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PSAT Math : Algebra

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Example Questions

Example Question #2791 : Sat Mathematics

If $\small f(x) = 4x^{2}+3x+2$ and $\small g(x) = x+7$ , what is $\small f(g(x))$ ?

Possible Answers:

$\small 4x^{2}+3x+72$

$\small 4x^{2}+3x+219$

$\small 4x^{2}+17x+72$

$\small 4x^{2}+59x+219$

$\small 4x^{2}+17x+219$

Correct answer:

$\small 4x^{2}+59x+219$

Explanation:

$\small 4(x+7)^{2} +3(x+7)+2$

$\small 4(x^{2} + 14x + 49)+ 3x +21 + 2$

$\small 4x^{2}+56x+196+3x+23$

$\small 4x^{2}+59x+219$

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Example Question #2792 : Sat Mathematics

If f(6)=7 and f(10)=17 , which of the following could represent f(x) ?

Possible Answers:

x + 4

1.5x - 2

2.5x - 8

2x + 5

3x - 1

Correct answer:

2.5x - 8

Explanation:

The number in the parentheses is what goes into the function.

For the function f(x) = 2.5x - 8 ,

f(6) = 2.5(6) - 8 = 7 and

f(10) = 2.5(10) - 8 = 17

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Example Question #2793 : 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)?

Possible Answers:

$\frac{1}{2}$

$\frac{7}{2}$

Correct answer:

Explanation:

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

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Example Question #11 : How To Find F(X)

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 = 0

x = –1

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 #12 : How To Find F(X)

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 #51 : Algebraic Functions

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 #983 : Psat Mathematics

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

Possible Answers:

132

104

100

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 #984 : Psat Mathematics

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

27 liters

48 liters

None of the other answers are correct.

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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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #2791 : Sat Mathematics

Example Question #2792 : Sat Mathematics

Example Question #2793 : Sat Mathematics

Example Question #11 : How To Find F(X)

Example Question #12 : How To Find F(X)

Example Question #51 : Algebraic Functions

Example Question #982 : Psat Mathematics

Example Question #983 : Psat Mathematics

Example Question #984 : Psat Mathematics

Example Question #985 : Psat Mathematics

All PSAT Math Resources

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