Question FBQ1 : A ___ is a phenomenon that relates one variable or quantity to other variables or quantities
Answer: Function

Question FBQ2 : The___ of the function is the set of all values taken on by the dependent variable
Answer: range

Question FBQ3 : In the equation,

y = 4 x^{2} + 3

x

is the ___ variable
Answer: Independent

Question FBQ4 : To decide whether an equation defines a function, it is helpful to isolate the ___on the left
Answer: Dependent variable

Question FBQ5 : The equation

y = \pm \sqrt{1 - x^{2}}

indicates that

y = + 1

y =

___________
Answer: -1

Question FBQ6 : The solution of

x^{2} + y^{2} = 4

when

x = 1

is ___
Answer: ±3

Question FBQ8 : The value of

f (x) = 2 x^{3} - 4 x + 1

when

x = 0

is ___
Answer: 1

Question FBQ9 : If p is a polynomial function and c is any real number, then

\lim_{x \to c} p (x) =___

Answer: p(c)

Question FBQ10 : In sketching the graph of a function, we allow the horizontal axis represent the ___ variable
Answer: Independent

Question FBQ11 : A function is ___ if every horizontal line intersects the graph of the function at most once
Answer: One to one

Question FBQ12 : If two values of

y

corresponds to an

x

value, then it is said that ___
Answer: y is not a function of x

Question FBQ13 : The function given by

(f . g) (x) = f (g (x))

is the ___ of

f

with

g

Answer: Composite

Question FBQ14 : If

f (x) = 2 x + 1

and

g (x) = x^{2} + 2

the value of

g (f (x))

is ___
Answer: 4x2 + 4x + 3

Question FBQ15 : Given that

f (x) = \sqrt{x}

and

g (x) = x^{2} - 1

f (g (1))

= ___
Answer: 0

Question FBQ16 : In an inverse function, the domain of

f

must be equal to the range of

f^{- 1}

, and the range of

f

must be equal to the domain of ___
Answer: f-1

Question FBQ17 : The inverse function of

f (x) = x^{3}

is ___
Answer: x3

Question FBQ18 :

f

has no inverse if does not pass the ________ test
Answer: Horizontal

Question FBQ19 : For a continuous function

\lim_{x \to x_{0}} f (x_{0})

=
Answer: f(x0)

Question FBQ20 :

\lim_{x \to - 2} \frac{5}{x + 2} =___

Answer: ∞

Question FBQ21 : Let c be a real number and

f (x) = g (x)

for all

x \neq c

. If the limit of

g (x)

exists as

x \to c

, then the limit of

f (x)

also exists and

\lim_{x \to 2} f (x) = \lim_{x \to 2} g (x)

. This theorem is known as the ___
Answer: Replacement theorem

Question FBQ22 : Evaluating

\lim_{x \to 1} \frac{x^{3} - 1}{x - 1}

gives ___
Answer: 2

Question FBQ23 : A polynomial function is continuous at every real ___
Answer: Number

Question FBQ24 : There are ___ categories of discontinuities
Answer: 2

Question FBQ25 : A function is said to be continuous if and only if it is continuous at every point of its ___
Answer: Domain

Question FBQ26 : The function

f (x) = \sqrt{3 - x}

is continuous in the interval ___
Answer: (-∞,3]

Question FBQ27 : Continuity of a function is expressed some times by saying if the x value are closed together, then the ___values of the function will also be close
Answer: Y

Question FBQ28 : Derivative is often described as the “___ rate of change”
Answer: Instantaneous

Question FBQ29 : The process of finding a derivative is called ___
Answer: Differentiation

Question FBQ30 : ___ is defined as the ratio of the vertical distance the line rises or falls between two points P and Q to the horizontal distance between P and Q
Answer: Gradient

Question FBQ31 : ___ theorem can be used to find the derivative of

y = x^{n}

Answer: Binomial

Question FBQ32 : The derivative of

\cot x

is ___
Answer: -cosec2x

Question FBQ33 : The derivative of

c o s e c x

is ___
Answer: –cosec x.cot⁡x

Question FBQ34 : If we differentiate

a^{x}

, we get ___
Answer: ax.lna

Question FBQ35 : If

y = u v

, then the product rule is given as

\frac{d y}{d x}

___
Answer: udvdx+vdudx

Question FBQ36 : The quotient rule for differentiation is given as

\frac{d y}{d x}

___
Answer: dydx=vdudx-udvdxv2

Question FBQ37 : The chain rule of differentiation is given as___

\frac{d y}{d x}

Answer: dydu.dudx

Question FBQ38 : The derivative of

y = t a n (3 x + 2)

is ___
Answer: 3sec2(3x+2)

