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HSPT Math : HSPT Mathematics

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #101 : Algebra

Simplify: $\frac{9x}{(\frac{2y}{9x})}$

Possible Answers:

$\frac{x}{2y}$

$\frac{2y}{81x^2}$

$\frac{1}{2y}$

$\frac{81x^2}{2y}$

Correct answer:

$\frac{81x^2}{2y}$

Explanation:

To solve this problem, rewrite the operation using a division sign.

$\frac{9x}{(\frac{2y}{9x})}= 9x \div \frac{2y}{9x}$

When dividing fractions, we replace the division sign with a multiplication sign and take the inverse of the second term.

$9x \div \frac{2y}{9x}= 9x \times \frac{9x}{2y}$

When we simplify the problem we get $\frac{9x}{1}\times \frac{9x}{2y}=\frac{81x^{2}}{2y}$

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Example Question #102 : Algebra

Simplify: $\frac{a^2b^6c^0}{a^{-4}b^{9}c^{-1}}$

Possible Answers:

$\frac{1}{a^6b^3c}$

$\frac{a^2c}{b^3}$

$\frac{a^6c}{b^3}$

$\frac{a^2}{b^3c}$

$\frac{b^3}{a^6c}$

Correct answer:

$\frac{a^6c}{b^3}$

Explanation:

The powers of like-terms can be subtracted top to bottom when the terms are divided. Simplify the terms.

$a^{2-(-4)}=a^6$

$b^{6-9}=b^{-3}$

$c^{0-(-1)}=c$

Combine the terms as one whole. Positive exponents go in the numerator and negative exponents go in the denominator to get rid of the negative. The correct answer is: $\frac{a^6c}{b^3}$

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Example Question #711 : Concepts

Simplify: $a^3 \times a^{-6}\times a^{-2}$

Possible Answers:

$\frac{1}{a}$

$\frac{1}{a^5}$

a^5

$a^{36}$

$\frac{1}{a^4}$

Correct answer:

$\frac{1}{a^5}$

Explanation:

To simplify the expression, notice that the bases are all alike and are multiplied.

The powers to the bases can then be added to be combined to one term.

$a^3 \times a^{-6}\times a^{-2}=a^{3-6-2}= a^{-5} = \frac{1}{a^5}$

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Example Question #712 : Concepts

Simplify: -x^2(2x+x^2)

Possible Answers:

-x^2+2x

-2x^3-x^4

-2x^3

-2x^3+x^4

-2x^2-x^4

Correct answer:

-2x^3-x^4

Explanation:

Distribute the negative outer term to the two inner terms inside the parenthesis.

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

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Example Question #721 : Concepts

Simplify: a^2+ 3a^2(a^2)

Possible Answers:

a^2 + 3a^4

4a^4

3a^6

5a^2

4a^2

Correct answer:

a^2 + 3a^4

Explanation:

Evaluate the parenthesis first by order of operations.

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

Since a^2 and a^4 are unlike terms, their coefficients cannot be added.

The answer is: a^2 + 3a^4

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Example Question #722 : Concepts

Simplify: $\frac{a^2b^{-2}}{a^{-2}}$

Possible Answers:

$\frac{1}{b^2}$

$\frac{1}{a^4b^2}$

$\frac{a^4}{b^2}$

a^4b^2

$\frac{a^2}{b-a}$

Correct answer:

$\frac{a^4}{b^2}$

Explanation:

The exponents of can be subtracted since they are divided.

$\frac{a^2}{a^{-2}} = a^{2-(-2)}= a^4$

$b^{-2}= \frac{1}{b^2}$

The product of both is: $a^4 \times \frac{1}{b^2} = \frac{a^4}{b^2}$

The answer is: $\frac{a^4}{b^2}$

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Example Question #723 : Concepts

Simplify the following expression: 2x-2x^2 +2x -3x^2+3x^3

Possible Answers:

-x^2+3x^3

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

6x-3x^2+3x^3

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

-5x^2 +3x^3

Correct answer:

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

Explanation:

In order to add or subtract the terms, the values must be like-terms. Like-terms have similar variable, and their coefficients can only be added or subtracted if they shared the same variable.

Reorganize the terms from least to greatest power.

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

Combine like-terms.

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

The answer is: 4x-5x^2 +3x^3

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Example Question #722 : Concepts

Simplify:

(xy^2z)^3

Possible Answers:

$\frac{1}{x^3y^6z^3}$

x^3y^6z^3

$\frac{1}{x^4y^5z^4}$

x^4y^5z^4

Correct answer:

x^3y^6z^3

Explanation:

To solve, simply multiply the inner powers by the outer one. Thus,

$(xy^2z)^3=x^{1*3}y^{2*3}z^{1*3}=x^3y^6z^3$

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Example Question #725 : Concepts

Simplify:

8(x-7) + 4(x+2)

Possible Answers:

12 x -48

12 x -5

12 x -9

12 x -64

Correct answer:

12 x -48

Explanation:

8(x-7) + 4(x+2)

$= 8 \cdot x-8 \cdot 7 + 4 \cdot x+4 \cdot 2$

= 8 x-56 + 4 x+8

= 8 x+ 4 x -56 +8

= (8 + 4) x -56 +8

= 12 x -48

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Example Question #726 : Concepts

Simplify:

5 (x+ 2y) - 2 (x+ 3y)

Possible Answers:

3x-y

3x+16y

3x+4y

3x+5y

Correct answer:

3x+4y

Explanation:

5 (x+ 2y) - 2 (x+ 3y)

$= 5 \cdot x+5 \cdot 2y - 2 \cdot x- 2 \cdot 3y$

= 5 x+10y - 2 x- 6y

= 5 x- 2 x+10y - 6y

= (5 - 2 )x+(10 - 6)y

= 3x+4y

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #101 : Algebra

Example Question #102 : Algebra

Example Question #711 : Concepts

Example Question #712 : Concepts

Example Question #721 : Concepts

Example Question #722 : Concepts

Example Question #723 : Concepts

Example Question #722 : Concepts

Example Question #725 : Concepts

Example Question #726 : Concepts

All HSPT Math Resources

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