 = 0$

Answer

$x + 3y - 5 = 0$

Answer

$3x - y + 5 = 0$

Answer

$x - 3y - 7 = 0$

Question 7

Find the area of triangle formed by lines $x=0$, $y=0$, and $x + y = 5$

Accepted Answer

$12.5$

Answer

$10$

Answer

$25$

Answer

$20$

Question 8

If a line passes through $(h,2)$ and $(3,4)$ and has slope $1$, find $h$

Accepted Answer

$1$

Answer

$2$

Answer

$3$

Answer

$4$

Question 9

Evaluate $$\lim_{x 	o 0} \frac{e^{2x} - 1}{x}$$

Accepted Answer

$2$

Answer

$\infty$

Answer

$0$

Answer

$1$

Question 10

Evaluate $$\lim_{x 	o 0} \frac{\sin(4x)}{x}$$

Accepted Answer

$4$

Answer

$1$

Answer

$0$

Answer

$2$

Question 11

If $f(x) = x^2 + 3x - 5$, find slope of tangent at $x = -2$

Accepted Answer

$-1$

Answer

$5$

Answer

$-7$

Answer

$1$

Question 12

If $y = (x^2 + 1)^4$, find $\frac{dy}{dx}$

Accepted Answer

$8x(x^2 + 1)^3$

Answer

$8x(x^2 + 1)^4$

Answer

$4x(x^2 + 1)^2$

Answer

$4x(x^2 + 1)^3$

Question 13

Find derivative of $$y = \frac{x^2 + 1}{x - 1}$$

Accepted Answer

$\frac{x^2 - 2x - 1}{(x - 1)^2}$

Answer

$\frac{2x - 1}{(x - 1)^2}$

Answer

$\frac{2x + 1}{x^2 - 1}$

Answer

$\frac{x^2 + 1}{(x - 1)^2}$

Question 14

If $f(x) = e^{3x} \sin(x)$, find $f'(x)$

Accepted Answer

$e^{3x}(3\sin x + \cos x)$

Answer

$e^{3x}(3\cos x - \sin x)$

Answer

$3e^{3x}\sin x$

Answer

$e^{3x}(\sin x + 3\cos x)$

Question 15

At what value of $x$ is $f(x) = x^3 - 6x^2 + 9x$ minimum?

Accepted Answer

$x=3$

Answer

$x=0$

Answer

$x=2$

Answer

$x=1$

Question 16

If $y = \ln(x^2 + 1)$, find $\frac{dy}{dx}$

Accepted Answer

$\frac{2x}{x^2 + 1}$

Answer

$\frac{1}{2(x^2 + 1)}$

Answer

$2x\ln(x^2 + 1)$

Answer

$\frac{1}{x^2 + 1}$

Question 17

Find $$\int (3x^2 - 4x + 5)\,dx$$

Accepted Answer

$x^3 - 2x^2 + 5x + C$

Answer

$3x^3 - 4x^2 + 5x + C$

Answer

$x^3 - 4x + 5 + C$

Answer

$x^3 - 4x^2 + 5x + C$

Question 18

Find $$\int x e^{x^2} dx$$

Accepted Answer

$\frac{1}{2} e^{x^2} + C$

Answer

$x e^{x^2} + C$

Answer

$e^{x^2} + C$

Answer

$2e^{x^2} + C$

Question 19

Find $$\int (x^3 + 2x^2)\,dx$$

Accepted Answer

$\frac{x^4}{4} + \frac{2x^3}{3} + C$

Answer

$x^4 + 2x^3 + C$

Answer

$x^3 + x^2 + C$

Answer

$\frac{x^3}{3} + \frac{x^2}{2} + C$

Question 20

Evaluate $$\int_0^1 (2x + 3)\,dx$$

Accepted Answer

$4$

Answer

$2$

Answer

$5$

Answer

$3.5$

Question 21

Evaluate $$\int_0^{\pi/2} \sin x\,dx$$

Accepted Answer

$1$

Answer

$\pi/2$

Answer

$0$

Answer

$2$

Question 22

If $\frac{dy}{dx} = 6x^2 + 2x$, find $y$ when constant of integration $C=0$

Accepted Answer

$2x^3 + x^2$

Answer

$3x^2 + 2x$

Answer

$x^3 + 2x^2$

Answer

$6x^3 + 2x$

Question 23

Find $$\int (\frac{1}{x^2 + 4})\,dx$$

Accepted Answer

$\frac{1}{2}	an^{-1}(\frac{x}{2}) + C$

Answer

$	an^{-1}(2x) + C$

Answer

$\frac{1}{4}	an^{-1}(x/2) + C$

Answer

$2	an^{-1}(x/2) + C$

Question 24

Find $$\int (2x + 1)^3 dx$$

Accepted Answer

$\frac{(2x + 1)^4}{8} + C$

Answer

$(2x + 1)^4 + C$

Answer

$\frac{(2x + 1)^3}{6} + C$

Answer

$\frac{(2x + 1)^4}{4} + C$

Question 25

If velocity $v = 3t^2 + 2t$, find distance covered between $t = 0$ and $t = 2$

Accepted Answer

$16$

Answer

$10$

Answer

$20$

Answer

$12$

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