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SAT Math : SAT Mathematics

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Example Questions

Example Question #2671 : Act Math

Which of the statements describes the solution set for –7(x + 3) = –7x + 20 ?

Possible Answers:

All real numbers are solutions.

There are no solutions.

x = –1

x = 0

Correct answer:

There are no solutions.

Explanation:

By distribution we obtain –7x – 21 = – 7x + 20. This equation is never possibly true.

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Example Question #2672 : Act Math

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 f(p) = 2p+6 , where represents the number of meetings Will has attended. Using this function, how many poems has Will written after 7 classes?

Possible Answers:

Correct answer:

Explanation:

For this function, simply plug 7 in for and solve:

f(p)=2p+6=2(7)+6=20

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Example Question #2801 : Sat Mathematics

If $f(x)=x^{3} +\frac{4}{x} + \frac{x^{2}}{2}$ what is $f\left ( 4 \right )$

Possible Answers:

Correct answer:

Explanation:

$f(x)=x^{3} +\frac{4}{x} + \frac{x^{2}}{2}$

$f(4)=4^{3} +\frac{4}{4} + \frac{4^{2}}{2}$

$f(4)=64 + 1 + 8$

$f(4)=73$

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Example Question #982 : Psat Mathematics

If $f(x)=x+\frac{1}{x}$ , find the value of f(4) .

Possible Answers:

$\frac{41}{4}$

$\frac{17}{4}$

Correct answer:

$\frac{17}{4}$

Explanation:

f(4) = 4 + 1/4 = 16/4 + 1/4 = 17/4

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Example Question #61 : Algebraic Functions

If f(x) = x + 8 and g(x) = x^2 + x , what is g(f(3)) ?

Possible Answers:

100

132

104

Correct answer:

132

Explanation:

g is a function of f, and f is a function of 3, so you must work inside out.

f(3) = 11

g(f(3)) = g(11) = 121 + 11 = 132

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Example Question #62 : Algebraic Functions

Jamie buys a new fish tank. It is 45% full. She adds seven more liters of water, and it is 65% full. What is the capacity of Jamie's new fish tank?

Possible Answers:

22 liters

35 liters

None of the other answers are correct.

48 liters

27 liters

Correct answer:

35 liters

Explanation:

The algebraic expression for x, the capacity of the fishtank is:

$0.45x+7=0.65x$

$0.45x+7-0.45x=0.65x-0.45x$

$0.2x=7$

$0.2x\times\frac{1}{0.2}=7\times\frac{1}{0.2}$

$x=35\hspace{1 mm}L$

The capacity of the fishtank is 35 liters.

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Example Question #985 : Psat Mathematics

f(x)=2x+6

g(x)=3x-3

2f(x)-g(x)+2=?

Possible Answers:

5x + 11

x + 5

x + 11

7x + 17

x + 17

Correct answer:

x + 17

Explanation:

When we multiply a function by a constant, we multiply each value in the function by that constant. Thus, 2f(x) = 4x + 12. We then subtract g(x) from that function, making sure to distribute the negative sign throughout the function. Subtracting g(x) from 4x + 12 gives us 4x + 12 - (3x - 3) = 4x + 12 - 3x + 3 = x + 15. We then add 2 to x + 15, giving us our answer of x + 17.

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Example Question #101 : Algebraic Functions

Given the following functions, evaluate b(4) - w(5) .

b(x)=x^2+2x

w(x)=x^2-2x

Possible Answers:

Correct answer:

Explanation:

b(4)=4^2+2(4)=24

w(5)=5^2-2(5)=15

b(4)-w(5)=24-15=9

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Example Question #61 : How To Find F(X)

The point (3,w) is one of the points of intersection of the graphs of f(x) and g(x) . Given that f(x)=x^2-2 and g(x)=-x^2+u , find the value of .

Possible Answers:

Correct answer:

Explanation:

Since it’s given than f(3) = w , we know that w=3^2-2=7 . We now know that (3, 7) is a point of intersection. Therefore, g(3) = 7 as well. In other words, 7=-3^2+u , so u=16 .

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Example Question #62 : How To Find F(X)

Consider these functions:

b(x)=x^2+2x

w(x)=x^2-2x

Which of the following is equivalent to w(e-1) ?

Possible Answers:

b(e)+6e-3

b(e)-2e+1

b(e)+4e

b(e)-6e+3

b(e)-4e+3

Correct answer:

b(e)-6e+3

Explanation:

w(e-1)=(e-1)^2-2(e-1)

=e^2-2e+1-2e+2

=e^2-4e+3

=e^2+2e-6e+3

=b(e)-6e+3

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2671 : Act Math

Example Question #2672 : Act Math

Example Question #2801 : Sat Mathematics

Example Question #982 : Psat Mathematics

Example Question #61 : Algebraic Functions

Example Question #62 : Algebraic Functions

Example Question #985 : Psat Mathematics

Example Question #101 : Algebraic Functions

Example Question #61 : How To Find F(X)

Example Question #62 : How To Find F(X)

All SAT Math Resources

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