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HSPT Math : Algebra

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Example Questions

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Example Question #23 : How To Subtract Variables

Simplify:

$43x^{2} + 2xy - 3y - 4(7xy - 22x^{2})$

Possible Answers:

$131x^{2} - 29xy$

$-45x^{2} - 45xy - 3y$

$131x^{2} - 26xy - 3y$

$65x^{2} - 26xy - 3y$

$-45x^{2} - 26xy - 3y$

Correct answer:

$131x^{2} - 26xy - 3y$

Explanation:

Begin by multiplying through by :

$43x^{2} + 2xy - 3y + (-4)(7xy) - (-4)(22x^{2})$

Perform the multiplications:

$43x^{2} + 2xy - 3y - 28xy - (-88x^{2})$

The double negation becomes addition:

$43x^{2} + 2xy - 3y - 28xy + 88x^{2}$

Group like terms:

$43x^{2}+ 88x^{2} + 2xy - 28xy - 3y$

Combine like terms:

$131x^{2} + 26xy - 3y$

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Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

8(x+7) - 3 (x + 10)

Possible Answers:

9x + 43

5x+ 26

5x+ 46

9x+22

Correct answer:

5x+ 26

Explanation:

8(x+7) - 3 (x + 10)

$= 8 \cdot x+ 8 \cdot 7 - 3 \cdot x - 3 \cdot 10$

= 8 x+ 56 - 3x - 30

= 5x+ 26

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Example Question #711 : Concepts

Simplify:

$(2a)(3r^{2})(3a^{3})(5a^{3})(2a^{3})(b^{2})$

Possible Answers:

$180a^{10}b^{2}r^{2}$

$15a^{9}b^{2}r^{6}$

$45a^{4}b^{2}r^{7}$

$180a^{9}b^{2}r^{6}$

$15a^{7}b^{2}r^{5}$

Correct answer:

$180a^{10}b^{2}r^{2}$

Explanation:

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$(2 *3 *3 *5 *2)(a *a^{3} *a^{3} * a^{3})(b^{2})(r^{2})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(180)(a^{1+3+3+3})(b^2)(r^2)$

$(180)(a^{10})(b^{2})(r^{2})$

This is the same as:

$180a^{10}b^{2}r^{2}$

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Example Question #101 : Operations

14s - 3s=

Possible Answers:

11s

21s

42s

17s

Correct answer:

11s

Explanation:

Subtract the numbers and keep the variable:

14s-3s=11s

Answer: 11s

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Example Question #712 : Concepts

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

Possible Answers:

$\frac{1}{2y}$

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

$\frac{x}{2y}$

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

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 #713 : Concepts

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

Possible Answers:

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

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

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

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

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

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 #101 : Algebra

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

Possible Answers:

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

$\frac{1}{a}$

$a^{36}$

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

a^5

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 #102 : Algebra

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

Possible Answers:

-2x^3+x^4

-x^2+2x

-2x^3-x^4

-2x^2-x^4

-2x^3

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^2

5a^2

3a^6

4a^4

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:

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

a^4b^2

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

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

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

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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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #23 : How To Subtract Variables

Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #711 : Concepts

Example Question #101 : Operations

Example Question #712 : Concepts

Example Question #713 : Concepts

Example Question #101 : Algebra

Example Question #102 : Algebra

Example Question #721 : Concepts

Example Question #722 : Concepts

All HSPT Math Resources

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