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Q142 Measures of Location and Spread View

QUESTION 142
A student scored the following grades in four tests: 6.0, 7.5, 8.0, and 4.5. The arithmetic mean of the student's grades is
(A) 6.0
(B) 6.5
(C) 7.0
(D) 7.5
(E) 8.0

Q146 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View

QUESTION 146
The function $f(x) = 2x^2 - 3x + 1$ has roots
(A) $x = 1$ and $x = \frac{1}{2}$
(B) $x = -1$ and $x = \frac{1}{2}$
(C) $x = 1$ and $x = -\frac{1}{2}$
(D) $x = -1$ and $x = -\frac{1}{2}$
(E) $x = 2$ and $x = \frac{1}{2}$

Q147 Geometric Sequences and Series Derive General Term from Geometric Property View

QUESTION 147
In a geometric progression, the first term is 2 and the common ratio is 3. The fifth term of this progression is
(A) 54
(B) 81
(C) 162
(D) 243
(E) 486

Q148 Inequalities Solve Polynomial/Rational Inequality for Solution Set View

QUESTION 148
The solution set of the inequality $2x - 5 > 3$ is
(A) $x > 1$
(B) $x > 2$
(C) $x > 3$
(D) $x > 4$
(E) $x > 5$

Q149 Laws of Logarithms Simplify or Evaluate a Logarithmic Expression View

QUESTION 149
The value of $\log_2 32$ is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Q151 Probability Definitions Finite Equally-Likely Probability Computation View

QUESTION 151
A bag contains 5 red balls, 3 blue balls, and 2 green balls. The probability of randomly drawing a blue ball is
(A) $\frac{1}{5}$
(B) $\frac{3}{10}$
(C) $\frac{2}{5}$
(D) $\frac{1}{2}$
(E) $\frac{3}{5}$

Q152 Proof Geometric Combinatorics View

QUESTION 152
The number of diagonals of a polygon with 8 sides is
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24

Q153 Trig Graphs & Exact Values View

QUESTION 153
The value of $\sin 30^\circ + \cos 60^\circ$ is
(A) $\frac{1}{2}$
(B) $\frac{\sqrt{2}}{2}$
(C) 1
(D) $\frac{\sqrt{3}}{2}$
(E) $\sqrt{2}$

Q154 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View

QUESTION 154
The equation of a line passing through the points $(1, 2)$ and $(3, 6)$ is
(A) $y = x + 1$
(B) $y = 2x$
(C) $y = 2x + 1$
(D) $y = 3x - 1$
(E) $y = x + 3$

Q155 Circles Area and Geometric Measurement Involving Circles View

QUESTION 155
The area of a circle with radius 5 cm is
(A) $10\pi$ cm$^2$
(B) $15\pi$ cm$^2$
(C) $20\pi$ cm$^2$
(D) $25\pi$ cm$^2$
(E) $30\pi$ cm$^2$

Q156 Matrices Determinant and Rank Computation View

QUESTION 156
The matrix $A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$ has determinant
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Q157 Permutations & Arrangements Linear Arrangement with Constraints View

QUESTION 157
The number of ways to arrange 4 people in a row is
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28

Q158 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View

QUESTION 158
The distance between the points $A(1, 2)$ and $B(4, 6)$ is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Q159 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View

QUESTION 159
The value of $\int_0^2 (3x^2 + 2x)\, dx$ is
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16

Q160 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View

QUESTION 160
The sum of the first 10 terms of an arithmetic progression with first term 2 and common difference 3 is
(A) 145
(B) 155
(C) 165
(D) 175
(E) 185

Q161 Laws of Logarithms Algebraic Simplification and Expression Manipulation View

QUESTION 161
The value of $e^0 + \ln 1$ is
(A) 0
(B) 1
(C) 2
(D) $e$
(E) $e + 1$

Q163 Simultaneous equations View

QUESTION 163
The solution of the system $$\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}$$ is
(A) $x = 1, y = 4$
(B) $x = 2, y = 3$
(C) $x = 3, y = 2$
(D) $x = 4, y = 1$
(E) $x = 5, y = 0$

Q164 Chain Rule MCQ on derivative and graph interpretation View

QUESTION 164
The derivative of $f(x) = x^3 - 4x^2 + 5x - 2$ is
(A) $f'(x) = 3x^2 - 8x + 5$
(B) $f'(x) = 3x^2 - 4x + 5$
(C) $f'(x) = 3x^2 + 8x + 5$
(D) $f'(x) = x^2 - 8x + 5$
(E) $f'(x) = 3x^2 - 8x - 5$

Q165 Combinations & Selection Basic Combination Computation View

QUESTION 165
The number of combinations of 6 elements taken 2 at a time is
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24

Q166 Trig Graphs & Exact Values View

QUESTION 166
The value of $\tan 45^\circ + \cos 0^\circ$ is
(A) 1
(B) 2
(C) $\sqrt{2}$
(D) $1 + \sqrt{2}$
(E) $2\sqrt{2}$

Q168 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View

QUESTION 168
The equation $x^2 - 5x + 6 = 0$ has roots
(A) $x = 1$ and $x = 6$
(B) $x = 2$ and $x = 3$
(C) $x = -2$ and $x = -3$
(D) $x = 1$ and $x = -6$
(E) $x = -1$ and $x = 6$

Q169 Measures of Location and Spread View

QUESTION 169
The median of the data set $\{3, 7, 5, 9, 1, 6, 4\}$ is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Q170 Indices and Surds Evaluating Expressions Using Index Laws View

QUESTION 170
The value of $2^{10}$ is
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192

Q172 Combinations & Selection Basic Combination Computation View

QUESTION 172
The value of $\binom{5}{2}$ is
(A) 5
(B) 8
(C) 10
(D) 12
(E) 15

Q173 Exponential Functions MCQ on Function Properties View

QUESTION 173
The function $f(x) = 3^x$ passes through the point
(A) $(0, 0)$
(B) $(0, 1)$
(C) $(1, 0)$
(D) $(1, 3)$
(E) $(3, 1)$

Q175 Indices and Surds Simplifying Surd Expressions View

QUESTION 175
The value of $\sqrt{144} + \sqrt{25}$ is
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21

Q176 Number Theory Prime Number Properties and Identification View

QUESTION 176
The number of prime numbers between 10 and 30 is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Q178 Permutations & Arrangements Factorial and Combinatorial Expression Simplification View

QUESTION 178
The value of $5! - 3!$ is
(A) 108
(B) 112
(C) 114
(D) 116
(E) 120

Q179 Straight Lines & Coordinate Geometry Section Ratio and Division of Segments View

QUESTION 179
The midpoint of the segment with endpoints $A(2, 4)$ and $B(6, 8)$ is
(A) $(3, 5)$
(B) $(4, 6)$
(C) $(5, 7)$
(D) $(6, 8)$
(E) $(8, 12)$

Q180 Trig Proofs Trigonometric Identity Simplification View

QUESTION 180
The value of $\cos^2 30^\circ + \sin^2 30^\circ$ is
(A) $\frac{1}{2}$
(B) $\frac{\sqrt{3}}{2}$
(C) 1
(D) $\sqrt{3}$
(E) 2

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