PSAT Math : Algebra
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Example Questions
Example Question #221 : New Sat
If 
Example Question #1129 : Algebra
If 
Example Question #14 : Algebraic Functions
Given h(x) = 3x2 – 7. Which of the following values has the highest value?
Explanation: Because of the square in the equation you know the greatest magnitude (absolute value) x value will give you the greatest solution. The greatest magnitude of X listed is -3. Alternatively you could multiple everything out (Solutions: A) 41, B) 17, C) -7, D) 17 E)20)
Example Question #15 : Algebraic Functions
If 2 ≤ |t+1|, which number can it not be?
-2
-3
-4
4
3
-2
Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.
Example Question #16 : Algebraic Functions
If f(x) = 5x – 10, then what is the value of 5(f(10)) – 10?
190
110
50
200
40
190
The first step is to find what f(10) equals, so f(10)=5(10) – 10 = 40. Then substitute 40 into the second equation: 5(40) – 10 = 200 – 10 = 190.
190 is the correct answer
Example Question #17 : Algebraic Functions
f(x) = 0.1x + 7
g(x) = 1000x + 4
What is g(f(100))?
17004
1700400
170040
170.04
1700.4
17004
First find the value of f(100) = 0.1(100) + 7 = 10 + 7 = 17
Then find g(17) = 1000(17) + 4 = 17000 + 4 = 17004.
Example Question #21 : Algebraic Functions
The rate of a gym membership costs p dollars the first month and m dollars per month every month thereafter. Which of the following represents the total cost of the gym membership for n months, if n is a positive integer?
The one-time first-month cost is p, and the monthly cost is m, which gets multipled by every month but the first (of which there are n -1). The total cost is the first-month cost of p, plus the monthly cost for (i.e. times) n -1 months, which makes the total cost equal to p + m (n -1).
Example Question #13 : How To Find F(X)
1. If f(x) = (x + 4)/(x – 4) for all integers except x = 4, which of the following has the lowest value?
f(0)
f(–1)
f(1)
f(6)
f(–3)
f(1)
Plug each value for x into the above equation and solve for f(x). f(1) provides the lowest value –5/3
Example Question #281 : Algebra
If n and p are positive and 100n3p-1 = 25n, what is n-2 in terms of p ?
4p
4p–3
4p–1
4p–2
4p2
4p–1
To solve this problem, we look for an operation to perform on both sides that will leave n-2 by itself on one side. Dividing both sides by 25n-3 would leave n-2 by itself on the right side of the equqation, as shown below:
100n3p–1/25n–3 = 25n/25n–3
Remember that when dividing terms with the same base, we subtract the exponents, so the equation can be written as 100n0p–1/25 = n–2
Finally, we simplify to find 4p–1 = n–2.
Example Question #22 : Algebraic Functions
Given f(x)=|3x-2|. What values of x satisfy f(x)=10
4
0
0,4
-8/3,4
-8/3,0,4
-8/3,4
Setting f(x)=10 and taking the equation out of the absolute value you get 10=3x-2 and -10=3x-2. Solving both of these equations for x gives you x=4 or -8/3.
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