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HSPT Math : HSPT Mathematics

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Example Questions

Example Question #1221 : Hspt Mathematics

Simplify:

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

Possible Answers:

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

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

3x^3+4x^2+x

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

Correct answer:

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

Explanation:

Combine like terms:

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

=(x^3-4x^3)+(3x^2+x^2)+(-2x+x)

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

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Example Question #1222 : Hspt Mathematics

Simplify:

7x^2+8x^3+9x^2-6x+2-4x^3

Possible Answers:

2x^3+8x^2-3x+1

4x^3+16x^2-6x+2

6x^3+8x^2-3x+1

12x^3+16x^2-6x+2

Correct answer:

4x^3+16x^2-6x+2

Explanation:

Combine like terms:

7x^2+8x^3+9x^2-6x+2-4x^3

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

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Example Question #161 : Operations

f (x) = 5x + 1

Evaluate f (-3)

Possible Answers:

Correct answer:

Explanation:

f (x) = 5x + 1

f (-3) = 5 (-3) + 1 = -15+1 = -14

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Example Question #162 : Operations

6r+3r+3r=

Possible Answers:

12r

24r

108r

Correct answer:

12r

Explanation:

Add the numbers and keep the variable:

6r+3r+3r=12r

Answer: 12r

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Example Question #163 : Operations

Simplify:

(xy^2)^2+3x^2y^4

Possible Answers:

3x^2y^4

x^2y^4

4x^2y^4

2x^2y^4

4x^4y^4

Correct answer:

4x^2y^4

Explanation:

(xy^2)^2+3x^2y^4

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

$(xy^2)^2=(x)^2\times (y^2)^2=x^2\times y^{(2\times 2)}=x^2y^4$

Return to the original expression:

x^2y^4+3x^2y^4

Since the variables have the same exponents we can write:

x^2y^4+3x^2y^4=4x^2y^4

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Example Question #164 : Variables

Gina's mom baked 12 cookies. 8 were cinnamon and 4 were chocolate chip. If Gina eats one of the cinnamon cookies, how many more cinnamon cookies are there than chocolate chip?

Possible Answers:

Correct answer:

Explanation:

Gina's mom baked 12 cookies; 8 were cinnamon and 4 were chocolate chip. If Gina then eats a cinnamon cookie, there will be 7 cinnamon cookies left.

After she eats the cookie, we need to find the difference between the number of cinnamon cookies and chocolate chip cookies.

$\text{Cinnamon}-\text{Chocolate chip}$

7-4=3

There are 3 more cinnamon cookies than chocolate chip cookies.

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Example Question #1 : How To Divide Variables

$3\frac{2}{5} \div 1 \frac{1}{5}=$

Possible Answers:

$4\frac{2}{5}$

$2\frac{5}{6}$

$\frac{102}{25}$

Correct answer:

$2\frac{5}{6}$

Explanation:

First convert each mixed number into and improper fraction

$\frac{17}{5} \div \frac{6}{5}$

Then convert the operation to multiplication and flip the second fraction

$\frac{17}{5} \ast \frac{5}{6}=$

Reduce where possible and multiply to solve:

$\frac{17}{6}=2\frac{5}{6}$

The answer is $2\frac{5}{6}$

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Example Question #21 : Algebra

Simplify:

$\frac{8x^3-6x^2+2x}{2x}$

Possible Answers:

4x^3-3x^2+x

4x^2-3x+1

4x^3+3x-x

4x^2+3x-1

Correct answer:

4x^2-3x+1

Explanation:

$\frac{8x^3-6x^2+2x}{2x}=\frac{8x^3}{2x}-\frac{6x^2}{2x}+\frac{2x}{2x}=4x^2-3x+1$

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Example Question #2 : How To Divide Variables

Solve for B

AX+B(2Y)=C

Possible Answers:

$2B=\frac{C-AX}{Y}$

B=4

$\frac{C-2Y}{AX}=B$

Not enough information provided.

$B=\frac{C-AX}{2Y}$

Correct answer:

$B=\frac{C-AX}{2Y}$

Explanation:

This problem looks strange since it mostly contains variables, in particular unknown variables. Still remember the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. We still use those operations in this case. All we must do is move the variables around to solve for .

In this case we can subtract (additive inverse) to the other side first.

AX-AX+B(2Y)=C-AX

Rewrite our problem.

B(2Y)=C-AX

Stop for a moment and look at the progress. Go back to the original question, solve for . Our problem shows about to be multiplied to , but we do not necessarily have to multiply because we can divide by to both sides of the equation, which would save us a step as well as have B by itself.

$\frac{B(2Y)}{2Y}=\frac{C-AX}{2Y}$

$B=\frac{C-AX}{2Y}$

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Example Question #2 : How To Divide Variables

Suppose you know the values of , , and , and you want to evaluate the expression below.

$A + B^{2}\div C$

Which of the following is the first step you must complete?

Possible Answers:

Evaluate $A\div C$ .

Evaluate A+B .

Evaluate $B\div C$ .

Evaluate B^2 .

Evaluate A^2 .

Correct answer:

Evaluate B^2 .

Explanation:

Use the order of operations, PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

In our expression, there are no parentheses, so square first.

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1221 : Hspt Mathematics

Example Question #1222 : Hspt Mathematics

Example Question #161 : Operations

Example Question #162 : Operations

Example Question #163 : Operations

Example Question #164 : Variables

Example Question #1 : How To Divide Variables

Example Question #21 : Algebra

Example Question #2 : How To Divide Variables

Example Question #2 : How To Divide Variables

All HSPT Math Resources

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