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PSAT Math : Algebraic Functions

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Example Questions

Example Question #25 : Algebraic Functions

$a\ \mho \ b = a(b+1)-3$

Quantity A Quantity B

$1\ \mho\ 1$ $2\ \mho\ 0$

Possible Answers:

The relationship cannot be determined from the information given.

Quantity A and Quantity B are equal

Quantity B is greater

Quantity A is greater

Correct answer:

Quantity A and Quantity B are equal

Explanation:

Since $a\ \mho \ b = a(b+1)-3$ , then we have that

$1\ \mho \ 1=1(1+1)-3=-1$

and

$2\ \mho \ 0=2(0+1)-3=-1$ .

Thus, the two quantities are equal.

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Example Question #81 : Algebraic Functions

If the average of two numbers is $\dpi{100} \small 3y$ and one of the numbers is $\dpi{100} \small y+z$ , what is the other number, in terms of $\dpi{100} \small y$ and $\dpi{100} \small z$ ?

Possible Answers:

$\dpi{100} \small y+z$

$\dpi{100} \small 5y+z$

$\dpi{100} \small 5y-z$

$\dpi{100} \small 4y-z$

$\dpi{100} \small 3y+z$

Correct answer:

$\dpi{100} \small 5y-z$

Explanation:

The average is the sum of the terms divided by the number of terms. Here you have $\dpi{100} \small y+z$ and the other number which you can call $\dpi{100} \small x$ . The average of $\dpi{100} \small x$ and $\dpi{100} \small y+z$ is $\dpi{100} \small 3y$ . So $\dpi{100} \small 3y=\frac{(x+y+z)}{2}$

Multiply both sides by 2.

Solve for $\dpi{100} \small x=5y-z$ .

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Example Question #23 : Algebraic Functions

Alice is twice as old as Tom, but four years ago, she was three years older than Tom is now. How old is Tom now?

Possible Answers:

$\dpi{100} \small 3$

$\dpi{100} \small 13$

$\dpi{100} \small 21$

$\dpi{100} \small 9$

$\dpi{100} \small 7$

Correct answer:

$\dpi{100} \small 7$

Explanation:

The qustion can be broken into two equations with two unknows, Alice age $\dpi{100} \small (A)$ and Tom's age $\dpi{100} \small (T)$ .

$\dpi{100} \small A=2T$

$\dpi{100} \small A-4=T+3$

$\dpi{100} \small 2T-4=T+3$

$\dpi{100} \small T=7$

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Example Question #82 : Algebraic Functions

A jet goes from City 1 to City 2 at an average speed of 600 miles per hour, and returns along the same path at an average speed if 300 miles per hour. What is the average speed, in miles per hour, for the trip?

Possible Answers:

300miles/hour

400miles/hour

450miles/hour

500miles/hour

350miles/hour

Correct answer:

400miles/hour

Explanation:

Chose a number for the distance between City 1 and 2; 1800 works well, as it is a multiple of 600 and 300.

Now, find the time for each trip, the total distance, and the total time.

$t_1=\frac{d_1}{v_1}=\frac{1800}{600}=3$

$t_2=\frac{d_2}{v_2}=\frac{1800}{300}=6$

$total\ t=t_1+t_2=3+6=9$

$total\ d=d_1+d_2=1800+1800=3600$

Now we can find the average speed by dividing the total distance by the total time.

$average speed = \frac{total distance}{total time} = \frac{3600 miles}{9 hours} = 400 miles/hour$

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Example Question #29 : Algebraic Functions

$f(x)=3x^{2}-5$

g(x)=9-2x

Find f(g(5)) .

Possible Answers:

131

Correct answer:

Explanation:

Plug 5 into g(x) first:

g(5)=9-2(5)

=-1

Now, plug this answer into f(x) :

$f(-1)=3(-1)^{2}-5$

=3-5

=-2

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Example Question #83 : Algebraic Functions

If f(x) = 3x + 7 and g(x) = x^2 - 12 , what is f(g(x)) ?

Possible Answers:

9x^3 + 29

3x^2 + 29

9x^2 - 29

3x^2 - 29

3x^3 - 29

Correct answer:

3x^2 - 29

Explanation:

Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x²– 12) + 7.

Distribute the 3: 3x²– 36 + 7 = 3x²– 29

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Example Question #84 : Algebraic Functions

f(x) = 4x + 17

Solve f(x) for the equation above for x = 3.

Possible Answers:

Correct answer:

Explanation:

The correct answer is 29. We plug in 3 into the equation above and solve for x. So we find that f(x) = 4(3) + 17. 12 + 17 = 29

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Example Question #1211 : Algebra

For which value of are the following two functions equal?

$F(x)=2x+3^x+\frac{9x}{3}$

$G(x)=\frac{2^x+4^x}{2}-4x-5x+1$

Possible Answers:

Correct answer:

Explanation:

It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).

Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

The correct answer is 4 because

F(x) = 2x + 3^x+ (9x/3) = 2(4) + 3⁴ + ((9 * 4)/3) = 101, and

G(x) = (((2⁴ + 4⁴)/2) - 4 * 4) – 5(4) + 1 = 101.

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Example Question #201 : Algebraic Functions

The function is defined as f(x) = 3x^2 + 6x + 27 . What is f(-1) ?

Possible Answers:

-36

Correct answer:

Explanation:

Substitute -1 for in the given function.

$f(-1)=3(-1)^{2}+6(-1)+27$

f(-1)=3(1)-6+27

f(-1)=3-6+27

f(-1)=24

If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that (-1)^2 is 1, then you will have calculated 18.

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Example Question #2912 : Sat Mathematics

If the function h(x) is created by shifting f(x) up four units and then reflecting it across the x-axis, which of the following represents h(x) in terms of f(x) ?

Possible Answers:

f(x)+4

-f(x+4)

-f(x)-4

f(x-4)

f(x+4)

Correct answer:

-f(x)-4

Explanation:

We can take each of the listed transformations of f(x) one at a time. If f(x) is to be shifted up by four units, increase every value of f(x) by 4.

$f(x)_{\textup{shifted up by 4}}=f(x)+4$

Next, take this equation and reflect it across the x-axis. If we reflect a function across the x-axis, then all of its values will be multiplied by negative one. So, h(x) can be written in the following way:

h(x)=-(f(x)+4)

Lastly, distribute the negative sign to arrive at the final answer.

h(x)=-f(x)-4

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PSAT Math : Algebraic Functions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #25 : Algebraic Functions

Example Question #81 : Algebraic Functions

Example Question #23 : Algebraic Functions

Example Question #82 : Algebraic Functions

Example Question #29 : Algebraic Functions

Example Question #83 : Algebraic Functions

Example Question #84 : Algebraic Functions

Example Question #1211 : Algebra

Example Question #201 : Algebraic Functions

Example Question #2912 : Sat Mathematics

All PSAT Math Resources

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