Question FBQ39 : The derivative of

y = s i n (4 x + 3)

is ___
Answer: 4cos⁡(4x+3)

Question FBQ40 :

x y + c o s y = 5

is an example of an___ function
Answer: Implicit

Question FBQ41 : If

y = x^{5} e^{x}

\frac{d y}{d x}

gives ___
Answer: x4exx+5

Question FBQ42 : The

c

in integration is called an ___ constant
Answer: Arbitrary

Question FBQ43 : The general formula for integration

\int x^{n} d x

is given as ___
Answer: xn+1n+1+c

Question FBQ44 :

\int \frac{- 1}{\sqrt{1 - x^{2}}} d x

Answer: cos-1x+c

Question FBQ45 :

\int \frac{1}{\sqrt{x^{2} - 1}} d x =

Answer: cosh-1x+c

Question FBQ46 :

\int \frac{1}{\sqrt{x^{2} + 1}} d x =

Answer: Sinh-1x + c

Question FBQ47 :

\int \frac{f^{'} (x)}{f (x)} d x =

Answer: ln{f(x)} + c

Question FBQ48 : The volume of a cone

V_{c o n e} =

___
Answer: 13πr2h

Question FBQ49 : The volume of a sphere is given as

V_{x} =

___
Answer: 4πr33

Question FBQ50 :

\int a^{x} d x =

Answer: axlnx+c

Question FBQ7 : The equation of the tangent at x = 2 on the curve

x^{2} + y^{2} - 2 x + y = 6

is ___
Answer: 5y + 2x – 14 = 0

Question MCQ1 : Which of the equation below define y as a function of x?
Answer:

x^{2} + y = 1

Question MCQ2 : Find

f (- 1)

for the equation

y = {2 x}^{2} - 4 x + 1

Answer: 7

Question MCQ3 : Find the value of

f (x) = 1 - 5 x + x^{2}

for

x = 4

Answer: -3

Question MCQ4 : Let

f (x) = x^{2} - 4 x + 7

, find

\frac{f (x + ∆ x) - f (x)}{∆ x}

Answer:

2 x + ∆ x - 4

Question MCQ5 : Division by Zero is...
Answer: Undefined

Question MCQ6 : A function is said to be one to one if...
Answer: To each value of the dependent variable in the range, there corresponds exactly one value of the independent variable

Question MCQ7 : If

f (x) = 2 x - 4

and

g (x) = x^{2} + 3

, find

f (g (x))

Answer:

2 (x^{2} - 1)

Question MCQ8 : If

f^{- 1} (x) = x - 8

, then

f (x) =

?
Answer:

x + 8

Question MCQ9 : Let f

(x) = \frac{1}{x}

, then

f^{- 1} (x)

is given as...
Answer:

x

Question MCQ20 : Which of the following conditions does NOT determine the continuity of

f

at point c?
Answer:

\lim_{x \to c} f (c) = f (x)

Question MCQ21 :

f (x) = \frac{(x^{2} - 1)}{(x - 1)}

is continuous on the interval ...
Answer:

(- \infty, 1) a n d (1, \infty)

Question MCQ22 : Discontinuities fall into two categories namely ...
Answer: Removable and non-removable

Question MCQ23 : The representation

\lim_{x \to b^{-}} f (x) = f (b)

shows that ...
Answer:

f

is continuous from the left at b

Question MCQ24 : Which of the following statements is true about the continuity of

f (x) = \sqrt{3 - x}

Answer:

f

is continuous on the interval

(- \infty, 3]

Question MCQ25 : Which of the following about the continuity of

g (x) = \{\begin{matrix} 5 - x, - 1 \leq x \leq 2 \\ x^{2} - 1, 2 < x \leq 3 \end{matrix}

is NOT correct?
Answer:

\lim_{x \to 2} g (x)

is continuous on the interval

[- \infty, \infty]

Question MCQ26 : Differentiate

y = x^{3} + 5 x^{2} - 4 x + 2

with respect to

x

Answer:

3 x^{2} + 10 x - 4

Question MCQ27 : Find the value of

\frac{d y}{d x}

x = 2

, if

y = x^{4} + 6 x^{3} - 4 x^{2} + 7 x - 2

Answer: 95

Question MCQ28 : The derivative of

s i n x + c o s x = \dots

Answer:

c o s x - s i n x

Question MCQ29 : What is the derivative of

l n (x)

?
Answer:

1 / x

Question MCQ30 : If the derivative of

\sec x = \sec x \tan x

, find the derivative of

c o s e c x

.
Answer:

