Question 1

Which of the following expressions is equivalent to $ (2x^3y^2)^2 $?

Accepted Answer

$ 4x^6y^4 $

Question 2

A biologist is studying the growth of a bacteria population that doubles every 3 hours. If the initial population is 500, which equation models the population $ P $ after $ t $ hours?

Accepted Answer

$ P = 500 	imes 2^{t/3} $

Question 3

Simplify the expression $ \dfrac{3x^2y^{-3}}{6x^{-1}y^2} $.

Accepted Answer

$ \dfrac{1}{2}x^3y^{-5} $

Question 4

Which of the following is the correct factorization of $ x^2 - 9 $?

Accepted Answer

$ (x + 3)(x - 3) $

Question 5

A company’s profit $ P $ (in thousands of dollars) is modeled by the quadratic equation $ P = -2x^2 + 8x + 10 $, where $ x $ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

$ 26 $ thousand dollars at $ x = 2 $ thousand units

Question 6

Which of the following is the solution set for $ 2x^2 - 8x = 0 $?

Accepted Answer

$ \{0, 4\} $

Question 7

Simplify the following expression: $ (3x^2y^3)^2 \cdot (2xy)^3 $.

Accepted Answer

$ 72x^7y^9 $

Question 8

A quadratic equation $ ax^2 + bx + c = 0 $ has real and equal roots. Which of the following must be true?

Accepted Answer

$ b^2 - 4ac = 0 $

Question 9

Which of the following is the correct simplification of $ \sqrt{50} + 2\sqrt{8} $?

Accepted Answer

$ 5\sqrt{2} + 4\sqrt{2} = 9\sqrt{2} $

Question 10

A ball is thrown upward from the ground with an initial velocity of $ 32 $ ft/s. Its height $ h $ (in feet) after $ t $ seconds is given by $ h = -16t^2 + 32t $. At what time does the ball reach its maximum height?

Accepted Answer

$ t = 1 $ second

Question 11

Which of the following is the correct result of dividing $ (x^3 - 8) $ by $ (x - 2) $?

Accepted Answer

$ x^2 + 2x + 4 $

Question 12

If $ f(x) = 2x^2 - 3x + 5 $, what is $ f(-2) $?

Accepted Answer

$ 19 $

Question 13

Which of the following is the correct solution to $ \sqrt{x + 5} = 3 $?

Accepted Answer

$ x = 4 $

Question 14

A rectangular garden has a length that is 3 meters more than twice its width. If the area is $ 99 $ square meters, what is the width of the garden?

Accepted Answer

$ 6 $ meters

Question 15

Which of the following is the correct simplification of $ (x^2 - 4x + 4) $?

Accepted Answer

$ (x - 2)^2 $

Question 16

If $ x = 3 $ is a solution to the equation $ x^2 - kx + 6 = 0 $, what is the value of $ k $?

Accepted Answer

$ 5 $

Question 17

Which of the following is the correct result of $ (2x - 5)(x + 3) $?

Accepted Answer

$ 2x^2 + x - 15 $

Question 18

A chemist mixes a solution that is $ 30\% $ salt with another that is $ 10\% $ salt to make $ 20 $ liters of a $ 15\% $ salt solution. How many liters of the $ 30\% $ solution are needed?

Accepted Answer

$ 5 $ liters

Question 19

Which of the following is the correct solution to $ 2^{x} = 16 $?

Accepted Answer

$ x = 4 $

Question 20

If $ x^2 + 6x + 9 = 0 $, what are the solutions for $ x $?

Accepted Answer

$ x = -3 $

Math 980: Algebraic Problem Solving II – Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards