TSIA2 Math Review 2025

Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?

• 30 feet

• 40 feet

• 50 feet

• 60 feet

Answer explanation

Question 1 Explanation: 

The correct answer is (A). The formula for the area of a rectangle:

A=Width⋅LengthA=Width⋅Length

From the question we know that L=2WL=2W and that A=50A=50. So we can plug these values into our equation and solve for WW:

50=W⋅L50=W⋅L
50=W⋅2W50=W⋅2W
50=2W250=2W2
W2=25W2=25
W=5W=5

We know that L=2WL=2W, so L=10L=10
Perimeter =2L+2W=2L+2W
Perimeter =2⋅10+2⋅5=2⋅10+2⋅5
Perimeter =30

What is the probability of selecting a male from a group of 4 males and 8 females?

• 1/3

• 1/2

• 2/3

• 4/5

• -2

• 2

• 1/2

• 3

Answer explanation

Question 3 Explanation: 

The correct answer is (D). We can simplify the equation as follows:

3(x+1)=5(x−2)+7
3x+3=5x−10+7

3x+3=5x−3
We can add 3 to both sides to get the following:

3x+6=5x

We can subtract 3x from both sides and then divide the resulting equation by 2 to solve for x as follows:

6=2x
3=x

Answer explanation

Question 4 Explanation: 

The correct answer is (B). The slope-intercept form of a line is:

y=mx+b

Since the line passes through (−1,2), there are three possibilities: The line will have a slope (the “m” in front of the “x” variable), it will be vertical (x=−1), or it will be horizontal (y=2).

Plug x=−1 into all four equations to see which equation is not satisfied. The only answer choice that doesn’t give us y=2 is y=x+1.

Answer explanation

Question 5 Explanation: 

The correct answer is (C). Martina’s age ten years ago is:
m−10

So Diego’s age is:

5(m−10)
=5m−50

• 5

• 10

• 15

• 20

Answer explanation

Question 6 Explanation: 

The correct answer is (B). Here is the easiest way to solve this:

2x+5=8x
8x−2x=5
6x=5
6x⋅2=5⋅2
12x=10

An airline asked its agents to assign convenience ratings on a scale of 1–7 to 114 flights leaving one of its hub cities. The histogram below shows the distribution of the ratings of the 114 flights. What is the median rating assigned by the agents?

• 3

• 4

• 5

• 6

Answer explanation

Question 7 Explanation: 

The correct answer is (C). The median is the value at the midpoint of a frequency distribution of observed values. Since we have an even number of ratings (114), the median will be the average of the two middle numbers. In this case, the median rating will be the average of the 57th and 58th rating.

Add the frequencies up, starting from the lowest rating:

Rating 1: Flights 1–8 (the first 8)
Rating 2: Flights 9–19 (the next 11)
Rating 3: Flights 20–38 (the next 19)
Rating 4: Flights 39–55 (the next 17)
Rating 5: Flights 56–78 (the next 23)
......

You could keep going, but you can see that both the 57th and the 58th rating will correspond to a rating of 5.

Therefore, the median rating is 5.

• 1

• 4

• 8

• 16

The market price of a house is directly proportional to the total area of the house in square feet. If the price of a 1,500 square foot home is $300,000, what is the price of a 2,000 square foot home?

• $350,000

• $400,000

• $450,000

• $500,000

• -2

• -1

• 1

• 2

Answer explanation

Question 10 Explanation: 

The correct answer is (D). At the x-intercept, y=0. We can solve for the x-intercept by setting y=0 in the equation of the line:

2y=3x−6
2(0)=3x−6
0=3x−6
3x=6
x=2