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ISEE Upper Level Math : Numbers and Operations

Study concepts, example questions & explanations for ISEE Upper Level Math

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #51 : Numbers And Operations

What is the least common multiple of and ?

Possible Answers:

Correct answer:

Explanation:

Find all of the multiples of both numbers:

6: 6,12,18,24,30,36,42,48,54,60

4:4,8,12,16,20,24,28,32,36,40

Find the first number that both sets have in common.

LCM=12

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Example Question #482 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the LCM of 12xy and 48x.

Possible Answers:

x^2y

48xy

48x^2y

96xy

144xy

Correct answer:

48xy

Explanation:

LCM is the least common multiple of the pair. There are a couple of terms at play here, so first find the LCM of 12 and 48. Since 12 goes into 48, 48 is the LCM. Then, look at xy and x. XY is the LCM between those two. So, multiply those together to get 48xy as your answer.

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Example Question #52 : Numbers And Operations

What is the least common multiple of and ?

Possible Answers:

Correct answer:

Explanation:

A multiple of x is a number that results when x is multiplied by another whole number.

The least common multiple of two numbers is the smallest number that is a multiple of both the numbers.

24 is a multiple of 8 because 8 times 3 is 24.

24 is also a multiple of 12 because 12 times 2 is 24.

There are no numbers that are smaller than 24 which are also multiples of 8 and 12. Therefore, 24 is the least common multiple.

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Example Question #1 : Exponential Operations

Simplify:

3a^3-a^2+4a^2-8a^3

Possible Answers:

a^2(-5a+3)

a(-5a+3)

a^2(5a+3)

a^2(5a-3)

a^2(-5a+2)

Correct answer:

a^2(-5a+3)

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

3a^3-a^2+4a^2-8a^3=(3a^3-8a^3)+(4a^2-a^2)

=-5a^3+3a^2=a^2(-5a+3)

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Example Question #2 : How To Subtract Exponents

Evaluate:

5^2+5^3-7^2-3(7^2)-4(5^3)

Possible Answers:

550

546

Correct answer:

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

5^2+5^3-7^2-3(7^2)-4(5^3)=5^2+(5^3-4(5^3))-(7^2+3(7^2))

=5^2+-3(5^3)-4(7^2)

Now they must be multiplied out before they can be added:

$=5\times 5- 3\times 5\times 5\times 5-4\times 7\times 7$

$=25-3\times 125-4\times 49$

=25-375-196=-546

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Example Question #1 : Exponents

Subtract and simplify:

$\left ( 11 x^{2}- 8x-7 \right )- \left (-7 x^{2}-5x+19\right )$

Possible Answers:

$18x^{2}-13x-26$

$4x^{2}-3x+12$

$4x^{2}-3x-26$

$18x^{2}-3x+12$

$18x^{2}-3x-26$

Correct answer:

$18x^{2}-3x-26$

Explanation:

Consider a vertical subtraction process:

$\begin{matrix} 11 x^{2}- 8x-7 \\\underline{ - (-7 x^{2}-5x+19)} \end{matrix}$

Rewrite as the addition of the opposite of the second expression, as follows:

$\begin{matrix} 11 x^{2}- 8x-7 \\\underline{ \; \; 7 x^{2}+5x-19 } \\ 18x^{2}-3x-26 \end{matrix}$

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Example Question #4 : How To Subtract Exponents

Define an operation $\Upsilon$ as follows:

For all real numbers a, b ,

$a \Upsilon b = a^{4} - b^{3}$ .

Evaluate: $\frac{1}{2} \Upsilon \frac{1}{4}$ .

Possible Answers:

$\frac{3}{64}$

$-\frac{1}{48}$

$\frac{1}{32}$

$\frac{1}{16}$

Correct answer:

$\frac{3}{64}$

Explanation:

$a \Upsilon b = a^{4} - b^{3}$ , so

$\frac{1}{2} \Upsilon \frac{1}{4} = \left ( \frac{1}{2} \right )^{4} - \left (\frac{1}{4} \right )^{3}$

$= \frac{1}{2^{4}} - \frac{1}{4^{3}}$

$= \frac{1}{16} - \frac{1}{64}$

$= \frac{4}{64} - \frac{1}{64}$

$= \frac{3}{64}$

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Example Question #1 : Exponents

Subtract and simplify:

$\left ( 4x^{2}+ 1.2x-7 \right )- \left ( 2x^{2}-3.8x+9\right )$

Possible Answers:

$2x^{2}-2.6x-16$

$2x^{2}+ 5x+2$

$2x^{2}-2.6x+2$

The correct answer is not among the other responses.

$2x^{2}+ 5x-16$

Correct answer:

$2x^{2}+ 5x-16$

Explanation:

Consider a vertical subtraction process:

$\begin{matrix} 4x^{2}+ 1.2x-7\\\underline{ - (2x^{2}-3.8x+9)} \end{matrix}$

Rewrite as the addition of the opposite of the second expression, as follows:

$\begin{matrix} \; \; 4x^{2}+ 1.2x-7\\\underline{ -2x^{2}+3.8x-9}\\ \; 2x^{2}+\; \; 5x-16\end{matrix}$

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Example Question #1 : How To Subtract Exponents

Define an operation $\Upsilon$ as follows:

For all real numbers a, b ,

$a \Upsilon b = a^{4} - b^{3}$ .

Evaluate: $0.2\; \Upsilon\; 0.1$ .

Possible Answers:

-0.0084

0.0015

-0.0015

-0.0006

0.0006

Correct answer:

0.0006

Explanation:

$a \Upsilon b = a^{4} - b^{3}$

$0.2\; \Upsilon\; 0.1= 0.2^{4} - 0.1^{3}$

= 0.0016 - 0.001

=0.0006

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Example Question #7 : How To Subtract Exponents

Define an operation $\Upsilon$ as follows:

For all real numbers a, b ,

$a \Upsilon b = a^{4} - b^{3}$ .

Evaluate: $(-4) \Upsilon (-3)$

Possible Answers:

283

229

Correct answer:

283

Explanation:

$a \Upsilon b = a^{4} - b^{3}$

$(-4) \Upsilon (-3) = (-4)^{4}- (-3) ^{3}$

= 256 - (-27)

=283

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ISEE Upper Level Math : Numbers and Operations

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #51 : Numbers And Operations

Example Question #482 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #52 : Numbers And Operations

Example Question #1 : Exponential Operations

Example Question #2 : How To Subtract Exponents

Example Question #1 : Exponents

Example Question #4 : How To Subtract Exponents

Example Question #1 : Exponents

Example Question #1 : How To Subtract Exponents

Example Question #7 : How To Subtract Exponents

All ISEE Upper Level Math Resources

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