Mathematics (Algebra, Calculus, Statistics) MCQs

What is the value of
3
𝑥
+
7
3x+7 when
𝑥
=
5
x=5?

A) 15
B) 16
C) 17
D) 18
Answer: A) 15
If
2
𝑥
−
5
=
11
2x−5=11, what is the value of
𝑥
x?

A) 3
B) 8
C) 9
D) 10
Answer: D) 8
What is the simplified form of
(
2
𝑥
2
−
3
𝑥
+
4
)
−
(
𝑥
2
+
5
𝑥
−
2
)
(2x
2
−3x+4)−(x
2
+5x−2)?

A)
𝑥
2
−
8
𝑥
+
6
x
2
−8x+6
B)
𝑥
2
+
8
𝑥
−
6
x
2
+8x−6
C)
𝑥
2
−
2
𝑥
+
6
x
2
−2x+6
D)
𝑥
2
+
2
𝑥
−
6
x
2
+2x−6
Answer: C)
𝑥
2
−
2
𝑥
+
6
x
2
−2x+6
If
𝑓
(
𝑥
)
=
2
𝑥
3
−
5
𝑥
2
+
3
𝑥
−
7
f(x)=2x
3
−5x
2
+3x−7, what is
𝑓
(
−
1
)
f(−1)?

A) -13
B) -11
C) -9
D) -7
Answer: D) -7
Calculus:

What is the derivative of
𝑓
(
𝑥
)
=
3
𝑥
2
+
4
𝑥
−
2
f(x)=3x
2
+4x−2?

A)
6
𝑥
+
4
6x+4
B)
6
𝑥
+
3
6x+3
C)
6
𝑥
+
2
6x+2
D)
3
𝑥
+
4
3x+4
Answer: A)
6
𝑥
+
4
6x+4
What is the integral of
2
𝑥
+
5
2x+5 with respect to
𝑥
x?

A)
𝑥
2
+
5
𝑥
+
𝐶
x
2
+5x+C
B)
𝑥
2
+
5
𝑥
x
2
+5x
C)
𝑥
2
+
5
x
2
+5
D)
𝑥
2
+
𝐶
x
2
+C
Answer: A)
𝑥
2
+
5
𝑥
+
𝐶
x
2
+5x+C
If
𝑔
(
𝑥
)
=
𝑥
3
−
4
𝑥
2
+
5
𝑥
+
9
g(x)=x
3
−4x
2
+5x+9, what is
𝑔
′
(
𝑥
)
g
′
(x) (the derivative of
𝑔
(
𝑥
)
g(x))?

A)
3
𝑥
2
−
8
𝑥
+
5
3x
2
−8x+5
B)
3
𝑥
2
−
8
𝑥
+
9
3x
2
−8x+9
C)
3
𝑥
2
−
4
𝑥
+
5
3x
2
−4x+5
D)
3
𝑥
2
−
4
𝑥
+
9
3x
2
−4x+9
Answer: A)
3
𝑥
2
−
8
𝑥
+
5
3x
2
−8x+5
Statistics:

What is the mean of the following data set: 5, 10, 15, 20, 25?

A) 15
B) 17
C) 18
D) 20
Answer: A) 15
If the median of a data set is 25 and the mode is 30, what is the range of the data set?

A) 10
B) 15
C) 20
D) 30
Answer: C) 20
In a normal distribution, what percentage of data falls within one standard deviation from the mean?

A) 34%
B) 50%
C) 68%
D) 95%
Answer: C) 68%Solve for
𝑥
x in the equation
2
(
3
𝑥
+
4
)
=
30
2(3x+4)=30.

A) 5
B) 6
C) 7
D) 8
Answer: A) 5
Factorize the quadratic expression
𝑥
2
−
9
x
2
−9.

A)
(
𝑥
−
3
)
(
𝑥
+
3
)
(x−3)(x+3)
B)
(
𝑥
−
2
)
(
𝑥
+
2
)
(x−2)(x+2)
C)
(
𝑥
−
1
)
(
𝑥
+
1
)
(x−1)(x+1)
D)
(
𝑥
−
4
)
(
𝑥
+
4
)
(x−4)(x+4)
Answer: A)
(
𝑥
−
3
)
(
𝑥
+
3
)
(x−3)(x+3)
Solve the inequality
2
𝑥
+
5
>
15
2x+5>15.

