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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 #84 : Write And Interpret Simple Expressions That Record Calculations: Ccss.Math.Content.5.Oa.A.2

Select the equation that reflects the phrase below.

Add to the product of and

Possible Answers:

$36\div12\times7$

$36-12\times7$

$36+12\div7$

$36\times12\times7$

$36+12\times7$

Correct answer:

$36+12\times7$

Explanation:

Product means the answer to a multiplication problem. Becuase of our order of operation rules, the multiplication problem will come first, regardless of if it's listed first or second. Then we add.

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.

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Example Question #192 : Algebra

Simplify the expression $6x^{2} + 4y^{2} + 3x(2x-8y)$

Possible Answers:

$12x^{2} -20xy^{2}$

$20x^{2}y^{2} - 24xy$

$10x^{2}y^{2} +6x^{2} - 24xy$

$12x^{2} + 4y^{2} - 24xy$

Correct answer:

$12x^{2} + 4y^{2} - 24xy$

Explanation:

To simplify this expression, first apply the distributive property. The 3 must be distributed to all of the terms that are inside the parentheses.

$3x (2x) =6x^{2}$

3x (-8y) = -24xy

Rewrite the expression:

$6x^{2} + 4y^{2} + 6x^{2} - 24xy$

Combine like terms. In this expression $6x^{2}$ and $6x^{2}$ are like terms. They are like terms because each term consists $x^{2}$ and a numeric coefficient. Add the coefficients of these terms. Addition is the operation that you would use denoted by a plus sign next to the x. Because there are no other terms to combine, this is the correct answer.

$12x^{2} +4y^{2} - 24xy$

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Example Question #801 : Concepts

$6 (x^{2} + 3) + 3 (y^2{}-3x^{2}) - 7y^{2}$

Possible Answers:

$-3x^{2} + 10y^{^{2}}+18$

$15x^{2} +10y^{2} + 18$

$-3x^{2} - 4y^{2} + 18$

$15x^{2}-4y^{2} + 18$

Correct answer:

$-3x^{2} - 4y^{2} + 18$

Explanation:

To simplify this expression, first apply the distributive property.

$6 (x^{2}+3) = 6x^{2} + 18$

$3(y^{^{2}} -3x^{2}) = 3y^{2} -9x^{2}$

Rewrite the expression:

$6x^{2} + 18 +3y^{^{2}} - 9x^{2} -7y^{2}$

Combine like terms:

$6x^{2} - 9x^{2} = -3x^{2}$

$3y^{2} - 7y^{2} = -4y^{2}$

The constant, which is , has no other constants to perform any type of operation with, therefore, rewrite the expression. Even though the constant was first placed in the beginning of the expression, in the simplified version, the constant always comes at the end of the algebraic expression.

$-3x^{2} -4y^{2} + 18$ is the correct answer.

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Example Question #194 : Algebra

4 (p +q + 7) - 3 (2p +4q -5)

Possible Answers:

10p -8q +43

-2p + 8q -15

-2p +8q + 43

-2p -8q + 43

Correct answer:

-2p -8q + 43

Explanation:

To simplify this expression, apply the distributive property:

4 (p + q + 7) = 4p + 4q +28

3 (2p +4q -5) = 6p +12q +15

Rewrite the expression:

4p + 4q + 28 -6p - 12q + 15

Notice the signs have changed with some of the terms (, 12q , and the constant because of the subtraction sign.

Combine like terms:

-2p-8q + 43 is the correct answer.

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Example Question #195 : Algebra

$5x^{3} (7x^{2}) + \frac{x^{12}}{x^{9}}$

Possible Answers:

$35x^{5} + x^{3}$

$35x^{_{6}} +x^{-3 }$

$35x + x^{3}$

$35x - x^{3}$

Correct answer:

$35x^{5} + x^{3}$

Explanation:

Some algebraic expressions require multiplying or dividing exponential terms. Rather than computing each exponential term and multiplying or dividing manually, simply add exponents when multiplying and subtract when dividing to save time. This concept can also be used to simplify variable expressions.

$5x^{3} (7x^{2}) = (5x7) x^{3+2} = 35x^{5}$

$\frac{x^{12}}{x^{9}} = x^{12-9} = x^{3}$

$35x^{5} + x^{3}$ is the correct answer.

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Example Question #811 : Concepts

$\frac{1}{4} (16x^{2} +24x - 4)$

Possible Answers:

$-4x^{2} -6x + 1$

$64x^{2} +96x +16$

$4x^{2} + 6x -1$

$64x^{^{2}} -6x -1$

Correct answer:

$4x^{2} + 6x -1$

Explanation:

To simplify this algebraic expression, apply the distributive property:

$\frac{16x^{2}+ 24x-4}{4} = \frac{16^{2}}{4} + \frac{24x}{4} - \frac{4}{4}$

$4x^{2} + 24x -1$ is the correct answer.

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Example Question #812 : Concepts

Simplify the following algebraic expression:

$\frac{x^{2} -7x-8}{x^{2} +3x +1}$

Possible Answers:

$\frac{x+8}{x+2}$

$\frac{x-7}{x+1}$

$\frac{x-8}{x +2}$

$\frac{x-8}{x-2}$

Correct answer:

$\frac{x-8}{x +2}$

Explanation:

To simplify this algebraic expression, factor the numerator and the denominator using FOIL.

$\frac{(x-8)(x+1)}{(x+2) (x+1)}$

The $\frac{x+1}{x+1}$ will cancel out.

The correct answer is

$\frac{x-8}{x+2}$

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Example Question #813 : Concepts

$\frac{x+5}{x^{2} +2x -15}$

Possible Answers:

$\frac{1}{x-3}$

$\frac{-1}{x+3}$

x-3

$\frac{1}{x-15}$

Correct answer:

$\frac{1}{x-3}$

Explanation:

To simplify this algebraic expression, factor the denominator using the FOIL method.

$x^{2} + 2x - 15 = (x+5) (x-3)$

$\frac{x+5}{(x+5) (x-3)}$

The $\frac{x+5}{x+5} = 1$

Solve:

$\frac{1}{x-3}$

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Example Question #814 : Concepts

Simplify $\frac{9x^{2}-6x -3}{3x +1}$

Possible Answers:

3x + 1

3x -3

$\frac{1}{3x-3}$

$\frac{3x-3}{3x+1}$

Correct answer:

3x -3

Explanation:

To simplify, factor the numerator using the FOIL Method:

$9x^{2} -6x - 3 = (3x-3) (3x+1)$

Rewrite the expression:

$\frac{(3x-3) (3x+1)}{(3x+1)}$

$\frac{3x-3}{1} = 3x-3$

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Example Question #815 : Concepts

Which is a reduced version of the following expression?

4x-6y=8

Possible Answers:

4x-6y=4

2x-3y=8

2x-3y=4

2x+3y=4

Correct answer:

2x-3y=4

Explanation:

To reduce the expression, you need a common factor to take out from each part of the equation.

All the constants can be divided by so you just divide the whole equation by that to get,

$\\4x-6y=8 \\ \\2(2x-3y)=2(4) \\ \\\frac{2(2x-3y)}{2}=\frac{2(4)}{2}$

2x-3y=4 .

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #84 : Write And Interpret Simple Expressions That Record Calculations: Ccss.Math.Content.5.Oa.A.2

Example Question #192 : Algebra

Example Question #801 : Concepts

Example Question #194 : Algebra

Example Question #195 : Algebra

Example Question #811 : Concepts

Example Question #812 : Concepts

Example Question #813 : Concepts

Example Question #814 : Concepts

Example Question #815 : Concepts

All HSPT Math Resources

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