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PSAT Math : Algebra

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Example Questions

Example Question #44 : Expressions

What is the sixth term of the sequence: $\frac{1}{3}, \frac{1}{2}, \frac{3}{4}, \frac{9}{8} ... ?$

Possible Answers:

$2$

$\frac{27}{16}$

$\frac{81}{32}$

$\frac{81}{16}$

$\frac{3}{2}$

Correct answer:

$\frac{81}{32}$

Explanation:

Each term equals the previous term multiplied by $\frac{3}{2}$ .

The fifth term in the sequence is $\frac{9}{8} \cdot \frac{3}{2} = \frac{27}{16}$ .

The sixth term in the sequence is thus $\frac{27}{16} \cdot \frac{3}{2} = \frac{81}{32}$ .

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Example Question #32 : Evaluating And Simplifying Expressions

If $\dpi{100} \small z-3=n$ , then $\dpi{100} \small 2z=$ ?

Possible Answers:

$\dpi{100} \small n$

$\dpi{100} \small n+3$

$\dpi{100} \small n+6$

$\dpi{100} \small 3n+6$

$\dpi{100} \small 2n+6$

Correct answer:

$\dpi{100} \small 2n+6$

Explanation:

Begin by rearranging the equation to solve for z:

$\dpi{100} \small z=n+3$

This means that $\dpi{100} \small 2z=2\left ( n+3 \right )$ , which can be rewritten as $\dpi{100} \small 2n+6$ .

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Example Question #33 : How To Evaluate Algebraic Expressions

The symbol $\square$ is defined as follows:

$c\square d =(2c)^{d}$

Which of the following is equivalent to $4\square3$ ?

Possible Answers:

512

1296

1024

192

216

Correct answer:

512

Explanation:

Symbols may appear scary, but these problems are often easier than they first appear. Begin by taking the numbers you are given and replacing the letters in the equation with these numbers.

$c\square d = (2c)^{d}$

$4\square 3 = (2(4))^{3}$

We can now solve the equation. Be sure to perform the operations within the parentheses (PEMDAS) first.

$4\square 3=(2(4))^{^{3}}$

$4\square 3=(8)^{3}$

$4\square3 = 512$

The correct answer is 512.

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Example Question #38 : Expressions

If $\sqrt{3+x} = 3$ , then which of the following is equivalent to x^2-3x+1 ?

Possible Answers:

Correct answer:

Explanation:

Begin by solving for :

$\sqrt{3+x}=3$

First, square both sides of the equation:

$(\sqrt{3+x})^2 = 3^2$

3+x=9

Now, solve for :

3+x-3 = 9-3

x=6

Now that we know that is equal to 6, substitute 6 into the equation we need to solve:

x^2-3x+1

6^2-3(6)+1

Using the correct order of operations (PEMDAS), we find:

6^2-18+1

36-18+1

18+1

The answer is 19.

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Example Question #41 : Expressions

The function $\small f(x)$ is given as $\small f(x)=21-5x$ . If $\small \small f(a+2)=4$ , what is the value of $\small a$ ?

Possible Answers:

$\small \frac{17}{5}$

$\small -\frac{17}{5}$

$\small -\frac{7}{5}$

$\small 5$

$\small \frac{7}{5}$

Correct answer:

$\small \frac{7}{5}$

Explanation:

This is a simple substitution problem. Begin by setting the function $\small f(x)$ equal to $\small 4$ :

$\small 21-5x = 4$

Solve for $\small x$ :

$\small 21-5x-21=4-21$

$\small -5x = -17$

$\small \frac{-5x}{-5}=\frac{-17}{-5}$

$\small x=\frac{17}{5}$

A common mistake at this point is to believe that you have finished the question. We are given that $\small f(a+2) = 4$ . We must now substitute $\small a+2$ for $\small x$ and solve for $\small a$ :

$\small x=\frac{17}{5}$

$\small a+2 = \frac{17}{5}$

Subtract 2 from both sides:

$\small a+2-2 = \frac{17}{5}-2$

$\small a = \frac{17}{5}-\frac{10}{5}$

$\small a = \frac{7}{5}$

The answer is $\small \frac{7}{5}$ .