A)
𝑥
>
5
x>5
B)
𝑥
>
10
x>10
C)
𝑥
>
6
x>6
D)
𝑥
>
7
x>7
Answer: C)
𝑥
>
6
x>6
Calculus:

What is the derivative of
𝑔
(
𝑥
)
=
1
𝑥
2
g(x)=
x
2

1

?

A)
−
2
𝑥
3
−
x
3

B)
−
2
𝑥
2
−
x
2

C)
−
1
𝑥
3
−
x
3

D)
−
1
𝑥
2
−
x
2

Answer: A)
−
2
𝑥
3
−
x
3

Evaluate the definite integral
∫
0
2
(
3
𝑥
2
+
2
𝑥
+
1
)
𝑑
𝑥
∫
0
2

(3x
2
+2x+1)dx.

A) 10
B) 12
C) 14
D) 16
Answer: B) 12
If
ℎ
(
𝑥
)
=
𝑥
4
+
4
𝑥
3
−
3
𝑥
2
+
2
h(x)=x
4
+4x
3
−3x
2
+2, what is
ℎ
′
′
(
𝑥
)
h
′′
(x) (the second derivative of
ℎ
(
𝑥
)
h(x))?

A)
12
𝑥
+
24
12x+24
B)
12
𝑥
+
6
12x+6
C)
24
𝑥
+
12
24x+12
D)
24
𝑥
+
6
24x+6
Answer: C)
24
𝑥
+
12
24x+12
Statistics:

What is the mode of the data set: 8, 10, 12, 8, 14, 8?

A) 8
B) 10
C) 12
D) 14
Answer: A) 8
If the variance of a data set is 25 and the standard deviation is 5, how many data points are in the set?

A) 20
B) 25
C) 30
D) 35
Answer: B) 25
If the correlation coefficient between two variables is -0.75, what can you infer about their relationship?

A) Strong positive correlation
B) Weak positive correlation
C) Strong negative correlation
D) Weak negative correlation
Answer: C) Strong negative correlationSimplify the expression
3
𝑥
2
−
4
𝑥
+
5
𝑥
2
−
2
𝑥
+
1
x
2
−2x+1
3x
2
−4x+5

.

A)
3
3
B)
3
𝑥
−
4
𝑥
−
2
x−2
3x−4

C)
3
𝑥
+
4
𝑥
+
2
x+2
3x+4

D)
3
𝑥
+
4
𝑥
−
2
x−2
3x+4

Answer: C)
3
𝑥
+
4
𝑥
+
2
x+2
3x+4

Solve for
𝑥
x in the equation
∣
2
𝑥
−
7
∣
=
11
∣2x−7∣=11.

A)
𝑥
=
9
x=9 or
𝑥
=
−
2
x=−2
B)
𝑥
=
9
x=9 or
𝑥
=
4
x=4
C)
𝑥
=
9
x=9 or
𝑥
=
2
x=2
D)
𝑥
=
9
x=9 or
𝑥
=
−
4
x=−4
Answer: D)
𝑥
=
9
x=9 or
𝑥
=
−
4
x=−4
If
𝑓
(
𝑥
)
=
𝑥
2
+
4
𝑥
+
4
𝑥
+
2
f(x)=
x+2
x
2
+4x+4

, what is
𝑓
(
−
2
)
f(−2)?

A) 0
B) 1
C) 2
D) Undefined
Answer: D) Undefined
Calculus:

Find the critical points of the function
𝑔
(
𝑥
)
=
𝑥
3
−
6
𝑥
2
+
9
𝑥
g(x)=x
3
−6x
2
+9x.

A)
𝑥
=
0
x=0 and
𝑥
=
3
x=3
B)
𝑥
=
1
x=1 and
𝑥
=
3
x=3
C)
𝑥
=
0
x=0 and
𝑥
=
2
x=2
D)
𝑥
=
1
x=1 and
𝑥
=
2
x=2
Answer: A)
𝑥
=
0
x=0 and
𝑥
=
3
x=3
Evaluate the limit
lim
⁡
𝑥
→
3
𝑥
2
−
9
𝑥
−
3
lim
x→3

x−3
x
2
−9

.

