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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

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

Example Questions

Example Question #671 : Concepts

Simplify:

$2(f^{6})(u^{7})(e^{2}f^{2})(eu)$

Possible Answers:

$2e^{2}f^{12}u^{7}$

$2e^{3}f^{8}u^{6}$

$2e^{3}f^{8}u^{8}$

$2e^{2}f^{24}u^{7}$

$e^{3}f^{14}u^{8}$

Correct answer:

$2e^{3}f^{8}u^{8}$

Explanation:

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$(2)(e * e^{2})(f^{6}*f^{2})(u*u^{7})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(2)(e^{1+2})(f^{6+2})(u^{1+7})$

$(2)(e^{3})(f^{8})(u^{8})$

This is the same as:

$2e^{3}f^{8}u^{8}$

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Example Question #672 : Concepts

Simplify:

$(4g)(2r^{2})(r^{3})(g^{2})$

Possible Answers:

$4g^{5}r^{5}$

$8g^{3}r^{5}$

$8g^{2}r^{6}$

$8g^{2}r^{5}$

$6g^{3}r^{5}$

Correct answer:

$8g^{3}r^{5}$

Explanation:

$(2*4)(g*g^{2})(r^{2}*r^{3})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(8)(g^{1+2})(r^{2+3})$

$(8)(g^{3})(r^{5})$

This is the same as:

$8g^{3}r^{5}$

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Example Question #31 : How To Multiply Variables

Simplify:

$(2)(15y^{2})(x^{3})(10)$

Possible Answers:

$300x^{3}y^{2}$

$27 x^{4}y^{2}$

$27x^{3}y^{2}$

$30x^{31}y^{2}$

$20x^{4}y^{30}$

Correct answer:

$300x^{3}y^{2}$

Explanation:

$(2 * 15 * 10)(x^{3})(y^{2})$

There are no variables to combine. We only need to combine the numerical coefficient. This gets you:

$(300)(x^{3})(y^{2})$

This is the same as:

$300x^{3}y^{2}$

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Example Question #671 : Concepts

Simplify:

$x * y * (x^{3}) * (xy)$

Possible Answers:

$6x^{3}y$

$3x^{5}y^{2}$

10xy

$x^{3}y$

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

Correct answer:

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

Explanation:

$(x * x* x^{3})(y * y)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(x^{1+1+3})(y^{1+1})$

$(x^{5})(y^{2})$

This is the same as:

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

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Example Question #1267 : Hspt Mathematics

Simplify:

$x * a^{3} * y^{4} * x^{2} * x*a^{2}$

Possible Answers:

$a^{6}xy^{2}$

$a^{6}x^{2}y^{4}$

80axy

$a^{5}x^{3}y^{4}$

$a^{5}x^{4} y^{4}$

Correct answer:

$a^{5}x^{4} y^{4}$

Explanation:

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

When multiplying variables of the same type, you add their exponents together. This gets you:

$(a^{3+2})(x^{1+2+1})(y^4)$

$(a^{5})(x^{4})(y^{4})$

This is the same as:

$a^{5}x^{4} y^{4}$

Report an Error

Example Question #32 : How To Multiply Variables

Simplify:

$xy(x^{2} + 2aby)$

Possible Answers:

$3abx^{3}y^{2}$

$x^{2}y + 2abxy$

$3abx^{3}y$

$2x^{2}y + 4abxy$

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

Correct answer:

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

Explanation:

$xy(x^{2} + 2aby)$

Distribute the outside term into the parentheses. Multiply each term in parentheses by :

$(xy)(x^{2}) + (xy)(2aby)$

Now, for each member, move the similar variables into separate groups. You can do this because of the associative rule for multiplication:

$(x*x^{2})(y) + (2)(a)(b)(x)(y*y)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(x^{1+2})(y)+(2)(a)(b)(x)(y^{1+1})$

$(x^{3})(y) + (2)(a)(b)(x)(y^2)$

This is the same as:

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

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Example Question #31 : Algebraic Concepts

