Question 1

Which of the following is the correct formula for the volume of a sphere?

Accepted Answer

$$V = \frac{4}{3} \pi r^3$

Question 2

Given the quadratic equation $$2x^2 - 4x + 3 = 0$, what is the value of the discriminant, and what does it tell you about the solutions?

Accepted Answer

$$b^2 - 4ac$$ = $$(-4)^2 - 4(2)(3) = 16 - 24 = -8$, so there are two complex solutions.

Question 3

A rectangular garden has a length of 10 meters and a width of 6 meters. What is its perimeter?

Accepted Answer

$$P = 2l + 2w = 2(10) + 2(6) = 20 + 12 = 32$$ meters

Question 4

Which of the following is the correct definition of the imaginary unit $$i$$?

Accepted Answer

$$i = \sqrt{-1}$$

Question 5

If $$x^2 = 25$, what are the solutions for x$?

Accepted Answer

$$x = 5$$ and $$x = -5$$

Question 6

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 7

A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?

Accepted Answer

$$c = \sqrt{3^2$ + 4^2$} = \sqrt{9 + 16} = \sqrt{25} = 5$$

Question 8

Which of the following is the correct expression for the difference of two squares?

Accepted Answer

$$a^2$$ - $$b^2 = (a + b)(a - b$$)$$

Question 9

If $$x is a $$real number and $$|x| \u003c 3$$, which of the following is the correct interval notation for the solution set?

Accepted Answer

$$(-3, 3)$$

Question 10

What is the sum of the complex numbers $$3 + 2i$$ and $$5 - 4i$$?

Accepted Answer

$$8 - 2i$$

Question 11

Which of the following is the correct result of multiplying $$(x + 2)(x - 3)$$ using the FOIL method?

Accepted Answer

$$x^2 - x - 6$

Question 12

A circular cylinder has a radius of 2 cm and a height of 5 cm. What is its volume?

Accepted Answer

$$V = \pi r^2$ h = \pi (2)^2$ (5) = \pi (4)(5) = 20\pi cm$^3$$

Question 13

If $$a = 2 + 3i$$ and $$b = 2 - 3i$$, what is $$a \cdot b$$?

Accepted Answer

$$(2 + 3i)(2 - 3i) = 4 - 9i^2$ = 4 + 9 = 13$$

Question 14

Which of the following is the correct solution to the equation $$|x - 4| = 7$$?

Accepted Answer

$$x = 11$$ and $$x = -3$$

Question 15

Which of the following is the correct result of dividing $$6 + 8i by$$ $$2 - i$$?

Accepted Answer

$$\frac{6 + 8i}{2 - i} = 4 + 2i$$

Question 16

If $$x^2 + 6x + 9 = 0$, what is the solution for x$?

Accepted Answer

$$x = -3$$

Question 17

Which of the following is the correct interval notation for the solution set of $$x \geq -2$$?

Accepted Answer

$$[-2, \infty)$$

Question 18

A cone has a radius of 3 cm and a height of 4 cm. What is its volume?

Accepted Answer

$$V = \frac{1}{3} \pi r^2$ h = \frac{1}{3} \pi (3)^2$ (4) = \frac{1}{3} \pi (9)(4) = \frac{36}{3} \pi = 12\pi cm$^3$$

Question 19

Which of the following is the correct solution to the equation $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

College Algebra: Essential Concepts and Problem-Solving Strategies

스터디 가이드 - 연습 문제