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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 #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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Example Question #525 : Algebra

Solve for :

15=3x

Possible Answers:

x=3

x=15

x=45

x=5

Correct answer:

x=5

Explanation:

To get by itself, you must get rid of the .

To undo the multiplication, you must divide both sides of the equation by and $15\div3=5$ .

$\\15=3x \\ \\ \frac{15}{3}=\frac{3x}{3} \\ \\\frac{15}{3}=x \\ \\ \frac{5\cdot 3}{3}=x \\ \\5=x$

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Example Question #1132 : Concepts

Solve for :

45n=225

Possible Answers:

Correct answer:

Explanation:

In order to solve this equation we need to isolate the variable to one side. Do not forget to perform the same operation on both sides of the equation.

45n=225

Divide each side of the equation by :

$\frac{45n}{45}=\frac{225}{45}$

Solve.

n=5

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Example Question #1133 : Concepts

Solve for :

7t + 4 = 102 - 7t

Possible Answers:

t=98

t=-98

$t=15\frac{1}{7}$

t=7

The equation has no solution.

Correct answer:

t=7

Explanation:

7t + 4 = 102 - 7t

7t +7t + 4 = 102 - 7t+7t

14t + 4 = 102

14t + 4 -4= 102 -4

14t = 98

$14t \div 14 = 98 \div 14$

t=7

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Example Question #1134 : Concepts

Solve for :

9n + 16 = 97

Possible Answers:

n=9.5

n=10

n=8.5

n = 9

n=8

Correct answer:

n = 9

Explanation:

Subtract 16, then divide by 9:

9n + 16 = 97

9n + 16 -16 = 97 -16

9n=81

$9n \div 9= 81\div 9$

n = 9

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1131 : Concepts

Example Question #520 : Algebra

Example Question #521 : Algebra

Example Question #522 : Algebra

Example Question #523 : Algebra

Example Question #524 : Algebra

Example Question #525 : Algebra

Example Question #1132 : Concepts

Example Question #1133 : Concepts

Example Question #1134 : Concepts

All HSPT Math Resources

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