Simplify:

2ab(5xy - 3ax + 4by)

Possible Answers:

$12a^{4}b^{4}x^{2}y^{2}$

$7abxy – 5a^{2}bx + 6ab^{2}y$

6abxy - 6abx + 5aby

$10abxy - 6a^{2}bx + 8ab^{2}y$

12abxy

Correct answer:

$10abxy - 6a^{2}bx + 8ab^{2}y$

Explanation:

2ab(5xy - 3ax + 4by)

Distribute the outside term into the parentheses. Multiply each term in parentheses by 2ab :

(2ab)(5xy) - (2ab)(3ax)+ (2ab)(4by)

Now, for each member, move the similar variables into separate groups. You can do this because of the associative rule for multiplication:

(2*5)(abxy) - (2*3)(a*a)(bx)+ (2*4)(a)(b*b)(y)

When multiplying variables of the same type, you add their exponents together. This gets you:

$(10)(abxy)-(6)(a^{1+1})(bx)+(8)(a)(b^{1+1})(y)$

$(10)(abxy) - (6)(a^{2})(bx)+ (2*4)(a)(b^{2})(y)$

This is the same as:

$10abxy - 6a^{2}bx + 8ab^{2}y$

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Example Question #32 : Algebraic Concepts

Simplify:

$5bv(vx^{2} - 10bx - 5vb^{6})$

Possible Answers:

$5bv^{2}x^{2} + 50b^{2}v^{2}x – 25b^{7}$

$6bv^{2}x^{2} – 5b^{2}v^{2}x$

$10bv^{2}x^{2} – 50bv^{2}x – 10b^{5}v^{2}$

$6bv^{2}x^{2} – 5b^{2}v^{2}x$

$5bv^{2}x^{2} - 50b^{2}vx - 25b^{7}v^{2}$

Correct answer:

$5bv^{2}x^{2} - 50b^{2}vx - 25b^{7}v^{2}$

Explanation:

$5bv(vx^{2} - 10bx - 5vb^{6})$

Distribute the outside term into the parentheses. Multiply each term in parentheses by 5bv :

$(5bv)(vx^{2}) - (5bv)(10bx) - (5bv)(5vb^{6})$

Now, for each member, move the similar variables into separate groups. You can do this because of the associative rule for multiplication:

$(5)(b)(v * v)(x^{2}) - (5 * 10)(b *b)(vx) - (5*5)(b *b^{6})(v*v)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(5)(b)(v^{1+1})(x^2)-(50)(b^{1+1})(vx)-(25)(b^{1+6})(v^{1+1})$

$(5)(b)(v^{2})(x^{2}) - (50)(b^{2})(vx) - (25)(b^{7})(v^{2})$

This is the same as:

$5bv^{2}x^{2} - 50b^{2}vx - 25b^{7}v^{2}$

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Example Question #33 : Algebraic Concepts

$x^{2}* x^{5}=$

Possible Answers:

Cannot be simplified further

$x^{3}$

$x^{7}$

Correct answer:

$x^{7}$

Explanation:

To simplify, add the exponents:

$x^{2}* x^{5}=x^{7}$

Answer: $x^{7}$

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Example Question #34 : Algebraic Concepts

$y^{5}* y^{9}=$

Possible Answers:

$y^{59}$

$y^{4}$

Cannot be simplified further

$y^{14}$

Correct answer:

$y^{14}$

Explanation:

Because the two terms have the same base, they can be multiplied together by adding the exponents:

$y^{5}* y^{9}=y^{14}$

Answer: $y^{14}$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #671 : Concepts

Example Question #672 : Concepts

Example Question #31 : How To Multiply Variables

Example Question #671 : Concepts

Example Question #1267 : Hspt Mathematics

Example Question #32 : How To Multiply Variables

Example Question #31 : Algebraic Concepts

Example Question #32 : Algebraic Concepts

Example Question #33 : Algebraic Concepts

Example Question #34 : Algebraic Concepts

All HSPT Math Resources

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