PSAT Math : PSAT Mathematics
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Example Questions
Example Question #2791 : Sat Mathematics
If a(x) = 2x3 + x, and b(x) = –2x, what is a(b(2))?
503
–132
128
132
–503
–132
When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.
Example Question #6 : How To Find F(X)
Let F(x) = x3 + 2x2 – 3 and G(x) = x + 5. Find F(G(x))
x3 + 17x2 + 95x + 172
x3 + x2 + x + 8
x3 + x2 + 2
x3 + 2x2 + x + 2
x3 + 2x2 – x – 8
x3 + 17x2 + 95x + 172
F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x3 + 17x2 + 95x + 172
G(F(x)) = x3 + x2 + 2
F(x) – G(x) = x3 + 2x2 – x – 8
F(x) + G(x) = x3 + 2x2 + x + 2
Example Question #2792 : Sat Mathematics
What is the value of xy2(xy – 3xy) given that x = –3 and y = 7?
–2881
2881
3565
–6174
–6174
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
Example Question #8 : How To Find F(X)
Find 
Alternatively, we can find that 
Example Question #2793 : Sat Mathematics
It takes no more than 40 minutes to run a race, but at least 30 minutes. What equation will model this in m minutes?
If we take the mean number of minutes to be 35, then we need an equation which is less than 5 from either side of 35. If we subtract 35 from 
Example Question #2794 : Sat Mathematics
If 
Example Question #2795 : Sat Mathematics
If 
The number in the parentheses is what goes into the function.
For the function 
Example Question #2796 : Sat Mathematics
A function F is defined as follows:
for x2 > 1, F(x) = 4x2 + 2x – 2
for x2 < 1, F(x) = 4x2 – 2x + 2
What is the value of F(1/2)?
For F(1/2), x2=1/4, which is less than 1, so we use the bottom equation to solve. This gives F(1/2)= 4(1/2)2 – 2(1/2) + 2 = 1 – 1 + 2 = 2
Example Question #1021 : Algebra
Which of the statements describes the solution set for –7(x + 3) = –7x + 20 ?
x = 0
All real numbers are solutions.
x = –1
There are no solutions.
There are no solutions.
By distribution we obtain –7x – 21 = – 7x + 20. This equation is never possibly true.
Example Question #1022 : Algebra
Will just joined a poetry writing group in town that meets once a week. The number of poems Will has written after a certain number of meetings can be represented by the function 
For this function, simply plug 7 in for 
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