Quiz about PA Alg1 Keystone Review Module 1

Question 1

Which of these numbers lies between 4 and 4.5 on a number line?

Accepted Answer

$$\sqrt[]{17}$$

Answer

$$\sqrt[]{13}$$

Answer

$$\sqrt[]{22}$$

Answer

$$\sqrt[]{28}$$

Question 2

Which of the following inequalities is true for all real values of x?

Accepted Answer

$$\frac{1}{x^2+1}>0$$

Answer

$$\frac{1}{x^2}>0$$

Answer

$$\frac{1}{x^3}>0$$

Answer

$$\frac{1}{x^3+1}>0$$

Question 3

What is the simplified form of $$\sqrt[]{54}$$ ?

Accepted Answer

$$3\sqrt[]{6}$$

Answer

$$6\sqrt[]{3}$$

Answer

$$9\sqrt[]{3}$$

Answer

$$9\sqrt[]{6}$$

Question 4

An expression is shown below

$$5\sqrt[]{48a}$$

If this expression is equivalent to 60, what must be the value of a?

Accepted Answer

3

Answer

4

Answer

9

Answer

16

Question 5

What is the greatest common factor (GCF) of the monomials $$a^2b^5\ and\ a^3b^3$$ .

Accepted Answer

$$a^2b^3$$

Answer

$$a^2b^5$$

Answer

$$a^3b^3$$

Answer

$$a^3b^5$$

Question 6

What is the least common Multiple (LCM) of the monomials $$60xy^3\ and\ 100x^2y$$ ?

Accepted Answer

$$300x^2y^3$$

Answer

$$20xy$$

Answer

$$600x^3y^4$$

Answer

$$6,000x^3y^4$$

Question 7

Find the value of this expression.

$$\left|-14+6-12\right|$$

Accepted Answer

20

Answer

-32

Answer

-20

Answer

32

Question 8

If $$\frac{2^7\cdot2^5}{2^p}$$ simplifies to $$2^3$$ , what must be the value of p?

Accepted Answer

9

Answer

2

Answer

4

Answer

6

Question 9

Evaluate $$\left(10x^4y^3\right)\left(3x^2y\right).$$

Accepted Answer

$$30x^6y^4$$

Answer

$$30x^6y^3$$

Answer

$$30x^8y^3$$

Answer

$$30x^8y^4$$

Question 10

Simplify this expression: $$\sqrt[]{4a^8b^2}$$

Accepted Answer

$$2a^4b$$

Answer

$$2a^4b^4$$

Answer

$$16a^4b$$

Answer

$$16a^4b^4$$

Question 11

Aaron bought a large basket of 59 apples for $22.95. He also bought a small basket of 18 apples for $8.95. Which amount is the closest estimate of the cost per apple?

Accepted Answer

$0.40

Answer

$0.20

Answer

$0.30

Answer

$0.50

Question 12

One moth, 53% of the dinner entrees sold at a restaurant cost $28 or more. That month, the restaurant sold 2,635 dinner entrees of all prices. What is the best estimate of the least total amount the $28-or-more dinner entrees brought in?

Accepted Answer

$39,000

Answer

$40,500

Answer

$42,000

Answer

$45,000

Question 13

What is the simplified form of the expression below?

$$\left(2w^3+4w^2+5\right)+\left(3w^3+w^2+4w\right)$$

Accepted Answer

$$5w^3+5w^2+4w+5$$

Answer

$$5w^3+5w^2+9$$

Answer

$$5w^3+5w^2+9w$$

Answer

$$5w^3+5w^2+5w+4$$

Question 14

Look at this expression.

$$\left(5x+3\right)\left(x^2-x-4\right)$$

Which is an equivalent expression?

