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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 #727 : Concepts

Simplify:

y (x+ 5) +x (y + 6)

Possible Answers:

2xy + 11

xy + 6x + 5 y

2xy + 6x + 5 y

13xy

Correct answer:

2xy + 6x + 5 y

Explanation:

y (x+ 5) +x (y + 6)

$= y \cdot x+ y \cdot 5 +x \cdot y + x \cdot 6$

= xy + 5 y + xy + 6x

= xy + xy + 6x + 5 y

= 2xy + 6x + 5 y

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Example Question #728 : Concepts

Simplify:

x(y + 6) - y (x - 2)

Possible Answers:

6 x +2 y

xy+ 6 x +2 y

6 x -2 y

xy+ 6 x -2 y

Correct answer:

6 x +2 y

Explanation:

x(y + 6) - y (x - 2)

$= x \cdot y + x \cdot 6 - y \cdot x + y \cdot 2$

= x y + 6 x - xy +2 y

= 6 x +2 y

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Example Question #723 : Concepts

Simplify:

x (x- 8) - x (x+ 5)

Possible Answers:

$x ^{2}- 3x$

-3x

-13x

$x ^{2}-13x$

Correct answer:

-13x

Explanation:

x (x- 8) - x (x+ 5)

$= x \cdot x- x \cdot 8- x \cdot x- x \cdot 5$

$= x ^{2}-8x- x ^{2} - 5x$

$= x ^{2}- x ^{2} -8x- 5x$

= -13x

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Example Question #730 : Concepts

Simplify:

x (x- 8) - x (5-x)

Possible Answers:

$2 x ^{2} -13x$

-3x

$2 x ^{2} - 3x$

-13x

Correct answer:

$2 x ^{2} -13x$

Explanation:

x (x- 8) - x (5-x)

$= x \cdot x- x \cdot 8- x \cdot 5+ x \cdot x$

$= x ^{2}-8x - 5x+ x ^{2}$

$= x ^{2}+ x ^{2} -8x - 5x$

$= 2 x ^{2} -13x$

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Example Question #731 : Concepts

"Eight less than the quotient of a number and nine" can be expressed as which of the following algebraic expressions?

Possible Answers:

$\frac{8 - y}{9}$

$\frac{y- 8}{9}$

$8 - \frac{y}{9}$

$\frac{y}{9} - 8$

Correct answer:

$\frac{y}{9} - 8$

Explanation:

Let "a number" be represented by the variable .

"The quotient of a number and nine" is divided by 9, or

$\frac{y}{9}$ .

"Eight less than" means we subtract 8 from this (we do not subtract this from eight):

$\frac{y}{9} - 8$

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Example Question #732 : Concepts

"Two-thirds of a number increased by twelve" can be written as which algebraic expression?

Possible Answers:

$\frac{2}{3}x \cdot 12$

$\frac{2}{3}(x \cdot 12)$

$\frac{2}{3}x+ 12$

$\frac{2}{3}(x+ 12)$

Correct answer:

$\frac{2}{3}x+ 12$

Explanation:

Let " a number" be expressed as the variable .

"Two-thirds of a number" is the product of the two, and is expressed as

$\frac{2}{3}x$

"Increased by twelve" means 12 is added to the expression. The correct response is therefore

$\frac{2}{3}x+ 12$

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Example Question #121 : Algebra

"Seven divided into the sum of a number and three" can be written as which algebraic expression?

Possible Answers:

$\frac{7}{t}+3$

$\frac{7}{t+3}$

$\frac{t}{7}+3$

$\frac{t+3}{7}$

Correct answer:

$\frac{t+3}{7}$

Explanation:

"A number" can be represented by the variable .

"The sum of a number and three" is the result of an addition and can be represented as

t+ 3

"Seven divided into" this expression is the expression t+ 3 divided by seven, so this expression can be represented as

$\frac{t+3}{7}$ .

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Example Question #122 : Algebra

Take the following equation and arrange it into a simplified, slope-intercept form:

6x-3y=-24

Possible Answers:

-2x+8=y

2x+8=y

6x+24=3y

-y=-2x-8

Correct answer:

2x+8=y

Explanation:

The first step is to get by itself and it is also helpful to do away with negative values. When manipulating an equation perform the opposite algebraic operation to keep the equivalency of the equation true.

So you must add both and to each side resulting in

6x+24=3y .

The final step is dividing both sides by which gives you an answer of

2x+8=y .

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Example Question #31 : How To Add Variables

Simplify:

15x + 22xy + 5(10y + 3xy)

Possible Answers:

15x + 25xy + 50y

15x + 88xy

15x + 37xy + 50y

15x + 38xy + 50y

103xy

Correct answer:

15x + 37xy + 50y

Explanation:

Begin by distributing the to its entire group:

15x + 22xy + 50y + 15xy

Next, group the like terms:

15x + 22xy + 15xy+ 50y

Finally, combine the like terms:

15x + 37xy + 50y

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Example Question #12 : Write And Interpret Simple Expressions That Record Calculations: Ccss.Math.Content.5.Oa.A.2

Select the equation that reflects the phrase below.

Find the sum of and and then divide

Possible Answers:

$(4\times11)\div3$

$(4+11)\div3$

$(4-11)\div3$

$(11-4)\div3$

$(4+11)\times3$

Correct answer:

$(4+11)\div3$

Explanation:

When you are asked to find the sum that means we are going to add. Because the phrase says "then divide" we need to put the addition problem in parentheses because of our order of operations. Then we can divide.

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

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #727 : Concepts

Example Question #728 : Concepts

Example Question #723 : Concepts

Example Question #730 : Concepts

Example Question #731 : Concepts

Example Question #732 : Concepts

Example Question #121 : Algebra

Example Question #122 : Algebra

Example Question #31 : How To Add Variables

Example Question #12 : Write And Interpret Simple Expressions That Record Calculations: Ccss.Math.Content.5.Oa.A.2

All HSPT Math Resources

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