- c o s e c x . c o t x

Question MCQ31 : If we differentiate

e^{x}

, we get ...
Answer:

e^{x}

Question MCQ32 : Find the derivative of

y = x^{3} s i n x

Answer:

x (x^{2} c o s x + 3 s i n x)

Question MCQ33 : Differentiate

y = x^{2} {(2 x - 5)}^{4}

with respect to

x

yields ...
Answer:

2 x {(2 x - 5)}^{3} (6 x - 5)

Question MCQ34 : Differentiate with respect to

x

y = \frac{s i n x}{x^{2}}

Answer:

\frac{x c o s x - 2 s i n x}{x^{3}}

Question MCQ35 : The gradient of a curve is found ...
Answer: At a point on the curve

Question MCQ36 : In differentiation, the chain rule technique is used when differentiating ...
Answer: A function of a function

Question MCQ37 : Find

\int (s^{3} + 4 s) d s

Answer:

\frac{s^{4}}{4} + 2 s^{2} + c

Question MCQ38 : Evaluate

\int {(3 x - 2)}^{6} d x

Answer:

\frac{{(3 x - 2)}^{7}}{21} + c

Question MCQ39 : Evaluate

\int c o s (6 x + 4) d x

Answer:

\frac{s i n (6 x + 4)}{6} + c

Question MCQ40 : Evaluate

\int {(s e c}^{2} 8 x) d x

Answer:

$\frac{t a n 8 x}{8} + c$

Question MCQ41 : Find $\int \frac{2 x - 5}{x^{2} - 5 x + 6} d x$
Answer: $\ln (x^{2} - 5 x + 6) + c$

Question MCQ42 : Find $\int c o t x d x$
Answer:

$\ln s i n x + c$

Question MCQ43 : Evaluate $\int x e^{2 x} d x$ using integration by parts
Answer: $\frac{e^{2 x}}{2} [x - \frac{1}{2}] + c$

Question MCQ44 : Definite integrals can also be used to calculate ...
Answer: Volume of solids

Question MCQ45 : The infinitesimal volume of a cylinder representing an element of integration revolving around the $x$ axis is given by ...
Answer: $V_{x} = π - \int_{a}^{b} y^{2} d x$

Question MCQ46 : The infinitesimal volume of a cylinder representing an element of integration revolving around the $y$ axis is given by ...
Answer: $V_{y} = π \int_{a}^{b} x^{2} d x$

Question MCQ47 : Find the volume of a sphere generated by a semicircle $y = \sqrt{r^{2} - x^{2}}$ revolving around the $x - a x i s .$
Answer: $4 π r^{2} / 3$

Question MCQ48 : Find the volume of a right circular cone generated by the line (segment) passing through the origin and point $(h, r)$ , where $h$ denotes the height of the cone and $r$ is the radius of its base revolving around the $x - a x i s$ .
Answer: $V_{c o n e} = \frac{1}{3} π r^{2} h$

Question MCQ49 : Find the value of $d y / d x$ for $y = {(2 x + 5)}^{3}$ at $x = 4$
Answer: 1014

Question MCQ50 : What is the value of $\int c o s x d x$ at $x = 30$ ?
Answer: $\frac{1}{2}$

Question MCQ15 : If $\lim_{x \to c} f (x) = L a n d \lim_{x \to c} g (x) = K$ , then $\lim_{x \to c} [b f (x)] = b L$ is called...
Answer: Scalar multiple

Question MCQ16 : Find $\lim_{x \to 2} {(x}^{2} + 2 x - 3)$
Answer: $5$

Question MCQ17 : Evaluate $\lim_{x \to 1} f (x)$ if $f (x) = \frac{x^{3} - 1}{x - 1}$
Answer: $3$

Question MCQ18 : Find $\lim_{x \to 0} f (x)$ if $f (x) = \frac{\sqrt{x + 1} - 1}{x}$
Answer: $\frac{1}{2}$

Question MCQ19 : Let $\lim_{x \to c} f (x) = 9 a n d \lim_{x \to c} g (x) = \frac{1}{2}$ , then $\frac{f (x)}{g (x)}$ = ...
Answer: 18

Question MCQ10 : Find the inverse function of $f (x) = \sqrt{2 x - 3}$
Answer: $\frac{x^{2} + 3}{2}$

Question MCQ11 : Find the domain and range of $f (x) = 4 - x^{2}$ , leaving your result in interval notation.
Answer: $[4, \infty], [0, \infty]$

Question MCQ13 : Find the limit: $\lim_{x \to 1} f (x)$ if $f (x) = \frac{x^{2} - 1}{x - 1}$
Answer: 2

Question MCQ14 : Evaluate $\lim_{x \to 1} (x^{2} + 1)$
Answer: 1

Question MCQ12 :
Answer: