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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #62 : Operations

$-4x (-2x^{2} +3y -4) =$

Possible Answers:

$8x^{3} +12xy -16x$

$-8x^{3} -12xy + 16y$

$8x^{3} -12xy +16x$

$8x^{2} -12xy +16x$

Correct answer:

$8x^{3} -12xy +16x$

Explanation:

First distribute the -4x to all terms in the parenthesis.

$(-4x \times -2x^{2}) + (-4x \times 3y) + (-4x \times -4)$

$(-4x \times -2x^{2}) = 8x ^{1+2} = 8x^{3}$ (When multiplying variables with exponents, the exponents are added together).

$(-4x \times 3y) = -4\times 3 \times x\times y = -12xy$

-4x (-4) = 16x

$8x^{3} -12xy + 16x$

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Example Question #66 : Variables

$(-6x^{4}y^{2}) \times (-3x^{2}y^{2})=$

Possible Answers:

$18x^{8}y^{4}$

$-9x^{6}y^{4}$

$-18x^{6}y^{4}$

$18x^{6}y^{4}$

Correct answer:

$18x^{6}y^{4}$

Explanation:

To solve $(-6x^{4}y^{2}) \times(-3x^{2}y^{2})$

Separate the parts of the terms. Multiply the coefficients:

$-6 \times - 3 = 18$

Multiply the terms with as the variable. When multiplying, the exponents get added.

$x^{4}\times x^{2} = x^{4+2} = x^{6}$

Multiply the terms with as the variable. When multiplying, the exponents get added.

$y^{2}\times y^{2} = y^{2+2} = y^{4}$

Put it all together:

$18x^{6}y^{4}$

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Example Question #67 : Variables

The length of a rectangle is and the width is 9{y}. What is the area of this rectangle?

Possible Answers:

36y

26y

$36y^{2}$

13y

Correct answer:

$36y^{2}$

Explanation:

The formula for the Area of a rectangle is length times width or l x w. Multiply the length which is times the width which is 9y.

First multiply

$4 \times 9 =36$

Then multiply the variables; add the exponents:

$y\timesy = y^{1+1} = y^{2}$

Area or A of the rectangle is

$36y^{2}$

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Example Question #68 : Variables

The length of a rectangular prism is centimeters. The width is centimeters. The height is centimeters. Find the volume of this rectangular prism.

Possible Answers:

$9x^{3}centimeters^{3}$

$240 centimeters^{3}$

$240x^{3} centimeters^{3}$

$19x^{3} centimeters ^{3}$

Correct answer:

$240x^{3} centimeters^{3}$

Explanation:

The volume of a rectangular prism is determined by using the formula

V = length x width x height

$8 \times 6\times 5 = 240$

$x \ast x \ast x = x^{1+1+1} =x^{3}$

$240x^{3} centimeters^{3}$

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Example Question #2181 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Multiply the following:

$x \cdot 3x$

Possible Answers:

x^2

3x^2

Correct answer:

3x^2

Explanation:

When multiplying variables, we multiply them together just like we would integers. We have

$x \cdot 3x$

The first term isn't showing a coefficient, so it is automatically 1. So,

$1x \cdot 3x$

Now, we will multiply the coefficients together, then we multiply the variables together.

So, we get

$1x \cdot 3x = (1 \cdot 3)(x \cdot x) = 3x^2$

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Example Question #70 : Variables

Simplify the following expression:

$9x^3t^7*4x^5t^{12}$

Possible Answers:

$36x^8t^{19}$

$9x^8t^{19}$

$36x^8t^{84}$

$13x^8t^{19}$

Correct answer:

$36x^8t^{19}$

Explanation:

Simplify the following expression:

$9x^3t^7*4x^5t^{12}$

Let's begin by rewriting the expression with similar terms next to each other.

$(9*4)(x^3*x^5)(t^7*t^{12})$

Next, multiply the terms out.

Our first pair of terms is just like regular multiplication.

For the next two terms, we need to add the exponents.

In doing so, we get:

$36x^8t^{19}$

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Example Question #71 : Variables

Simplify the following statement

(14b^2t^5)(2b^3t^9)

Possible Answers:

$14b^5t^{14}$

$28b^5t^{14}$

$28b^4t^{4}$

$28t^5b^{14}$

Correct answer:

$28b^5t^{14}$

Explanation:

Simplify the following statement

(14b^2t^5)(2b^3t^9)

To multiply these terms, first multiply the 2 and the 14

28(b^2t^5)(b^3t^9)

Next, we can combine the b's and the t's by adding together their exponents.

$28(b^2t^5)(b^3t^9)=28b^5t^{14}$

So our answer is:

$28b^5t^{14}$

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Example Question #71 : Variables

Combine the following terms:

$5q^3*8q^4*9q^{11}$

Possible Answers:

$360q^{18}$

$360q^{7}$

$36q^{18}$

$360q^{12}$

Correct answer:

$360q^{18}$

Explanation:

Combine the following terms:

$5q^3*8q^4*9q^{11}$

Let's begin by multiplying the coefficients (numbers out in front)

5*8*9=40*9=360

So our answer must have 360 in front.

Next, let's multiply our q's. To do so, we need to add up our exponents.

$q^3*q^4*q^{11}=q^{3+4+11}=q^{18}$

So, put it together to get:

$360q^{18}$

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Example Question #72 : Variables

$x^{2} = 64$ . Evaluate $x^{4}$ .

Possible Answers:

512

4,096

Correct answer:

4,096

Explanation:

$x^{2} = 64$ , so either $x = \sqrt{64} = 8$ or $x = - \sqrt{64} =- 8$ .

If the former is true,

$x^{4} = 8^{4} = 8 \cdot 8 \cdot 8 \cdot 8 = 4,096$ .

If the latter is true, then, since an even-numbered power of any number is positive,

$x^{4} =( - 8)^{4} = 8^{4} = 4,096$ .

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Example Question #73 : Variables

Simplify the following expression

$54x^3*8x^2*\frac{x^2}{9}$

Possible Answers:

48x^7

$1244x^{12}$

540x^7

$48x^{12}$

Correct answer:

48x^7

Explanation:

Simplify the following expression

$54x^3*8x^2*\frac{x^2}{9}$

Let's begin by grouping our x's and our coefficients

$(54*8*\frac{1}{9})(x^3*x^2*x^2)$

We can combine our coefficents by multiplying them, and we can combine the x's by adding the exponents

$(54*\frac{1}{9}*8)(x^7)=(6*8)x^7=48x^7$

So, our answer is:

48x^7

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #62 : Operations

Example Question #66 : Variables

Example Question #67 : Variables

Example Question #68 : Variables

Example Question #2181 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #70 : Variables

Example Question #71 : Variables

Example Question #71 : Variables

Example Question #72 : Variables

Example Question #73 : Variables

All ISEE Middle Level Math Resources

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