A) 6
B) 9
C) 12
D) Undefined
Answer: B) 9
What is the antiderivative of
1
𝑥
2
x
2

1

?

A)
−
1
𝑥
+
𝐶
−
x
1

+C
B)
−
1
𝑥
3
+
𝐶
−
x
3

1

+C
C)
−
1
2
𝑥
+
𝐶
−
2x
1

+C
D)
−
1
2
𝑥
2
+
𝐶
−
2x
2

1

+C
Answer: A)
−
1
𝑥
+
𝐶
−
x
1

+C
Statistics:

If a data set has a mean of 50 and a median of 55, what can you infer about the distribution?

A) Positively skewed
B) Negatively skewed
C) Symmetric
D) Bimodal
Answer: A) Positively skewed
Calculate the z-score for a data point with a value of 60 in a data set with a mean of 50 and a standard deviation of 5.

A) 2
B) 2.5
C) 3
D) 3.5
Answer: B) 2.5
If the coefficient of determination (R-squared) for a linear regression model is 0.85, what does this value indicate about the model’s fit?

A) Strong fit
B) Weak fit
C) No fit
D) Perfect fit
Answer: A) Strong fitSolve the equation
3
(
2
𝑥
+
1
)
=
15
3(2x+1)=15.

A)
𝑥
=
2
x=2
B)
𝑥
=
3
x=3
C)
𝑥
=
4
x=4
D)
𝑥
=
5
x=5
Answer: A)
𝑥
=
2
x=2
Factorize the expression
4
𝑥
2
−
25
4x
2
−25.

A)
(
2
𝑥
−
5
)
(
2
𝑥
+
5
)
(2x−5)(2x+5)
B)
(
2
𝑥
−
3
)
(
2
𝑥
+
3
)
(2x−3)(2x+3)
C)
(
2
𝑥
−
7
)
(
2
𝑥
+
7
)
(2x−7)(2x+7)
D)
(
2
𝑥
−
4
)
(
2
𝑥
+
4
)
(2x−4)(2x+4)
Answer: A)
(
2
𝑥
−
5
)
(
2
𝑥
+
5
)
(2x−5)(2x+5)
Solve the inequality
2
𝑥
2
−
3
𝑥
−
2
>
0
2x
2
−3x−2>0.

A)
𝑥
<
−
0.5
x<−0.5 or
𝑥
>
2
x>2
B)
𝑥
<
1
x<1 or
𝑥
>
−
2
x>−2
C)
𝑥
<
0.5
x<0.5 or
𝑥
>
−
2
x>−2
D)
𝑥
<
1
x<1 or
𝑥
>
2
x>2
Answer: A)
𝑥
<
−
0.5
x<−0.5 or
𝑥
>
2
x>2
Calculus:

Find the derivative of
ℎ
(
𝑥
)
=
𝑥
2
+
1
h(x)=
x
2
+1

.

A)
𝑥
𝑥
2
+
1
x
2
+1

B)
1
𝑥
2
+
1
x
2
+1

C)
𝑥
𝑥
2
+
1
x
2
+1
x

D)
𝑥
2
𝑥
2
+
1
x
2
+1

x
2

Answer: A)
𝑥
𝑥
2
+
1
x
2
+1

Compute the integral
∫
0
3
(
2
𝑥
3
−
3
𝑥
2
+
4
)
𝑑
𝑥
∫
0
3

(2x
3
−3x
2
+4)dx.

A) 15
B) 18
C) 20
D) 24
Answer: B) 18
What is the derivative of
𝑓
(
𝑥
)
=
𝑒
3
𝑥
f(x)=e
3x
?

A)
3
𝑒
3
𝑥
3e
3x

B)
𝑒
3
𝑥
e
3x

C)
9
𝑒
3
𝑥
9e
3x

D)
3
𝑒
𝑥
3e
x

Answer: A)
3
𝑒
3
𝑥
3e
3x

Statistics:

Calculate the interquartile range (IQR) for the data set: 10, 15, 20, 25, 30.

A) 10
B) 12.5
C) 15
D) 17.5
Answer: C) 15
If the standard deviation of a data set is 8 and the mean is 40, what is the coefficient of variation?

