Question 1

What is the greatest common factor (GCF) of the monomials $$18x^3y^2$, 24x^2$y^4$$, and $$30x^4y$?

Accepted Answer

$$6x^2y$

Question 2

Factor the trinomial completely: $$x^2 - 5x + 6$.

Accepted Answer

$$(x-2)(x-3)$$

Question 3

Simplify the expression: $$\left( \frac{3x^2$y^7$$}{$$2xy^4$$} \$$right)^5$.

Accepted Answer

$$\frac{243x$$^{5}$$y^{15}$$}{32}$

Question 4

Solve the quadratic equation by factoring: $$x^2 - 9 = 0$.

Accepted Answer

$$x = 3, x = -3$$

Question 5

Use the quadratic formula to solve $$2x^2 - 4x - 6 = 0$.

Accepted Answer

$$x = 3, x = -1$$

Question 6

A ladder is leaning against a wall. The foot of the ladder is 9 ft from the wall, and the ladder reaches 15 ft up the wall. How long is the ladder? (Use the Pythagorean Theorem.)

Accepted Answer

$$\sqrt{9^2$ + 15^2$} = 17 ft$$

Question 7

Given the relation $$\{(1,2), (2,3), (3,4), (1,5)\}$$, is this a function? What is the domain?

Accepted Answer

No, domain is $$\{1,2,3\}$$

Question 8

Let $$f(x) = 2x^2$ - 3x + 1. $$Find $$f(2).$$

Accepted Answer

$$3$$

Question 9

Find the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13).$$

Accepted Answer

$$2$$

Question 10

What is the equation of the line with a slope of $$-3$$ and a $$y-$$intercept of $$2$$?

Accepted Answer

$$y = -3x + 2$$

Question 11

Given $$f(x) = x^2$ and g(x) = x + 1$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$9$$

Question 12

Find the difference quotient for $$f(x) = x^2$.

Accepted Answer

$$\frac{(x+h)^2$ - x^2$}{h}$$

Question 13

A rectangular garden has a diagonal of 10 m and one side of 6 m. What is the length of the other side? (Round to the nearest tenth.)

Accepted Answer

$$8.0 m$$

Question 14

Given the linear equation $$2x - 3y = 6$$, what is the slope and $$y-$$intercept?

Accepted Answer

Slope: $$\frac{2}{3}$$, $$y-$$intercept: $$-2$$

Question 15

If $$f(x) = 3x - 1$$ and $$g(x) = x^2$, find f(g(2$$))$$.

Accepted Answer

$$11$$

Question 16

A car travels 18 miles east and then 6 miles north. What is the straight-line distance from the starting point to the ending point? (Use the Pythagorean Theorem.)

Accepted Answer

$$\sqrt{18^2$ + 6^2$} = 18.97$$ miles

College Algebra Supplemental Practice Guidance

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드