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HSPT Math : Concepts

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Example Questions

Example Question #621 : Concepts

Simplify:

$\displaystyle 2x + 15xy - 3x + 4y - 5xz + 4x$

Possible Answers:

13xy+4y $\displaystyle 13xy+4y$

$\displaystyle 3x + 4y + 15xy - 5xz$

x+2xyz $\displaystyle x+2xyz$

$\displaystyle 15xy+4y-x-5xz$

Correct answer:

$\displaystyle 3x + 4y + 15xy - 5xz$

Explanation:

First, group together your like variables:

$\displaystyle 2x + 4x - 3x + 4y + 15xy - 5xz$

The only like variables needing to be combined are the x-variables. You can do this in steps or all at once:

$\displaystyle 2x + x + 4y + 15xy - 5xz$

$\displaystyle 3x + 4y + 15xy - 5xz$

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Example Question #622 : Concepts

Simplify:

$\displaystyle 20x + 3y - 14x + 12y - 4z - 2xy$

Possible Answers:

$\displaystyle 8x+4y+12xy$

$\displaystyle 6x + 15y - 4z - 2xy$

15xy $\displaystyle 15xy$

$\displaystyle 6x+15y-16xy$

Correct answer:

$\displaystyle 6x + 15y - 4z - 2xy$

Explanation:

First, move the like terms to be next to each other:

$\displaystyle 20x - 14x + 3y + 12y - 4z - 2xy$

Now, combine the x-variables and the y-variables:

$\displaystyle 6x + 15y - 4z - 2xy$

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Example Question #623 : Concepts

Simplify:

$\displaystyle 14xy + x + 12yz + 15x + 3zy$

Possible Answers:

$14xy + 16x^{2} + 15y^{2}z^{2}$ $\displaystyle 14xy + 16x^{2} + 15y^{2}z^{2}$

$\displaystyle 30xy +15yz$

$14xy + 16x^{2} + 12yz + 3zy$ $\displaystyle 14xy + 16x^{2} + 12yz + 3zy$

$\displaystyle 30xy +12yz + 3zy$

$\displaystyle 14xy + 16x + 15yz$

Correct answer:

$\displaystyle 14xy + 16x + 15yz$

Explanation:

Let's begin by moving the like terms toward each other. Notice the following: zy is the same as yz. (Recall the commutative property of multiplication.)

$\displaystyle 14xy + x + 15x + 12yz + 3yz$

Now, all you have to do is combine the x-variables and the yz-terms:

$\displaystyle 14xy + 16x + 15yz$

Notice that you do not end up with any exponent changes. That would only happen if you multiplied those variables.

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Example Question #624 : Concepts

Simplify:

$x^{2} + 5y^{4} + 3y^{2} + 15x^{2} + 12x^{2}y^{4}$ $\displaystyle x^{2} + 5y^{4} + 3y^{2} + 15x^{2} + 12x^{2}y^{4}$

Possible Answers:

$3y^{2} + 33x^{2}y^{4}$ $\displaystyle 3y^{2} + 33x^{2}y^{4}$

$16x^{2} + 8y^{6} + 12x^{2}y^{4}$ $\displaystyle 16x^{2} + 8y^{6} + 12x^{2}y^{4}$

$36x^{24y^{10}$ $\displaystyle 36x^{24y^{10}$

$16x^{2} + 5y^{4} + 3y^{2} + 12x^{2}y^{4}$ $\displaystyle 16x^{2} + 5y^{4} + 3y^{2} + 12x^{2}y^{4}$

$18x^{2}y^{2} + 5y^{4} + 12x^{2}y^{4}$ $\displaystyle 18x^{2}y^{2} + 5y^{4} + 12x^{2}y^{4}$

Correct answer:

$16x^{2} + 5y^{4} + 3y^{2} + 12x^{2}y^{4}$ $\displaystyle 16x^{2} + 5y^{4} + 3y^{2} + 12x^{2}y^{4}$

Explanation:

Remember, when you have exponents like this, you will treat each exponented variable as though it were its own "type." Likewise, pairs of variables are to be grouped together. Therefore, group the problem as follows:

$(x^{2} + 15x^{2}) + 3y^{2} + 5y^{4} + 12x^{2}y^{4}$ $\displaystyle (x^{2} + 15x^{2}) + 3y^{2} + 5y^{4} + 12x^{2}y^{4}$

Notice that the only thing to be combined are the $x^{2}$ $\displaystyle x^{2}$ terms.

