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HSPT Math : Concepts

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Example Questions

Example Question #721 : Concepts

Simplify: a^2+ 3a^2(a^2)

Possible Answers:

a^2 + 3a^4

4a^4

3a^6

5a^2

4a^2

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:

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

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

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

a^4b^2

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

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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Example Question #723 : Concepts

Simplify the following expression: 2x-2x^2 +2x -3x^2+3x^3

Possible Answers:

-x^2+3x^3

4x-5x^2 +3x^3

6x-3x^2+3x^3

4x-5x^2 -3x^3

-5x^2 +3x^3

Correct answer:

4x-5x^2 +3x^3

Explanation:

In order to add or subtract the terms, the values must be like-terms. Like-terms have similar variable, and their coefficients can only be added or subtracted if they shared the same variable.

Reorganize the terms from least to greatest power.

2x +2x -2x^2-3x^2+3x^3

Combine like-terms.

2x +2x -2x^2-3x^2+3x^3 = 4x-5x^2 +3x^3

The answer is: 4x-5x^2 +3x^3

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Example Question #722 : Concepts

Simplify:

(xy^2z)^3

Possible Answers:

$\frac{1}{x^3y^6z^3}$

x^3y^6z^3

$\frac{1}{x^4y^5z^4}$

x^4y^5z^4

Correct answer:

x^3y^6z^3

Explanation:

To solve, simply multiply the inner powers by the outer one. Thus,

$(xy^2z)^3=x^{1*3}y^{2*3}z^{1*3}=x^3y^6z^3$

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Example Question #725 : Concepts

Simplify:

8(x-7) + 4(x+2)

Possible Answers:

12 x -48

12 x -5

12 x -9

12 x -64

Correct answer:

12 x -48

Explanation:

8(x-7) + 4(x+2)

$= 8 \cdot x-8 \cdot 7 + 4 \cdot x+4 \cdot 2$

= 8 x-56 + 4 x+8

= 8 x+ 4 x -56 +8

= (8 + 4) x -56 +8

= 12 x -48

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Example Question #726 : Concepts

Simplify:

5 (x+ 2y) - 2 (x+ 3y)

Possible Answers:

3x-y

3x+16y

3x+4y

3x+5y

Correct answer:

3x+4y

Explanation:

5 (x+ 2y) - 2 (x+ 3y)

$= 5 \cdot x+5 \cdot 2y - 2 \cdot x- 2 \cdot 3y$

= 5 x+10y - 2 x- 6y

= 5 x- 2 x+10y - 6y

= (5 - 2 )x+(10 - 6)y

= 3x+4y

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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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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #721 : Concepts

Example Question #722 : Concepts

Example Question #723 : Concepts

Example Question #722 : Concepts

Example Question #725 : Concepts

Example Question #726 : Concepts

Example Question #727 : Concepts

Example Question #728 : Concepts

Example Question #723 : Concepts

Example Question #730 : Concepts

All HSPT Math Resources

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