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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 #1125 : Concepts

$3\frac{1}{2} + d + 2.1 = 1\frac{9}{10}$

Possible Answers:

d = 7.5

d = 4.2

d = 3.7

d = -3.7

Correct answer:

d = -3.7

Explanation:

First change the fractions to decimals:

3.5 + d + 2.1 = 1.9

Simplify:

d + 5.6 = 1.9

Isolate the variable and solve:

d + 5.6 -5.6 = 1.9 -5.6

d = -3.7

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Example Question #1126 : Concepts

8s = 46-14

Possible Answers:

s = 5

s = -4

s = 4

s = 7.5

Correct answer:

s = 4

Explanation:

First simplify:

8s = 32

Isolate the variable by dividing (the inverse operation of multiplication), both sides by the coefficient of the variable, which in this equation is 8.

$\frac{8s}{8} = \frac{32}{8}$

s = 4

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Example Question #517 : Algebra

x - (-12.2) = 2

Possible Answers:

x = 10.2

x = 12.4

x = -10.2

x = 12.0

Correct answer:

x = -10.2

Explanation:

Recall that subtraction of a negative value is the same as adding a positive number.

a-(-b)=a+b

Therefore, rewrite the equation:

x + 12.2 = 2.0

Isolate the variable by subtracting the 12.2 from both sides.

x + 12.2 -12.2 = 2.0 - 12.2

x = -10.2

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Example Question #1127 : Concepts

-27 + d = 61

Possible Answers:

d = -88

d = 88

d = -34

d = 34

Correct answer:

d = 88

Explanation:

To solve this one step equation, isolate the variable:

In this particular case add 27 to both sides.

-27 + 27 + d = 61+ 27

Then solve:

d = 88

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Example Question #1131 : Concepts

$x + 8 = 20 -4^2{}$

Possible Answers:

x = 12

x = -12

x = -4

x = 4

Correct answer:

x = -4

Explanation:

The first step is to simplify the equation on the right hand side by subtracting 16 from 20:

x + 8 = 20 - 16

x + 8 = 4

Then, isolate the variable by subtracting 8 from each side:

x + 8 - 8 = 4 -8

Solve:

x = -4

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Example Question #520 : Algebra

$\frac{1}{5}r = 15$

Possible Answers:

r = 15

$r = \frac{1}{3}$

r = 3

r = 75

Correct answer:

r = 75

Explanation:

To solve this equation, isolate the variable.

This is done by multiplying both sides of the equation by the reciprocal of $\frac{1}{5}$ which is $\frac{5}{1}$ .

$\frac{1}{5}\times\frac{5}{1} = \frac{15}{1} \times \frac{5}{1}$

$r = \frac{75}{1}$

r = 75

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Example Question #521 : Algebra

$-\frac{x}{6} =22 - 27$

Possible Answers:

x = -5

x = 30

x = 294

x = -30

Correct answer:

x = 30

Explanation:

First, simplify the equation by subtracting 27 from 22. Since 27 is greater than 22 the resulting difference will be negative:

$-\frac{x}{6} =22 - 27$

$-\frac{n}{6} = -5$

Then isolate the variable by multiplying each side of the equation by -6.

$-\frac{n}{6} \times -\frac{6}{1} = -\frac{5}{1} \times -\frac{6}{1}$

Recall that when two negatives are multiplied together their product becomes positive.

n = 30

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Example Question #522 : Algebra

$-\frac{1}{3}y = \frac{4}{9}$

Possible Answers:

$-1\frac{2}{3}$

$1\frac{2}{3}$

$-1\frac{2}{9}$

$-1\frac{1}{3}$

Correct answer:

$-1\frac{1}{3}$

Explanation:

First, isolate the variable.

This is done by multiplying both sides of the equation by the reciprocal of $-\frac{1}{3}$ which is $-\frac{3}{1}$ .

$-\frac{1}{3} \times - \frac{3}{1} = \frac{4}{9} \times -\frac{3}{1}$

$y = -\frac{12}{9}$

$y = -1\frac{1}{3}$

Note: If you wanted to simplify the fraction $\frac{4}{9} = \frac{2}{3}$ , that would have made it easier to do this problem.

However, the answer is still,

$y = -1\frac{1}{3}$ .

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Example Question #523 : Algebra

A piece of wood is cut into 14 equal pieces. The wood was originally 196 cm long. What algebraic equation would you use to solve this, and what would the answer be?

Possible Answers:

196 + 14 = x

x = 210cm

196 = 14x

x = 14cm

196 - 14 = x

x = 182cm

196x = 14

$x = \frac{1}{14}$

Correct answer:

196 = 14x

x = 14cm

Explanation:

To write this statement as an algebraic equation we need to pick out some identifiers.

A piece of wood is cut into 14 equal pieces. This means that each piece of wood is the same length or in mathematical terms: 14x

The wood was originally 196 cm long, in mathematical terms 196=

The equation will be in the form of,

$Length\ of\ Wood=length\times\ number\ of\ pieces$

Therefore the equation becomes,

14x = 196cm .

To solve, divide each side by 14.

x = 14cm

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Example Question #524 : Algebra

$\frac{n}{0.15} = -4.1 + 3.83$

Possible Answers:

n = -0.0405

n= -40.5

n = -405

n = -4.05

Correct answer:

n = -0.0405

Explanation:

To solve this function first simplify the right hand side of the equation by adding the two terms together.

$\frac{n}{0.15} = -4.1 + 3.83$

$\frac{n}{0.15} = -0.27$

From here isolate the variable by multiplying both sides by 0.15.

$\frac{n}{0.15} \times\frac{0.15}{1} = -0.27 \times 0.15$

n = -0.0405

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1125 : Concepts

Example Question #1126 : Concepts

Example Question #517 : Algebra

Example Question #1127 : Concepts

Example Question #1131 : Concepts

Example Question #520 : Algebra

Example Question #521 : Algebra

Example Question #522 : Algebra

Example Question #523 : Algebra

Example Question #524 : Algebra

All HSPT Math Resources

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