Accepted Answer

$$5x^3-2x^2-23x^{ }-12$$

Answer

$$5x^3-3x^{ }-4$$

Answer

$$5x^3-3x^{ }-12$$

Answer

$$5x^3+3x^2-20x^{ }-12$$

Question 15

What expression shows the factored form of $$a^2b^5+a^3b^3$$

Accepted Answer

$$a^2b^3\left(b^2+a\right)$$

Answer

$$a^2b^3\left(1+ab^2\right)$$

Answer

$$a^3b^3\left(b^2+1\right)$$

Answer

$$a^2b^5\left(1+ab^2\right)$$

Question 16

Which shows the factored form of the expression below?

$$100-p^{16}$$

Accepted Answer

$$\left(10+p^8\right)\left(10-p^8\right)$$

Answer

$$\left(10+p^4\right)\left(10-p^4\right)$$

Answer

$$\left(100+p^4\right)\left(100-p^4\right)$$

Answer

$$\left(10+p^{16}\right)\left(10-p^{16}\right)$$

Question 17

Which binomial is a factor of $$w^2-w-20$$

Accepted Answer

(w-5)

Answer

(w+1)

Answer

(w-4)

Answer

(w+5)

Question 18

What value of b makes the equation below true?

$$x^2+bx-35=\left(x+5\right)\left(x-7\right)$$

Accepted Answer

-2

Answer

12

Answer

2

Answer

-12

Question 19

What is the simplified form of the rational expression below?

$$\frac{5x+10}{10x}$$

Accepted Answer

$$\frac{x+2}{2x}$$

Answer

$$5$$

Answer

$$\frac{5}{x}$$

Answer

$$\frac{x+2}{x}$$

Question 20

What is the simplified form of the expression below?

$$\frac{6y}{4y^2+10y}$$

Accepted Answer

$$\frac{3}{2y+5}$$

Answer

$$\frac{1}{2y+5}$$

Answer

$$\frac{3}{2\left(2y+5\right)}$$

Answer

$$\frac{1}{4y^2+4y}$$

Question 21

What is the solution to the linear equation $$-6z+1=13$$

Accepted Answer

$$z=-2$$

Answer

$$z=-6$$

Answer

$$z=2$$

Answer

$$z=6$$

Question 22

A restaurant meal for a group of people cost $85 total. This amount included a 6% tax and an 18% tip, both based on the price of the food. Which equation could be used to find f, the cost of the food?

Accepted Answer

$$85=1.24f$$

Answer

$$85=0.24c$$

Answer

$$85=1.06f+0.18$$

Answer

$$85=f+0.24$$

Question 23

A 50-foot roll of fencing will be used to enclose a rectangular garden. Which equation below could not be solved to find the possible lengths, l, and widths, w, of the garden?

Accepted Answer

$$50=2\left(l\right)\left(w\right)$$

Answer

$$\frac{50}{2}=l+w$$

Answer

$$2\left(l+w\right)=50$$

Answer

$$50=2l+2w$$

Question 24

Look at the linear equation below.

$$2x-3y=-13$$

Which pair of numbers is a solution to the equation?

Accepted Answer

(-5,1)

Answer

(-5,-1)

Answer

(5,-1)

Answer

(5,1)

Question 25

Look at this system of equations.

$$y=2x-1$$

$$4x+y=2$$

Which shows a correct step in using substitution to solve the system of equations?

Accepted Answer

$$4x+2x-1=2$$

Answer

$$4x+y=2x-1$$

Answer

$$6x-2=y$$

Answer

$$6x+2=2y$$

Question 26

What is the y-value of the solution to the system of equations shown below?

$$5x+4y=12$$

$$-5x-2y=-16$$

Accepted Answer

-2

Answer

-4

Answer

2

Answer

4

Question 27

Which inequality matches the graph?

Accepted Answer

x<3

Answer

x>3

Answer

x<3

Answer

x>3

Question 28

Which point below is NOT part of the solution set?

Accepted Answer

(-10, -10)

Answer

(0, 0)

Answer

(-1, 5)

Answer

(5, 20)

Question 29

Jina is raising money for a charity. She makes either 18 telephone calls per day or 10 home visits per day. Jina wants to contact at least 100 people next week. This situation can be represented by the following system of inequalities, where x = number of days making telephone calls and y = number of days making home visits.

$$x+y\le7$$

$$18x+10y\ge100$$

Which of the following is a true statement?

Accepted Answer

If Jina makes telephone calls for 5 days, she only needs 1 day of home visits.

Answer

Jina can reach her goal by making home visits only.

Answer

Jina can reach her goal with only 2 days of telephone calls.

Answer

If Jina does home visits for 4 days, she only needs 2 days of telephone calls.

PA Alg1 Keystone Review Module 1

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