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HSPT Math : Concepts

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

Example Questions

Example Question #15 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the sale price of a television if it is on sale for % off the original price of $\$175.00?$

Possible Answers:

$\$52.50$

$\$125.00$

$\$50.00$

$\$122.50$

$\$75.00$

Correct answer:

$\$52.50$

Explanation:

First, multiply:

$175.00\ast .70=122.50$

Then subtract that amount from the original price:

175.00-122.50=52.50

Answer: The sale price is $\$52.50$ .

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Example Question #611 : Concepts

24 is what percent of 96?

Possible Answers:

$25\%$

$15\%$

$33\%$

$45\%$

Correct answer:

$25\%$

Explanation:

Translate the sentence into an equation

24=x(96)

Isolate and you get .

Remember that the question is asking for a percentage, so convert into $25\%$ .

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Example Question #612 : Concepts

If you rewrite the phrase "the product of nine and a number added to the sum of six and twice the number" as an algebraic expression, then simplify the expression, the result is:

Possible Answers:

21x

10x+6

18x+54

17x

11x+6

Correct answer:

11x+6

Explanation:

"The product of nine and a number" is . "Twice the number" is , and "The sum of six and twice the number" is 6+2x .

"The product...added to the sum..." is 9x + (6 + 2x) ; simplify to get

9x + (6 + 2x) = 11x + 6

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Example Question #613 : Concepts

Simplify the expression: 9-3x + 4(x-1)

Possible Answers:

7x+8

10x-4

12x-9

x + 5

7x-8

Correct answer:

x + 5

Explanation:

9-3x + 4(x-1)

$= 9-3x + 4 \cdot x-4 \cdot 1$

= 9-3x + 4 x-4

=4 x-3x + 9 -4

=(4 -3)x + 9 -4

=1x + 5

=x + 5

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Example Question #614 : Concepts

Simplify: (9x+6) - (3x-5)

Possible Answers:

6x+11

6x-1

12x+11

12x-1

12x+1

Correct answer:

6x+11

Explanation:

(9x+6) - (3x-5) = (9x-3x)+[6-(-5)] = 6x +11

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Example Question #1 : How To Add Variables

7n+3n=

Possible Answers:

10n

21n

Correct answer:

10n

Explanation:

Add the numbers and keep the variable:

7n+3n=10n

Answer: 10n

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Example Question #2 : How To Add Variables

14s + 3s=

Possible Answers:

42s

17s

18s

11s

Correct answer:

17s

Explanation:

Add the numbers and keep the variable: 14s+3s=17s

Answer: 17s

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Example Question #6 : Algebra

Simplify

$x^{1}y^{3}+ xy^{3} +x^{2}y^{3}=$

Possible Answers:

$2xy^{3}+x^{2}y^{3}$

Already simplified

$3x^{4}y^{9}$

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

$x^{3}y^{9}$

Correct answer:

$2xy^{3}+x^{2}y^{3}$

Explanation:

In order to add variables the terms must be like. In order for terms to be like, the variables must be exactly alike also being raised to the same power by the exponent.

In this case the like terms are $x^{1}y^{3}$ and $xy^{3}$ . Just because there is a 1 in the exponent for the first term doesnt mean it is different from the second term. With exponents if a variable does not show an exponent, that means it is still to the first power.

We add the coefficients of the like terms. The coefficient is the number in front of the first variable, in this case it is 1 for both terms because of the identity property of multiplication stating any variable, term, or number multiplied by 1 is itself.

$x^{1}y^{3}= 1(x^1y^3)$ xy^3= 1(xy^3)

Our last term is not like because the variable is raised to a different power than the other two. In this case we do not combine it to the like terms, we just add it to the end of the term.

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Example Question #3 : How To Add Variables

$2x^{2} + 15y + 14y^{2} + 2x + 3x^{2} + 15x + 2y + 3y^{2}$

Possible Answers:

$22x^{2} + 34y^{2}$

$2x^{3} + 34y^{3}$

$2x^{6} + 34y^{6}$

$36x^{3}y^{3}$

$17x + 5x^{2} + 17y + 17y^{2}$

Correct answer:

$17x + 5x^{2} + 17y + 17y^{2}$

Explanation:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable. Therefore, you can group your problem as follows:

$(2x + 15x) + (2x^{2} + 3x^{2}) + (15y + 2y) + (14y^{2} + 3y^{2})$

Now, just combine like terms:

$17x + 5x^{2} + 17y + 17y^{2}$

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Example Question #7 : Algebra

Simplify:

23x + 22y + 2(4x + 3y)

Possible Answers:

27x + 28y

31x + 25y

31x + 28y

59xy

27x + 25y

Correct answer:

31x + 28y

Explanation:

You should begin by distributing through the whole group that it precedes:

23x + 22y + 8x + 6y

Now, move your like variables next to each other:

23x + 8x + 22y + 6y

Finally, combine the like terms:

31x + 28y

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #15 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

Example Question #611 : Concepts

Example Question #612 : Concepts

Example Question #613 : Concepts

Example Question #614 : Concepts

Example Question #1 : How To Add Variables

Example Question #2 : How To Add Variables

Example Question #6 : Algebra

Example Question #3 : How To Add Variables

Example Question #7 : Algebra

All HSPT Math Resources

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