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PSAT Math : Algebra

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Example Questions

Example Question #264 : Exponents

Simplify:

$\frac{\sqrt[3]{x^{5}y^{-2}}}{\sqrt[3]{x^{-1}y^{4}}}$

Possible Answers:

$\frac{x\sqrt[3]{x^{2}}}{y\sqrt[3]{y}}$

$\frac{x^{2}}{y^{2}}$

$\frac{\sqrt[3]{y^{-2}}}{\sqrt[3]{x^{-1}}}$

$\frac{x^{15}y^{-6}}{x^{-3}y^{12}}$

$\frac{\sqrt[3]{x^{5}}}{\sqrt[3]{y^{4}}}$

Correct answer:

$\frac{x^{2}}{y^{2}}$

Explanation:

Convert the given expression into a single radical e.g. $\sqrt[3]{\frac{x^{5}y^{-2}}{x^{-1}y^{4}}}$ the expression inside the radical is:

$\frac{x^{6}}{y^{6}}$

and the cube root of this is :

$\frac{x^{2}}{y^{2}}$

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Example Question #581 : Algebra

Solve for .

$\log _{\frac{1}{5}}\left ( \frac{1}{25} \right )=x$

Possible Answers:

Correct answer:

Explanation:

$\frac{1}{25}= \left ( \frac{1}{5} \right )^{x}$

Hence must be equal to 2.

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Example Question #266 : Exponents

Simplify:

$log\left (\frac{x}{y^{2}} \right )$

Possible Answers:

$logx+logy^{2}$

logx-2logy

$logx-logy^{2}$

$\left ( logx \right )\left ( logy^{2} \right )$

2logy-logx

Correct answer:

logx-2logy

Explanation:

$log\left ( \frac{x}{y^{2}} \right )=logx-logy^{2}$

Now $logy^{2} = 2logy$

Hence the correct answer is logx - 2logy

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Example Question #267 : Exponents

Solve for .

$\ln x=\ln (x-1)-\ln (x+3)$

Possible Answers:

$no\ solution$

Correct answer:

Explanation:

If we combine into a single logarithmic function we get:

$\ln x=\ln \frac{x-1}{x+3}$

$x = \frac{x-1}{x+3}$

Solving for we get x=-1 .

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Example Question #268 : Exponents

If is the complex number such that i^2=-1 , evaluate the following expression:

$i^{25}-i^{23}+i^{21}-i^{19}+i^{17}-i^{15}.\ .\ .+i$

Possible Answers:

13i

12i

-25i

Correct answer:

13i

Explanation:

The powers of i form a sequence that repeats every four terms.

i¹= i

i² = -1

i³ = -i

i⁴ = 1

i⁵ = i

Thus:

i²⁵ = i

i²³ = -i

i²¹ = i

i¹⁹= -i

Now we can evalulate the expression.

i²⁵ - i²³+ i²¹- i¹⁹ + i¹⁷..... + i

= i + (-1)(-i) + i + (-1)(i) ..... + i

= i + i + i + i + ..... + i

Each term reduces to +i. Since there are 13 terms in the expression, the final result is 13i.

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Example Question #1 : How To Use Scientific Notation

Express 0.000000076 in scientific notation.

Possible Answers:

$7.6 \times 10^{-8}$

$7 6 \times 10^{-8}$

$0.76\times 10^{-8}$

$7.6 \times 10^{-9}$

$7 6 \times 10^{-9}$

Correct answer:

$7.6 \times 10^{-8}$

Explanation:

Write the number:

$0.000\; 000\; 076$

Counting the number of places, move the decimal point to the right until it is after the first nonzero digit:

$0 \; 000\; 000\; 07.6$

The resulting number is 7.6; the number of places the decimal point moved to the right was 8. In scientific notation, this number is $7.6 \times 10^{-8}$ .

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Example Question #2 : How To Use Scientific Notation

Express the square of $7 \times 10^{15}$ in scientific notation.

Possible Answers:

$49 \times 10^{225}$

$4.9 \times 10^{226}$

$4.9 \times 10^{31}$

$49 \times 10^{30}$

$4.9 \times 10^{16}$

Correct answer:

$4.9 \times 10^{31}$

Explanation:

Take advantage of the exponent rules.

$\left (7 \times 10^{15} \right )^{2}$

$= 7^{2} \times \left ( 10^{15} \right )^{2}$

$= 49 \times 10^{15 \times 2}$

$= 49 \times 10^{30}$

$= 4.9 \times 10^{1} \times 10^{30}$

$= 4.9 \times 10^{1+30}$

$= 4.9 \times 10^{31}$

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Example Question #3 : How To Use Scientific Notation

The number 0.0000279 is equivalent to which of the following?

Possible Answers:

$2.79\cdot 10^{4}$

$2.79\cdot 10^{-6}$

$2.79\cdot 10^{5}$

$2.79\cdot 10^{-5}$

$2.79\cdot 10^{-4}$

Correct answer:

$2.79\cdot 10^{-5}$

Explanation:

Each of the answers to this question are in scientific notation. To determine the exponent on the 10, see how many places you need to move the decimal over to get from your original number to 2.79.

Scientific_notation

Because the decimal place moves 5 places, the exponent will be 5, and because the decimal moves to the RIGHT, the exponent is going to be negative.

So the answer to the quesiton is $2.79\cdot 10^{-5}$

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Example Question #1 : How To Use Scientific Notation

Put the following value in scientific notation:

19540000

Possible Answers:

$19.54 \times 10^{7}$

$1954 \times 10^{4}$

$1.954 \times 10^{6}$

$1.954 \times 10^{7}$

Correct answer:

$1.954 \times 10^{7}$

Explanation:

Our first value for scientific notation should be between and . We then multiply this value by raised to a power equal to the number of spaces our decimal has moved to the left.

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Example Question #1 : Algebraic Fractions

Given the expression, $\frac{x^{2}-4}{x^2-x-2}$ , which value CANNOT be equal to ?

Possible Answers:

Correct answer:

Explanation:

cannot equal a value which would make the denominator equal to 0. In order to figure out what that value is, we must first simplify this fraction, then set each factor of the denominator equal to 0. As follows:

$\frac{x^{2}-4}{x^2-x-2}$

First, simplify by finding the original binomial multiples:

$\frac{(x-2)(x+2)}{(x-2)(x+1)}$

Now, set each factor of the denominator equal to 0

x+1=0

x=-1

x-2=0

x=2

If x=-1 OR x=2 , the denominator will equal 0. is the only choice provided by the answers.

Note: Even though you can cancel out x-2 from the numerator and denominator, still cannot be equal to two. The graph would have a hole at x=2 and an aymptote at x=-1 .

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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #264 : Exponents

Example Question #581 : Algebra

Example Question #266 : Exponents

Example Question #267 : Exponents

Example Question #268 : Exponents

Example Question #1 : How To Use Scientific Notation

Example Question #2 : How To Use Scientific Notation

Example Question #3 : How To Use Scientific Notation

Example Question #1 : How To Use Scientific Notation

Example Question #1 : Algebraic Fractions

All PSAT Math Resources

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