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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 #31 : Algebraic Concepts

Simplify:

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

Possible Answers:

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

6abxy - 6abx + 5aby

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

12abxy

$7abxy – 5a^{2}bx + 6ab^{2}y$

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:

$6bv^{2}x^{2} – 5b^{2}v^{2}x$

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

$6bv^{2}x^{2} – 5b^{2}v^{2}x$

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

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

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 #672 : Concepts

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

Possible Answers:

Cannot be simplified further

$x^{7}$

$x^{3}$

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 #673 : Concepts

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

Possible Answers:

$y^{59}$

Cannot be simplified further

$y^{4}$

$y^{14}$

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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Example Question #31 : How To Multiply Variables

$z^{3}* z^{6}=$

Possible Answers:

$z^{6}$

$z^{3}$

$z^{9}$

Cannot be simplified further

Correct answer:

$z^{9}$

Explanation:

To simplify the expression, add the exponents and keep the base unchanged:

$z^{3}* z^{6}=z^{9}$

Answer: $z^{9}$

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Example Question #32 : How To Multiply Variables

$w^{10}* w^{10}=$

Possible Answers:

$w^{20}$

$w^{100}$

Cannot be simplified further

20w

w+20

Correct answer:

$w^{20}$

Explanation:

To multiply two terms with the same base and different exponents, add the exponents and leave the base unchanged:

$w^{10}* w^{10}=w^{20}$

Answer: $w^{20}$

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Example Question #683 : Concepts

$t^{2}*t^{2}=$

Possible Answers:

$t^{4}$

$t^{22}$

Cannot be simplified further

Correct answer:

$t^{4}$

Explanation:

Because the two terms have the same base, add the exponents and leave the base unchanged:

$t^{2}*t^{2}=t^{4}$

Answer: $t^{4}$

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Example Question #72 : Algebra

$y^{15}*y^{3}=$

Possible Answers:

$y^{18}$

$y^{158}$

Cannot be simplified further

$y^{12}$

$y^{45}$

Correct answer:

$y^{18}$

Explanation:

Add the exponents because we are multiplying two terms with the same base:

$y^{15}*y^{3}=y^{18}$

Answer: $y^{18}$

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Example Question #73 : Algebra

$f^{8}*f^{9}=$

Possible Answers:

$f^{11}$

$f^{89}$

Cannot be simplified further

$f^{17}$

Correct answer:

$f^{17}$

Explanation:

To solve, add the exponents:

$f^{8}*f^{9}=f^{17}$

Answer: $f^{17}$

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Example Question #684 : Concepts

$g^{6}*g^{6}=$

Possible Answers:

$g^{12}$

$g^{36}$

$g^{0}$

Cannot be simplified further

Correct answer:

$g^{12}$

Explanation:

To simplify, add the exponents:

$g^{6}*g^{6}=g^{12}$

Answer: $g^{12}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #31 : Algebraic Concepts

Example Question #32 : Algebraic Concepts

Example Question #672 : Concepts

Example Question #673 : Concepts

Example Question #31 : How To Multiply Variables

Example Question #32 : How To Multiply Variables

Example Question #683 : Concepts

Example Question #72 : Algebra

Example Question #73 : Algebra

Example Question #684 : Concepts

All HSPT Math Resources

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