TSIA 2.0 Math Practice Test #1 with Explanations 2023

TSIA 2.0 Math Practice Test with Answers Explained

Multiple Choice

If there are $$2.2$$ pounds in $$1$$ kilogram, how many pounds are there in $$x$$ kilograms?

• $$\frac{x}{2.2}$$

• $$2.2x$$

• $$2.2\ +\ x$$

• $$\frac{2.2}{x}$$

If there are 2.2 pounds in 1 kilogram, then there are 2.2x pounds in x kilograms.

Explanation:

Multiple Choice

The bar graph shows the number of customers

who shopped at a store Monday through Thursday of

one week. If the number of customers on Friday was

a one-fifth increase from the number of customers on

Thursday, how many customers shopped at the store

on Friday?

• 480

• 500

• 525

• 600

​According to the graph, 400 customers shopped at the store on Thursday. The number of customers at the store on Friday was a one-fifth increase from the number of customers on Thursday. Thus, the number of customers on Friday was 400 + 1 /5 (400) = 400 + 80 = 480.

​Explanation:

Multiple Choice

Last year, a bakery sold $$w$$ loaves of bread. This year,

the bakery sold three more than twice the number of

loaves of bread sold last year. If next year the bakery

plans on selling twice the number of loaves of bread

sold this year, how many loaves of bread does the

bakery expect to sell next year?

• $$2w$$

• $$2w+3$$

• $$4w+3$$

• $$4w+6$$

E​xplanation:

Last year, a bakery sold w loaves of bread. This year, the bakery sold three more than twice the number of loaves of bread sold last year, which is 2w + 3. Next year, the bakery plans on selling twice the number of loaves of bread sold this year, which is 2(2w + 3) = 4w + 6 loaves of bread.

Multiple Choice

If $$7p-4=8$$  , what is the value of $$p$$ ?

• $$\frac{4}{7}$$  

• $$\frac{7}{12}$$  

• $$\frac{12}{7}$$  

• $$\frac{7}{4}$$  

​If 7p − 4 = 8 1. Add 4 to both sides

+4 = + 4 2. Divide both sides by 7.

7p = 12

7 7

p = 12/7

Multiple Choice

Running at an average rate of 6 miles per hour, how many minutes would it take Kyle to run 3 miles?

• 18

• 30

• 40

• 45

Multiple Choice

The dot plot above identifies the number of pets living with each of 20 families in an apartment building. What fraction of the families have more than two pets?

• $$\frac{3}{20}$$

• $$\frac{1}{5}$$

• $$\frac{1}{4}$$

• $$\frac{9}{20}$$

Multiple Choice

The formula for the volume of the right circular

cylinder shown is $$V=\pi r^2h$$ .

If $$r=2b$$ , and $$h=5b+3$$ , what is the volume of the cylinder in terms of $$b$$ ?

• $$10\pi b^2+6\pi b$$

• $$20\pi b^3+12\pi b^2$$

• $$20\pi^2b^3+12\pi^2b^2$$

• $$50\pi b^3+20\pi b^2+90\pi b$$

Multiple Choice

Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?

• $3.25

• $5.25

• $7.75

• $17.25

Multiple Choice

If $$5c-2=3c$$ , then  $$24c=$$   ?

• 6

• 8

• 16

• 24

Multiple Choice

In the $$xy$$ -plane, the slope of the line $$y=mx−4$$ is less than the slope of the line $$y=x−4$$ . Which of the following must be true about m?

• $$m=-1$$

• $$m=1$$

• $$m<1$$

• $$m>1$$

Explanation:

If an equation of a line in the xy-plane is in

slope-intercept form, the slope is the coefficient of x, so the slope of the line

y = mx − 4 is m, and the slope of the line y = x − 4 is 1. The slope of the line y = mx − 4

is less than the slope of the line y = x − 4, so it must be true that m < 1.

Multiple Choice

A history class is made up of 12 tenth graders and 9 eleventh graders. The tenth graders averaged 77 on the midterm exam, and the eleventh graders averaged 91 on the midterm exam. What was the average grade on the midterm exam for the entire class?

• 82

• 83

• 84

• 85

​Explanation:

Since the 12 tenth graders averaged 77 on the

midterm exam, the sum of their scores was 12 × 77 = 924; since the 9 eleventh graders

averaged 91 on the exam, the sum of their scores was 9 × 91 = 819. Therefore, the

sum of the scores of all 12 + 9 = 21 students in the class was 924 + 819 = 1,743, and

their average score on the midterm exam was 1,743 ÷ 21 = 83.

Multiple Choice

Which of the following is NOT equivalent to  $$\left(3x-12\right)\left(x+4\right)$$ ?

• $$3\left(x^2-8x+16\right)$$  

• $$3\left(x^2-16\right)$$  

• $$3x^2-48$$  

• $$3x\left(x+4\right)-12\left(x+4\right)$$  

Multiple Choice

If the cost of carpeting a floor is $2.50 per square foot, how much will it cost to carpet a rectangular floor that is 10 feet by 12 feet?

• $112.00

• $120.00

• $250.00

• $300.00

​Explanation:

The floor is 10 feet by 12 feet, so the area of the floor

is (10)(12) = 120 square feet. The cost of carpeting a floor is $2.50 per square foot, so

the cost of carpeting this floor is $2.50 × 120 = $300.00.

Multiple Choice

If $$n$$ is the least of two consecutive odd integers, which of the following represents the sum of the two integers?

• $$n+1$$

• $$n+2$$

• $$2n+1$$

• $$2n+2$$

​Explanation:

If n is the least of two consecutive odd integers, then

the greater odd integer is n + 2. It then follows that the sum of the two consecutive

odd integers is n + (n + 2) = 2n + 2.

Multiple Choice

Simplify the following expression:

$$\left(\frac{x^{-5}y}{y^3}\right)^{-1}$$

• $$\frac{x^5}{y^2}$$  

• $$\frac{y^2}{x^5}$$  

• $$x^5y^2$$  

• $$x^5y^{-3}$$  

Multiple Choice

Reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. If she chooses two of these coins at random, what is the probability that the two coins combined will be worth at least 35 cents?

• $$\frac{5}{18}$$

• $$\frac{5}{9}$$

• $$\frac{13}{18}$$

• $$\frac{71}{72}$$

Multiple Choice

In the xy-plane, what is the y-intercept of the graph of the equation  $$y=6\left(x-\frac{1}{2}\right)\left(x+3\right)$$ ?

• -9

• $$-\frac{1}{2}$$  

• 3

• 9

Multiple Choice

The area of the triangle shown is 21. What is the value of x?

• 3

• 6

• 7

• 11

Multiple Choice

For which of the following values of x is the function  $$f\left(x\right)=\sqrt{4-x^2}$$  NOT defined as a real number?

• -2

• 0

• 2

• 4

Multiple Choice

Under ideal conditions, the population of a certain species doubles every nine years. If the population started with 100 individuals, which of the following expressions gives the population of the species t years after the population started, assuming that the population has been living under ideal conditions?

• $$2\times100^{9t}$$

• $$2\times100^{\frac{t}{9}}$$

• $$100\times2^{9t}$$

• $$100\times2^{\frac{t}{9}}$$