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ISEE Middle Level Math : How to add variables

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All ISEE Middle Level Math Resources

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Example Questions

Example Question #101 : Ssat Middle Level Quantitative (Math)

Simplify:

$15x + 2x^{2} + 4(x + 22x^{2})$

Possible Answers:

$19x + 24x^{2}$

$33x^{3}$

$19x + 90x^{2}$

$109x^{3}$

$109x^{2}$

Correct answer:

$19x + 90x^{2}$

Explanation:

Begin by distributing the through the parentheses:

$15x + 2x^{2} + 4x + 88x^{2}$

Next, move the like terms next to each other. Remember, treat $x^{2}$ like it is its own, separate variable.

$15x+ 4x + 2x^{2} + 88x^{2}$

Finally, combine like terms:

$19x + 90x^{2}$

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Example Question #153 : Algebraic Concepts

Simplify:

x^3-2x-4x^3+3x^2+x+x^2

Possible Answers:

-5x^3+4x^2+3x

-3x^3+4x^2-x

5x^3+4x^2-3x

3x^3+4x^2+x

Correct answer:

-3x^3+4x^2-x

Explanation:

Combine like terms:

x^3+2x-4x^3+3x^2-x+x^2

=(x^3-4x^3)+(3x^2+x^2)+(-2x+x)

=-3x^3+4x^2-x

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Example Question #101 : Algebra

Simplify:

7x^2+8x^3+9x^2-6x+2-4x^3

Possible Answers:

4x^3+16x^2-6x+2

12x^3+16x^2-6x+2

6x^3+8x^2-3x+1

2x^3+8x^2-3x+1

Correct answer:

4x^3+16x^2-6x+2

Explanation:

Combine like terms:

7x^2+8x^3+9x^2-6x+2-4x^3

=(8x^3-4x^3)+(7x^2+9x^2)-6x+2=4x^3+16x^2-6x+2

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Example Question #102 : Algebra

f (x) = 5x + 1

Evaluate f (-3)

Possible Answers:

Correct answer:

Explanation:

f (x) = 5x + 1

f (-3) = 5 (-3) + 1 = -15+1 = -14

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Example Question #103 : Algebra

6r+3r+3r=

Possible Answers:

24r

108r

12r

Correct answer:

12r

Explanation:

Add the numbers and keep the variable:

6r+3r+3r=12r

Answer: 12r

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Example Question #111 : Algebra

Simplify:

(xy^2)^2+3x^2y^4

Possible Answers:

2x^2y^4

4x^2y^4

x^2y^4

3x^2y^4

4x^4y^4

Correct answer:

4x^2y^4

Explanation:

(xy^2)^2+3x^2y^4

First we should simplify the first expression. We can first apply the power of a product rule and then apply the power of a power rule. So we can write:

$(xy^2)^2=(x)^2\times (y^2)^2=x^2\times y^{(2\times 2)}=x^2y^4$

Return to the original expression:

x^2y^4+3x^2y^4

Since the variables have the same exponents we can write:

x^2y^4+3x^2y^4=4x^2y^4

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Example Question #164 : Variables

Gina's mom baked 12 cookies. 8 were cinnamon and 4 were chocolate chip. If Gina eats one of the cinnamon cookies, how many more cinnamon cookies are there than chocolate chip?

Possible Answers:

Correct answer:

Explanation:

Gina's mom baked 12 cookies; 8 were cinnamon and 4 were chocolate chip. If Gina then eats a cinnamon cookie, there will be 7 cinnamon cookies left.

After she eats the cookie, we need to find the difference between the number of cinnamon cookies and chocolate chip cookies.

$\text{Cinnamon}-\text{Chocolate chip}$

7-4=3

There are 3 more cinnamon cookies than chocolate chip cookies.

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Example Question #2281 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Add 8 + 7 + 6 + 5 in modulo 13 arithmetic.

Possible Answers:

Correct answer:

Explanation:

In modulo 13 arithmetic, a number is congruent to the remainder of the divison of that number by 13. Since

8 + 7 + 6 + 5 = 26

and

$26 \div 13 = 2 \textrm{ R }0$ ,

$8 + 7 + 6 + 5 \equiv 0 \mod 13$ ,

making the correct response 0.

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Example Question #42 : Operations

Suppose you know the values of all variables in the expression

$t - w \cdot \left (k + n \right )$

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Adding, multiplying, subtracting

Subtracting, adding, multiplying

Multiplying, adding, subtracting

Multiplying, subtracting, adding

Adding, subtracting, multiplying

Correct answer:

Adding, multiplying, subtracting

Explanation:

By the order of operations, the operation within parentheses, which is addition, is carried out first; of the remaining two, multiplication precedes subtraction.

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Example Question #43 : Operations

Suppose you know the values of all variables in the expression

$x \cdot y + b ^{2}$

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Multiplying, squaring, adding

Multiplying, adding, squaring

Adding, multiplying, squaring

Squaring, multiplying, adding

Squaring, adding, multiplying

Correct answer:

Squaring, multiplying, adding

Explanation:

By the order of operations, in the absence of grouping symbols, exponentiation (squaring here) takes precedence, followed by, in order, multiplication and addition.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : How to add variables

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #101 : Ssat Middle Level Quantitative (Math)

Example Question #153 : Algebraic Concepts

Example Question #101 : Algebra

Example Question #102 : Algebra

Example Question #103 : Algebra

Example Question #111 : Algebra

Example Question #164 : Variables

Example Question #2281 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #42 : Operations

Example Question #43 : Operations

All ISEE Middle Level Math Resources

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