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Example Question #421 : Algebra

Which of the following numbers is eight more than half of itself?

Possible Answers:

Correct answer:

Explanation:

Word problems like this are a common occurrence on the PSAT. Begin by setting the number we are looking for, let's call it $\small x$ , equivalent to the equation we are given in the words.

$\small x = \frac{1}{2}x+8$

Move all terms with the variable to one side:

$\small x-\frac{1}{2}x=\frac{1}{2}x+8-\frac{1}{2}x$

$\small \frac{1}{2}x = 8$

Multiply both sides by 2:

$\small x=16$

The correct answer is 16.

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Example Question #41 : Expressions

Fahrenheit temperature can be converted to its Celsius equivalent using the formula

$C = \frac{5}{9} (F-32)$ .

Celsius temperature can be converted to its Fahrenheit equivalent using the formula

$F = \frac{9}{5} C + 32$ .

Mercury boils at $357 ^{\circ } C$ . To the nearest degree, convert this to its equivalent Fahrenheit temperature.

Possible Answers:

$181^{\circ } F$

$166^{\circ } F$

$675^{\circ } F$

$700^{\circ } F$

None of the other responses is correct.

Correct answer:

$675^{\circ } F$

Explanation:

The formula to use is

$F = \frac{9}{5} C + 32$ .

Substitute 357 for :

$F = \frac{9}{5} (357) + 32 = 642.6 + 32 = 674.6$

To the nearest degree, this is $675^{\circ } F$ .

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Example Question #1 : How To Simplify An Expression

Increase 6d - 13 by 70%. Which of the following will this be equal to?

Possible Answers:

6d+57

10.2d-13

10.2d +57

10.2 d - 22.1

6 d - 22.1

Correct answer:

10.2 d - 22.1

Explanation:

A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.

Therefore, 6d - 13 increased by 70% is 1.7 times this, or

$1.7\left ( 6d - 13 \right ) = 1.7 \cdot 6d - 1.7 \cdot 13 = 10.2 d - 22.1$

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Example Question #422 : Algebra

Which of the following phrases can be written as the algebraic expression $\left (x - 19 \right )^{3}$ ?

Possible Answers:

The cube of the difference of a number and nineteen

The cube of the difference of nineteen and a number

Nineteen less than the cube of a number

Three times the difference of a number and nineteen

Three times the difference of nineteen and a number

Correct answer:

The cube of the difference of a number and nineteen

Explanation:

$\left (x - 19 \right )^{3}$ is the cube of x - 19 , which is the difference of a number and nineteen; therefore, $\left (x - 19 \right )^{3}$ is "the cube of the difference of a number and nineteen."

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Example Question #423 : Algebra

Which of the following phrases can be written as the algebraic expression $17 - y^{3}$ ?

Possible Answers:

Three times the difference of seventeen and a number

The cube of the difference of a number and seventeen

The cube of the difference of seventeen and a number

Three times the difference of a number and seventeen

Seventeen decreased by the cube of a number

Correct answer:

Seventeen decreased by the cube of a number

Explanation:

$17 - y^{3}$ is seventeen decreased by $y^{3}$ , which is the cube of a number; therefore, $17 - y^{3}$ is "seventeen decreased by the cube of a number."

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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #44 : Expressions

Example Question #32 : Evaluating And Simplifying Expressions

Example Question #33 : How To Evaluate Algebraic Expressions

Example Question #38 : Expressions

Example Question #41 : Expressions

Example Question #421 : Algebra

Example Question #41 : Expressions

Example Question #1 : How To Simplify An Expression

Example Question #422 : Algebra

Example Question #423 : Algebra

All PSAT Math Resources

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