Math Multiple-Choice Questions with Answers

Below is a set of carefully designed multiple-choice math questions that test conceptual understanding across algebra, functions, transformations, trigonometry, probability, and statistics. Final answers are listed at the bottom of the page. Detailed step-by-step solutions are available here.

Question 1

If \( \log_x\!\left(\frac{1}{8}\right) = -\frac{3}{2} \), then the value of \( x \) is

  1. \(-4\)
  2. \(4\)
  3. \(\frac{1}{4}\)
  4. \(10\)

Question 2

\(20\%\) of \(2\) is equal to

  1. \(20\)
  2. \(4\)
  3. \(0.4\)
  4. \(0.04\)

Question 3

If \( \log_{4}(x) = 12 \), then \[ \log_{2}\!\left(\frac{x}{4}\right) \] is equal to

  1. \(11\)
  2. \(48\)
  3. \(-12\)
  4. \(22\)

Question 4

The population of a country increased by \(2\%\) per year from 2000 to 2003. If the population was \(2\,000\,000\) on December 31, 2003, then the population on January 1, 2000 (to the nearest thousand) was

  1. \(1\,846\,000\)
  2. \(1\,852\,000\)
  3. \(1\,000\,000\)
  4. \(1\,500\,000\)

Question 5

Let \(f\) be a quadratic function opening upward with vertex on the \(x\)-axis. The function \[ g(x) = 2 - f(x - 5) \] has range

  1. \([ -5 , +\infty )\)
  2. \([ 2 , +\infty )\)
  3. \(( -\infty , 2 ]\)
  4. \(( -\infty , 0 ]\)

Question 6

If \(f(x) < 0\) for all \(x\), then the graph of \[ g(x) = |f(x)| \] is a reflection of the graph of \(f\)

  1. about the \(y\)-axis
  2. about the \(x\)-axis
  3. about the line \(y = x\)
  4. about the line \(y = -x\)

Question 7

If the graph of \(y = f(x)\) is transformed into \[ 2y - 6 = -4f(x - 3), \] then the point \((a,b)\) becomes \((A,B)\) where

  1. \(A = a - 3,\; B = b\)
  2. \(A = a - 3,\; B = b\)
  3. \(A = a + 3,\; B = -2b\)
  4. \(A = a + 3,\; B = -2b + 3\)

Question 8

The parabola \[ y - 2x^2 = 8x + 5 \] is translated 3 units left and 2 units up. The new vertex is

  1. \((-5,-1)\)
  2. \((-5,-5)\)
  3. \((-1,-3)\)
  4. \((-2,-3)\)

Question 9

The graphs of \[ ax + by = c \quad \text{and} \quad bx - ay = c \] where none of the coefficients \(a, \; b, \; c \) is equal to zero, are

  1. parallel
  2. intersecting at \((0,0)\)
  3. intersecting at two points
  4. perpendicular

Question 10

The graphs of \[ y = ax^2 + bx + c \quad \text{and} \quad y = Ax^2 + Bx + C \] with opposite signs for \(a\) and \(A\), and negative discriminants,

  1. intersect at two points
  2. intersect at one point
  3. do not intersect
  4. none of the above

Question 11

For \(0 \le x \le 2\pi\), both \(\sin x\) and \(\cos x\) are decreasing on

  1. \(\left(0,\frac{\pi}{2}\right)\)
  2. \(\left(\frac{\pi}{2},\pi\right)\)
  3. \(\left(\pi,\frac{3\pi}{2}\right)\)
  4. \(\left(\frac{3\pi}{2},2\pi\right)\)

Question 12

The solutions of \(f(x)=0\) are \(-2\), \(0\), and \(3\). The solutions of \[ f(x-2)=0 \] are

  1. \(-4,-2,1\)
  2. \(-2,0,3\)
  3. \(4,2,5\)
  4. \(0,2,5\)

Question 13

The solutions of \(f(x)=0\) are \(-4\), \(8\), and \(11\). The solutions of \[ f(2x)=0 \] are

  1. \(-2,4,\frac{11}{2}\)
  2. \(-8,16,22\)
  3. \(-4,8,11\)
  4. \(2,\frac{19}{2},\frac{7}{2}\)

Question 14

A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is

  1. \(10\)
  2. \(15\)
  3. \(2100\)
  4. \(8\)

Question 15

Five different books \(A,B,C,D,E\) are placed on a shelf. Books \(C\) and \(D\) occupy the first two positions from the right. The number of different arrangements of books \(A,B,E\) is

  1. \(5!\)
  2. \(3!\)
  3. \(2!\)
  4. \(3!\times2!\)

Question 16

A data set has mean \(10\) and standard deviation \(1\). If \(5\) is added to each data value, the new mean and standard deviation are

  1. mean \(=15\), standard deviation \(=6\)
  2. mean \(=10\), standard deviation \(=6\)
  3. mean \(=15\), standard deviation \(=1\)
  4. mean \(=10\), standard deviation \(=1\)

Question 17

The exam scores of 500 students are normally distributed. If Jane’s score is \(0.8\) standard deviations above the mean, the number of students scoring above Jane (to the nearest unit) is

  1. \(394\)
  2. \(250\)
  3. \(400\)
  4. \(106\)

Question 18

If \(f(x)\) is an odd function, then \(|f(x)|\) is

  1. an odd function
  2. an even function
  3. neither odd nor even
  4. both odd and even

Question 19

The period of \[ |\sin(3x)| \] is

  1. \(2\pi\)
  2. \(\frac{2\pi}{3}\)
  3. \(\frac{\pi}{3}\)
  4. \(3\pi\)

Question 20

A metallic ball bearing is placed inside a cylindrical container of radius \(2\text{ cm}\). The height of the water increases by \(0.6\text{ cm}\). The radius of the ball bearing (to the nearest tenth) is

  1. \(1.0\text{ cm}\)
  2. \(1.2\text{ cm}\)
  3. \(2.0\text{ cm}\)
  4. \(0.6\text{ cm}\)

Question 21

The period of \[ 2\sin x \cos x \] is

  1. \(4\pi^2\)
  2. \(2\pi\)
  3. \(4\pi\)
  4. \(\pi\)

Question 22

The probability that an electronic device does not function properly is \(0.1\). If 10 devices are purchased, the probability that exactly 7 function properly is

  1. \(0.057\)
  2. \(0.478\)
  3. \(0.001\)
  4. \(0\)

Answers

More math questions with detailed solutions

Home Page