Maths Question
Question 35

The expression of $a{{x}^{2}}+bx+c$equals 5 at x =1. If its derivative is 2x + 1, what are the value of a, b,  respectively.

Question 37

Find the value of $\int_{0}^{\pi }{\frac{{{\cos }^{2}}\theta -1}{{{\sin }^{2}}\theta }d\theta }$ 

Question 38

The function f (x) passes through the origin and its first derivative is 3x + 2. What is f(x)?

Question 39

A bowl is designed by resolving completely the area enclosed by y = x2 – 1, y = 0, y = 3 and x ≥ 0 around the y –axis. What is the volume of this bowl?

Question 40

If the diagram above is the graph of y = x2, the shaded area is

Question 34

Evaluate $\int{2{{(2x-3)}^{\tfrac{2}{3}}}dx}$

Question 36

Find the area bounded by the curve $y=4-{{x}^{2}}$and $y=2x+1$

Question 7

If $\frac{dy}{dx}=2x-3$and y = 3 when x = 0. Find y in terms of x

Question 10

Evaluate $\int{\sin 3xdx}$

Question 37

Evaluate $\int_{2}^{3}{({{x}^{2}}-2x)dx}$ 

Question 2

Find the area of the figure bounded by the given pair of curves $y={{x}^{2}}-x+3$and y =3

Question 4

Evaluate $\int_{0}^{\tfrac{\pi }{2}}{\sin 2xdx}$

Question 1

The gradient of a curve is 2x + 7 and the curve passes through point (2,0). Find the equation of the curve

Question 2

Evaluate $\int_{-4}^{0}{(1-2x)dx}$

Question 5

If $\frac{dy}{dx}=x+\cos x$ find y 

Question 39

Integrate $\frac{{{x}^{2}}-\sqrt{x}}{x}$ with respect x

Question 40

Determine the value of $\int\limits_{0}^{\tfrac{\pi }{2}}{(-2\cos x)dx}$

Question 39

Evaluate $\int_{1}^{2}{(6{{x}^{2}}-2x)dx}$

Question 40

Evaluate $\int{{{\sec }^{2}}\theta }d\theta $

Question 43

Evaluate  $\int_{0}^{2}{({{x}^{3}}+{{x}^{2}})dx}$

Question 44

Find $\int{(\sin x+2})dx$

Question 39

Evaluate $\int\limits_{0}^{1}{(3-2x)dx}$

Question 40

Find $\int{\cos 4xdx}$

Question 39

Evaluate $\int_{1}^{2}{({{x}^{2}}-4x)dx}$

Question 40

Evaluate $\int_{0}^{\tfrac{\pi }{4}}{{{\sec }^{2}}\theta d\theta }$

Question 38

$\begin{align}  & \text{Integrate }\left( \frac{1+x}{{{x}^{3}}} \right)dx \\ & \text{(A) }-\frac{1}{2{{x}^{2}}}-\frac{1}{x}+k\text{  (B) }-\frac{{{x}^{2}}}{2}-\frac{1}{x}+k\text{   (C) }{{x}^{2}}-\frac{1}{x}+k\text{   (D)  }2{{x}^{2}}-\frac{1}{x}+k \\\end{align}$

Question 39

$\text{Evaluate }\int_{0}^{\tfrac{\pi }{4}}{\sin xdx}$

Question 41

Evaluate $\int{\sin 2xdx}$

Question 42

Evaluate $\int{{{(2x+3)}^{\tfrac{1}{2}}}dx}$

Question 29

Evaluate $\int{\sin 4xdx}$

Question 39

Evaluate $\int\limits_{0}^{1}{{{(2x+1)}^{2}}dx}$