A) 20%
B) 25%
C) 30%
D) 35%
Answer: A) 20%
A random variable X follows a normal distribution with a mean of 50 and a standard deviation of 10. What is the probability that X is between 40 and 60?

A) 0.50
B) 0.68
C) 0.80
D) 0.95
Answer: C) 0.80Solve the system of equations:
2
𝑥
+
3
𝑦
=
11
𝑥
−
2
𝑦
=
4
2x+3y
x−2y

=11
=4

A)
𝑥
=
3
,
𝑦
=
2
x=3,y=2
B)
𝑥
=
2
,
𝑦
=
3
x=2,y=3
C)
𝑥
=
4
,
𝑦
=
1
x=4,y=1
D)
𝑥
=
1
,
𝑦
=
4
x=1,y=4
Answer: A)
𝑥
=
3
,
𝑦
=
2
x=3,y=2
Factorize the expression
𝑥
3
−
8
𝑦
3
x
3
−8y
3
.
A)
(
𝑥
−
2
𝑦
)
(
𝑥
2
+
2
𝑥
𝑦
+
4
𝑦
2
)
(x−2y)(x
2
+2xy+4y
2
)
B)
(
𝑥
+
2
𝑦
)
(
𝑥
2
−
2
𝑥
𝑦
+
4
𝑦
2
)
(x+2y)(x
2
−2xy+4y
2
)
C)
(
𝑥
−
2
𝑦
)
(
𝑥
2
+
4
𝑦
2
)
(x−2y)(x
2
+4y
2
)
D)
(
𝑥
+
2
𝑦
)
(
𝑥
2
+
2
𝑥
𝑦
+
4
𝑦
2
)
(x+2y)(x
2
+2xy+4y
2
)
Answer: C)
(
𝑥
−
2
𝑦
)
(
𝑥
2
+
4
𝑦
2
)
(x−2y)(x
2
+4y
2
)
Solve the inequality
3
𝑥
−
2
𝑥
+
1
<
2
x+1
3x−2

<2.
A)
𝑥
<
4
5
x<
5
4

B)
𝑥
>
4
5
x>
5
4

C)
𝑥
<
5
3
x<
3
5

D)
𝑥
>
5
3
x>
3
5

Answer: A)
𝑥
<
4
5
x<
5
4

Calculus:

Find the critical points of the function
𝑓
(
𝑥
)
=
𝑥
4
−
4
𝑥
3
+
6
𝑥
2
−
4
𝑥
f(x)=x
4
−4x
3
+6x
2
−4x.
A)
𝑥
=
0
,
1
,
2
x=0,1,2
B)
𝑥
=
0
,
1
,
3
x=0,1,3
C)
𝑥
=
0
,
2
,
3
x=0,2,3
D)
𝑥
=
1
,
2
,
3
x=1,2,3
Answer: A)
𝑥
=
0
,
1
,
2
x=0,1,2
Compute the definite integral
∫
1
4
(
2
𝑥
+
3
)
𝑑
𝑥
∫
1
4

(2x+3)dx.
A) 11
B) 12
C) 13
D) 14
Answer: C) 13
What is the derivative of
𝑔
(
𝑥
)
=
ln
⁡
(
3
𝑥
+
1
)
g(x)=ln(3x+1)?
A)
1
𝑥
x
1

B)
3
3
𝑥
+
1
3x+1
3

C)
3
𝑥
x
3

D)
1
3
𝑥
+
1
3x+1
1

Answer: D)
1
3
𝑥
+
1
3x+1
1

Statistics:

If a data set has a variance of 36 and a standard deviation of 6, how many data points are in the set?
A) 5
B) 10
C) 25
D) 36
Answer: A) 5
The correlation coefficient between two variables X and Y is -0.85. What does this indicate about their relationship?
A) Strong positive correlation
B) Weak positive correlation
C) Strong negative correlation
D) Weak negative correlation
Answer: C) Strong negative correlation
If a normally distributed data set has a mean of 100 and a standard deviation of 15, what percentage of data points fall between 85 and 115?
A) 34%
B) 68%
C) 95%
D) 99.7%
Answer: B) 68%