Free Printable Q1W6 Pre-Test

1.

Give the reduced form of $\frac{10}{2𝑎𝑏^2\ }\cdot\ \frac{^{𝑎^2𝑏^2}}{5}$

a)

2

b)

5

c)

a

d)

b

2.

What are the common factors in the numerators and denominators of $\frac{6𝑎𝑏^5}{𝑏𝑐^2}$

a)

$𝑎^2𝑏^2𝑐$

b)

$𝑎𝑏^2𝑐$

c)

$𝑎^2𝑏𝑐$

d)

𝑎𝑏𝑐

3.

Find the product of $\frac{4}{6−2𝑎}\cdot\frac{3−𝑎}{2}$

a)

4

b)

3

c)

2

d)

1

4.

Write as one fraction and simplify $\frac{2}{𝑥^2+𝑥}\cdot\frac{2𝑥+2}{x}$

a)

$\frac{8}{x^2}$

b)

$\frac{6}{x^2}$

c)

$\frac{3}{x^2}$

d)

$\frac{4}{x^2}$

5.

Find the common factors of the numerator and denominator of $\frac{𝑥^2−16}{𝑥^2+𝑥−20}\cdot\frac{𝑥^2−8𝑥+16}{2𝑥−8}$

a)

𝑥 − 3

b)

𝑥 − 4

c)

(𝑥 − 3)(𝑥 − 4)

d)

(𝑥 − 4)(𝑥 − 4)

6.

What is the product of $\frac{𝑥−3}{𝑥^2+𝑥−20}\cdot\frac{𝑥^2−8𝑥+16}{𝑥−3}$

a)

$\frac{𝑥+4}{𝑥+5}$

b)

$\frac{𝑥+4}{𝑥−5}$

c)

$\frac{𝑥−4}{𝑥−5}$

d)

$\frac{𝑥−4}{𝑥+5\ }$

7.

What is the quotient of $\frac{2𝑥+5}{4}\div\frac{2𝑥+5}{6}$

a)

$\frac{2}{3}$

b)

$\frac{1}{2}$

c)

$\frac{1}{4}$

d)

$\frac{3}{2}$

8.

From $\frac{𝑥−5}{5}\div\frac{𝑥−2}{3}$ what is the divisor?

a)

$\frac{𝑥−5}{5}$

b)

$\frac{𝑥−3}{𝑥−5}$

c)

$\frac{𝑥−5}{𝑥−3}$

d)

$\frac{𝑥−2}{3}$

9.

$\frac{2𝑥−5}{4}\div\frac{4𝑥−10}{4}$

a)

2 and 𝑥 − 5

b)

4 and 𝑥 − 10

c)

4 and 2𝑥 − 5

d)

4 and 4𝑥 − 10

10.

Perform the indicated operation $\frac{𝑥−2}{2}\div\frac{𝑥^2−4}{3}$

a)

$\frac{3}{2𝑥+4}$

b)

$\frac{4}{2𝑥−4}$

c)

$\frac{6}{2(𝑥+2)}$

d)

$\frac{8}{2(𝑥−2)}$

11.

Given $\frac{𝑥−4}{4}$ as one factor of the rational algebraic expression $\frac{𝑥^2−16}{4}$ , what is the other factor?

a)

$\frac{𝑥+2}{2}$

b)

$\frac{𝑥+4}{2}$

c)

$\frac{𝑥+6}{2}$

d)

$\frac{𝑥+8}{2}$

12.

$Divide\ \frac{𝑟+1}{𝑟−2}with\ \frac{2𝑟+2}{𝑟+2}$

a)

$\frac{𝑟−2}{2𝑟}$

b)

$\frac{𝑟+2}{2𝑟−1}$

c)

$\frac{𝑟+2}{2𝑟−4}$

d)

$\frac{𝑟−2}{2𝑟+4}$

13.

Below are the steps in finding the quotients of rational algebraic expressions. Which of the following is in correct order?

I. Divide out common factors.

II. Simplify the remaining factors.

III. Find the reciprocal of the divisor and proceed to multiplication.

IV. Determine the dividend and divisor of the given expression.

a)

I, II, III

b)

II, III, IV

c)

IV, III, I, II

d)

IV, I, II, III

14.

Given the expression $\frac{𝑎^2+𝑎}{3𝑎−15}\div\frac{𝑎^2+2𝑎+1}{6𝑎−30}$ which of the following statements is true?

a)

The divisor is $\frac{𝑎^2+𝑎}{3𝑎−15}$

b)

The reciprocal of the divisor is $\frac{3𝑎−15}{𝑎^2+𝑎}$

c)

The common factors that can be divided out are (𝑎 + 1)(3𝑎 − 15).

d)

The quotient obtained after dividing the expressions $\frac{𝑎^2+𝑎}{3𝑎−15}\div\frac{𝑎^2+2𝑎+1}{6𝑎−30}is\ \frac{2𝑎}{a+1}$

15.

Your classmate multiplied rational algebraic expressions as presented below. $\frac{𝑥+3}{2}\cdot\frac{2}{𝑥+3}=\frac{𝑥+3}{2}\cdot\frac{𝑥+3}{2}=\frac{𝑥^2+6𝑥+9}{4}$

Is your classmate’s solution correct?

a)

Yes. There is a need to get the reciprocal of the second factor.

b)

No. Getting the reciprocal is not applicable in multiplying rational expressions.

c)

Yes. The product obtained after multiplying the expressions is correct.

d)

No. The product obtained after multiplying the rational algebraic expressions is wrong.

Q1W6 Pre-Test

Total questions: 15

Worksheet time: 8mins

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