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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #691 : Concepts

Simplify:

(435.35)^0

Possible Answers:

$435^{35}$

435.35

The expression is undefined

Correct answer:

Explanation:

Any non-zero number raised to the power of zero is equal to .

(435.35)^0=1

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Example Question #692 : Concepts

Simplify:

$(x^4)^{\frac{5}{2}}$

Possible Answers:

$x^{10}$

x^5

$x^{20}$

$x^{12}$

$x^{8}$

Correct answer:

$x^{10}$

Explanation:

We can apply the power of a power property:

$(x^4)^{\frac{5}{2}}=x^{(4\times \frac{5}{2})}=x^{10}$

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Example Question #51 : How To Multiply Variables

Simplify:

$(4x^2y^3)^{3}$

Possible Answers:

64x^3y^8

64x^6y^8

64x^6y^9

64x^4y^9

48x^6y^9

Correct answer:

64x^6y^9

Explanation:

We can first apply the power of a product rule and then apply the power of a power rule. So we can write:

$(4x^2y^3)^{3}=(4)^3\times (x^2)^3\times (y^3)^3=64\times x^{(2\times 3)}\times y^{(3\times 3)}=64x^6y^9$

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Example Question #52 : How To Multiply Variables

Simplify:

$(\frac{1}{4}x-\frac{3}{4})^{2}$

Possible Answers:

$\frac{x^2}{16}-\frac{3}{8}x+\frac{9}{16}$

$\frac{x^2}{16}-\frac{3}{16}x+\frac{9}{16}$

$\frac{x^2}{8}-\frac{3}{8}x+\frac{9}{16}$

$\frac{x^2}{16}+\frac{3}{8}x+\frac{9}{16}$

None of these

Correct answer:

$\frac{x^2}{16}-\frac{3}{8}x+\frac{9}{16}$

Explanation:

We can solve it using the pattern for the square of a binominal or by using FOIL:

$(\frac{1}{4}x-\frac{3}{4})^{2}=(\frac{1}{4}x)^2-(2)( \frac{1}{4}x)( \frac{3}{4})+(\frac{3}{4})^2$

$=\frac{x^2}{16}-\frac{3}{8}x+\frac{9}{16}$

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Example Question #53 : How To Multiply Variables

Simplify:

$(\frac{2}{5}x-\frac{1}{2})^{2}$

Possible Answers:

None of these

$\frac{4}{25}x^2+\frac{2}{5}x+\frac{1}{4}$

$\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{4}$

$\frac{4}{25}x^2-\frac{2}{5}x-\frac{1}{4}$

$\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{2}$

Correct answer:

$\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{4}$

Explanation:

We can solve it using the pattern for the square of a binominal or by using FOIL:

$(\frac{2}{5}x-\frac{1}{2})^{2}=(\frac{2}{5}x)^2-(2) (\frac{2}{5}x) (\frac{1}{2})+(\frac{1}{2})^2$

$=\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{4}$

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Example Question #53 : How To Multiply Variables

At Bess's candy warehouse, she charges M for the first 5 pounds of candy that customers buy and P for each additional pound of candy. What is the cost of buying 128 ounces of candy from Bess's warehouse? (*Note: there are 16 ounces in a pound.)

Possible Answers:

$(M+3P)\div16$

M+P+3

M +3P

3(M+P)

Correct answer:

M +3P

Explanation:

The first step is the convert ounces into pounds. Given that there are 16 ounces in a pound, there are 8 pounds in 128 ounces because 128 divided by 16 eequals 8.

Since the first 5 pounds cost M, and each additional pound costs P, there are 3 additional pounds that will have to be paid for at the P price per pound. Thus, the appropriate formula to express the value of the cost of 128 ounces of candy (8 pounds) is:

M +3P

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Example Question #1 : How To Subtract Variables

Simplify:

14x - 5 (x + 8)

Possible Answers:

9x - 8

9x -40

9x+ 40

9x + 8

Correct answer:

9x -40

Explanation:

14x - 5 (x + 8)

$= 14x - 5 \cdot x - 5 \cdot 8$

= 14x - 5x - 40

= (14- 5) x - 40

= 9x - 40

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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 + 2)

Possible Answers:

5x-9

11x - 62

5 x - 50

5 x - 62

11x-9

Correct answer:

5 x - 62

Explanation:

8 (x - 7) - 3(x + 2)

$= 8 \cdot x -8 \cdot 7 - 3 \cdot x + (-3) \cdot 2$

= 8x -56 - 3 x -6

= 8x - 3 x -56 -6

=( 8 - 3 ) x - (56 + 6)

=5 x - 62

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Example Question #4 : Expressions & Equations

Simplify:

3x + 2xy - 3y + 4x - 15y

Possible Answers:

3x + 3xy - 15y

-9xy

3x - xy + 4x - 15y

7x + 2xy - 18y

7x + 2xy - 12y

Correct answer:

7x + 2xy - 18y

Explanation:

This problem is just a matter of grouping together like terms. Remember that terms like are treated as though they were their own, different variable:

3x + 4x - 3y - 15y + 2xy

The only part that might be a little hard is:

-3y - 15y

If you are confused, think of your number line. This is like "going back" (more negative) from 15. Therefore, you ranswer will be:

7x + 2xy - 18y

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Example Question #1 : How To Subtract Variables

Simplify:

3x - 5y + 3xy + 9yz

Possible Answers:

-2x + 3xy + 9yz

xy + 4yz

xy + 9yz

3x - 5y + 3xy + 9yz

10xyz

Correct answer:

3x - 5y + 3xy + 9yz

Explanation:

This problem really is a trick question. There are no common terms among any of the parts of the expression to be simplified. In each case, you have an independent variable or set of variables: x, y, xy, and . Therefore, do not combine any of the elements!

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #691 : Concepts

Example Question #692 : Concepts

Example Question #51 : How To Multiply Variables

Example Question #52 : How To Multiply Variables

Example Question #53 : How To Multiply Variables

Example Question #53 : How To Multiply Variables

Example Question #1 : 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 #4 : Expressions & Equations

Example Question #1 : How To Subtract Variables

All HSPT Math Resources

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