Therefore, your answer will be:

$16x^{2} + 5y^{4} + 3y^{2} + 12x^{2}y^{4}$ $\displaystyle 16x^{2} + 5y^{4} + 3y^{2} + 12x^{2}y^{4}$

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Example Question #103 : Algebra

Simplify:

$3x + 5x^{2} + 15xy + 12x^{2} + 4y^{2}$ $\displaystyle 3x + 5x^{2} + 15xy + 12x^{2} + 4y^{2}$

Possible Answers:

$39x^{6}y^{3}$ $\displaystyle 39x^{6}y^{3}$

$20x^{2} + 15xy + 4y^{2}$ $\displaystyle 20x^{2} + 15xy + 4y^{2}$

$3x + 17x^{2} + 15xy + 4y^{2}$ $\displaystyle 3x + 17x^{2} + 15xy + 4y^{2}$

$39x^{2}y^{2}$ $\displaystyle 39x^{2}y^{2}$

$18x + 5x^{2} + 15xy + 4y^{2}$ $\displaystyle 18x + 5x^{2} + 15xy + 4y^{2}$

Correct answer:

$3x + 17x^{2} + 15xy + 4y^{2}$ $\displaystyle 3x + 17x^{2} + 15xy + 4y^{2}$

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:

$3x + (5x^{2} + 12x^{2})+ 15xy + 4y^{2}$ $\displaystyle 3x + (5x^{2} + 12x^{2})+ 15xy + 4y^{2}$

Then, all you need to do is to combine the $x^{2}$ $\displaystyle x^{2}$ terms:

$3x + (17x^{2})+ 15xy + 4y^{2}$ $\displaystyle 3x + (17x^{2})+ 15xy + 4y^{2}$

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Example Question #625 : Concepts

Simplify:

$15x + 2x^{2} + 4(x + 22x^{2})$ $\displaystyle 15x + 2x^{2} + 4(x + 22x^{2})$

Possible Answers:

$19x + 24x^{2}$ $\displaystyle 19x + 24x^{2}$

$109x^{3}$ $\displaystyle 109x^{3}$

$33x^{3}$ $\displaystyle 33x^{3}$

$109x^{2}$ $\displaystyle 109x^{2}$

$19x + 90x^{2}$ $\displaystyle 19x + 90x^{2}$

Correct answer:

$19x + 90x^{2}$ $\displaystyle 19x + 90x^{2}$

Explanation:

Begin by distributing the $\displaystyle 4$ through the parentheses:

$15x + 2x^{2} + 4x + 88x^{2}$ $\displaystyle 15x + 2x^{2} + 4x + 88x^{2}$

Next, move the like terms next to each other. Remember, treat $x^{2}$ $\displaystyle x^{2}$ like it is its own, separate variable.

$15x+ 4x + 2x^{2} + 88x^{2}$ $\displaystyle 15x+ 4x + 2x^{2} + 88x^{2}$

Finally, combine like terms:

$19x + 90x^{2}$ $\displaystyle 19x + 90x^{2}$

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Example Question #626 : Concepts

Simplify:

$\displaystyle x^3-2x-4x^3+3x^2+x+x^2$

Possible Answers:

$\displaystyle 3x^3+4x^2+x$

$\displaystyle 5x^3+4x^2-3x$

$\displaystyle -5x^3+4x^2+3x$

$\displaystyle -3x^3+4x^2-x$

Correct answer:

$\displaystyle -3x^3+4x^2-x$

Explanation:

Combine like terms:

$\displaystyle x^3+2x-4x^3+3x^2-x+x^2$

$\displaystyle =(x^3-4x^3)+(3x^2+x^2)+(-2x+x)$

$\displaystyle =-3x^3+4x^2-x$

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Example Question #627 : Concepts

Simplify:

$\displaystyle 7x^2+8x^3+9x^2-6x+2-4x^3$

Possible Answers:

$\displaystyle 2x^3+8x^2-3x+1$

$\displaystyle 12x^3+16x^2-6x+2$

$\displaystyle 4x^3+16x^2-6x+2$

$\displaystyle 6x^3+8x^2-3x+1$

Correct answer:

$\displaystyle 4x^3+16x^2-6x+2$

Explanation:

Combine like terms:

$\displaystyle 7x^2+8x^3+9x^2-6x+2-4x^3$

$\displaystyle =(8x^3-4x^3)+(7x^2+9x^2)-6x+2=4x^3+16x^2-6x+2$

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Example Question #628 : Concepts

$\displaystyle f (x) = 5x + 1$

Evaluate f (-3) $\displaystyle f (-3)$

Possible Answers:

$\displaystyle -14$

$\displaystyle -18$

$\displaystyle -16$

$\displaystyle -12$

Correct answer:

$\displaystyle -14$

Explanation:

$\displaystyle f (x) = 5x + 1$

$\displaystyle f (-3) = 5 (-3) + 1 = -15+1 = -14$

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Example Question #629 : Concepts

$\displaystyle 6r+3r+3r=$

Possible Answers:

108r $\displaystyle 108r$

24r $\displaystyle 24r$

12r $\displaystyle 12r$

$\displaystyle 0$

$\displaystyle 9r$

Correct answer:

12r $\displaystyle 12r$

Explanation:

Add the numbers and keep the variable:

$\displaystyle 6r+3r+3r=12r$

Answer: 12r $\displaystyle 12r$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #621 : Concepts

Example Question #622 : Concepts

Example Question #623 : Concepts

Example Question #624 : Concepts

Example Question #103 : Algebra

Example Question #625 : Concepts

Example Question #626 : Concepts

Example Question #627 : Concepts

Example Question #628 : Concepts

Example Question #629 : Concepts

All HSPT Math Resources

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