SAT Math : SAT Mathematics
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Example Questions
Example Question #2761 : Sat Mathematics
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 #2762 : Sat Mathematics
If 2 ≤ |t+1|, which number can it not be?
4
-2
3
-3
-4
-2
Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.
Example Question #55 : Algebraic Functions
If f(x) = 5x – 10, then what is the value of 5(f(10)) – 10?
110
40
50
200
190
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 #2763 : Sat Mathematics
f(x) = 0.1x + 7
g(x) = 1000x + 4
What is g(f(100))?
170.04
1700.4
17004
170040
1700400
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 #2764 : Sat Mathematics
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 #16 : 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(–3)
f(0)
f(6)
f(–1)
f(1)
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 #2765 : Sat Mathematics
If n and p are positive and 100n3p-1 = 25n, what is n-2 in terms of p ?
4p–1
4p
4p2
4p–2
4p–3
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 : How To Find F(X)
Given f(x)=|3x-2|. What values of x satisfy f(x)=10
0,4
-8/3,0,4
0
4
-8/3,4
-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.
Example Question #22 : How To Find F(X)
|
x |
f(x) |
g(x) |
|
9 |
4 |
0 |
|
10 |
6 |
1 |
|
11 |
9 |
0 |
|
12 |
13 |
–1 |
According to the figure above, what is the value of g(12) – √f(9)?
–5
–1
13
3
–3
–3
For this question, we "plug in" the value of x given, which is inside the parentheses, and follow along the table to see what value the f or g functions output. For g(12), the output value is –1, while for f(9), the output value is 4 (be careful not to reverse these!) Thus, we can plug into the equation given:
(–1) – √4) = –1 – 2 = –3.
Example Question #991 : Algebra
Let f(x, y) = x2y2 – xy + y. If a = f(1, 3), and b = f(–2, –1), then what is f(a, b)?
7
2005
9
4025
73
73
f(x, y) is defined as x2y2 – xy + y. In order to find f(a, b), we will need to first find a and then b.
We are told that a = f(1, 3). We can use the definition of f(x, y) to determine the value of a.
a = f(1, 3) = 1232 – 1(3) + 3 = 1(9) – 3 + 3 = 9 + 0 = 9
a = 9
Similarly, we can find b by determining the value of f(–2, –1).
b = f(–2, –1) = (–2)2(–1)2 – (–2)(–1) + –1 = 4(1) – (2) – 1 = 4 – 2 – 1 = 1
b = 1
Now, we can find f(a, b), which is equal to f(9, 1).
f(a, b) = f(9, 1) = 92(12) – 9(1) + 1 = 81 – 9 + 1 = 73
f(a, b) = 73
The answer is 73.
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