PSAT Math : Algebra
Study concepts, example questions & explanations for PSAT Math
All PSAT Math Resources
Example Questions
Example Question #4 : How To Use The Quadratic Function
A pitcher standing on top on a 600-foot building throws a baseball upward at an initial speed of 90 feet per second. The height 
How high does the ball get? (Nearest foot)
This can be solved by first finding the first coordinate (
The 
The ball takes 2.8 seconds to reach its peak. The height at that time is 
making the correct response 727 feet.
Example Question #7 : How To Use The Quadratic Function
A pitcher standing on top on a 600-foot-high building throws a baseball upward at an initial speed of 90 feet per second. The height 
How long does it take for the ball to hit the ground? (Nearest tenth of a second)
Set the height function equal to 0:
Set 
Evaluate separately, and select the positive value.
which is thrown out.
which is positive and is the result we keep.
The correct response is 9.6 seconds.
Example Question #1 : How To Use The Quadratic Function
A pitcher standing on top on a 600-foot building throws a baseball upward at an initial speed of 90 feet per second. The height
How long does it take for the ball to return to the level at which it started? (Nearest tenth of a second)
The question is essentially asking for the positive value of time 
Either 
The ball returns to a height of 600 feet after 5.6 seconds.
Example Question #111 : Algebraic Functions
A pitcher standing on top on a 600-foot building throws a baseball upward at an initial speed of 90 feet per second. The height 
How long does it take for the ball to reach its peak? (Nearest tenth of a second)
The time at which the ball reaches its peak can be found by finding the 
The 
The correct response is 2.8 seconds.
Example Question #1 : Evaluating And Simplifying Expressions
Half of one hundred divided by five and multiplied by one-tenth is __________.
2
1
1/2
5
10
1
Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.
Example Question #1 : How To Evaluate Algebraic Expressions
A total of 150 million votes were tallied in a presidential election. Votes were cast for either Hillary Clinton, Rand Paul, Al Gore, or Gary Johnson. If Clinton received 3 times the number of votes as Johnson, Paul received 30% of the vote, and Gore receieved 30 million total votes, who received the most votes in the election?
Hillary Clinton
Rand Paul
Al Gore
Gary Johnson
Hillary Clinton
There are a few ways to do this problem, but we will focus on the total number of votes method as follows. First, let Clinton = C, Gore = G, Paul = P, and Johnson = J. We know C + G + P + J = 150 million. We also know that C = 3J. Paul received 30% of the vote which is 150,000,000 * .3 = 45 million votes. Gore received 30 million votes. We can now create an equation with individual totals and substitute 3J for Clinton's vote total:
3J + 30 million + 45 million + J = 150 million
4J = 75 million
J = 18.75 million
Then C = 3J = 56.25 million. So Clinton received 56.25 million votes, Paul received 45 million votes, Gore received 30 million votes, and Johnson received 18.75 million votes. The correct answer is Hillary Clinton.
Example Question #1 : Evaluating Expressions
Justin makes 61.9% of his free throws. During the season he had 84 free throw attempts. How many of Jason’s shots did not go in?
52
32
21
40
36
32
Find how many free throws Justin made: 84 x 0.619 = 51.99. Since the problem talks free throws, we round to 52 shots went in. To calculate shots missed:
84 – 52 = 32.
Example Question #11 : Expressions
If 5x + 30 = 6 – 7x, then x = ?
x = –37
x = –10
x = –2
x = 2
x = –18
x = –2
Combine like terms by subtracting 6 from both sides so: 5x + 24 = –7x. Then subtract 5x from both sides: 24 = –12x. Divide both sides by –12 and x = –2.
Example Question #2 : Expressions
If ab - bc + d = d2 - c2, then what is the value of a when b is two, c is negative one, and d is zero?
ab - bc + d = d2 - c2
We need to substitute values in for b, c, and d, and then solve the equation for a.
a(2) - 2(-1) + 0 = 02 - (-1)2
2a +2 + 0 = 0 - (1)
2a + 2 = -1
2a = -3
a = -3/2
The answer is -3/2.
Example Question #3 : Evaluating And Simplifying Expressions
If 11x + 4 = 19x – 12, then what is 2x – 4?
0
2
Not possible
4
–8
0
First solve for x. The first equation would simplify as:
16 = 8x
x = 2
If we plug x = 2 into the second expression:
2(2) – 4 = 0
0 is the correct answer.
All PSAT Math Resources
