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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #71 : Equations

Solve for :

$\frac{n-2}{n}=\frac{3}{4}$

Possible Answers:

n=3

n=8

n=4

n=6

Correct answer:

n=8

Explanation:

$\frac{n-2}{n}=\frac{3}{4}$

Cross multiply.

3n=4(n-2)

3n=4n-8

3n+8=4n-8+8

3n+8=4n

3n+8-3n=4n-3n

8=n

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Example Question #77 : How To Find The Solution To An Equation

Solve for :

6x + 8 = 3x + 44

Possible Answers:

$x = 17 \frac {1}{3}$

$x = 5 \frac{7}{9}$

x = 12

x = 4

The equation has no solution.

Correct answer:

x = 12

Explanation:

6x + 8 = 3x + 44

6x - 3x + 8= 3x - 3x + 44

(6 - 3)x + 8= 44

3x + 8= 44

3x + 8-8 = 44 -8

3x = 36

$3x \div 3= 36 \div 3$

x = 12

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Example Question #882 : Concepts

Solve for y:

4y + 23 = 9y - 12

Possible Answers:

The equation has no solution.

y = 2.2

y = -7

y = -2.2

y = 7

Correct answer:

y = 7

Explanation:

4y + 23 = 9y - 12

4y- 4y + 23 = 9y - 4y - 12

23 = (9 - 4) y - 12

23 = 5 y - 12

23+ 12 = 5 y - 12 + 12

35 = 5 y

$35 \div 5 = 5 y \div 5$

7 = y

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Example Question #881 : Concepts

Find the mode in this set of numbers:

412, 421, 214, 241, 142, 124, 214

Possible Answers:

214

241

142

124

Correct answer:

214

Explanation:

Find the most recurring number: 214

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Example Question #80 : How To Find The Solution To An Equation

Solve for :

6 N - 17 = 4 (N - 7)

Possible Answers:

$N = - 22 \frac{1}{2}$

$N = - 5 \frac{1}{2}$

$N = - 1 \frac{1}{10}$

N = 5

$N = - 4 \frac{1}{2}$

Correct answer:

$N = - 5 \frac{1}{2}$

Explanation:

6 N - 17 = 4 (N - 7)

$6 N - 17 = 4 \cdot N - 4 \cdot 7$

6 N - 17 = 4 N - 28

6 N - 4N - 17 = 4 N - 4N - 28

(6 -4) N - 17 = - 28

2 N - 17 = - 28

2 N - 17 + 17 = - 28+ 17

$2 N = - \left ( 28- 17 \right )$

2 N = - 11

$2 N \div 2 = - 11\div 2$

$N = - 5 \frac{1}{2}$

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Example Question #81 : How To Find The Solution To An Equation

The three angles of a triangle measure $34^{\circ }, x ^{\circ }, 3x ^{\circ }$ .

What is ?

Possible Answers:

$x= 81 \frac{1}{2} ^{\circ }$

$x= 36 \frac{1}{2} ^{\circ }$

$x = 73^{\circ }$

$x = 34 ^{\circ }$

$x= 48 \frac{2}{3} ^{\circ }$

Correct answer:

$x= 36 \frac{1}{2} ^{\circ }$

Explanation:

The measures of three angles of a triangle total $180^{\circ }$ , so set up this equation and solve:

34 + x + 3x = 180

34 + 1x + 3x = 180

$34 + \left ( 1 + 3 \right ) x = 180$

34 + 4 x = 180

34 + 4 x -34 = 180-34

4 x = 146

$4 x \div 4= 146\div 4$

$x= 36 \frac{1}{2} ^{\circ }$

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Example Question #82 : How To Find The Solution To An Equation

The four angles of a quadrilateral measure $84 ^{\circ }, 97^{\circ }, x ^{\circ } , (x + 15)^{\circ }$ .

What is ?

Possible Answers:

$x=67^{\circ }$

$x=97^{\circ }$

$x=8^{\circ }$

$x=164^{\circ }$

$x=82^{\circ }$

Correct answer:

$x=82^{\circ }$

Explanation:

The measures of the four angles of a quadrilateral total $360^{\circ }$ , so set up this equation and solve:

84 + 97+ x + (x + 15) = 360

x + x + 84 + 97 + 15 = 360

2x + 196 = 360

2x + 196 -196 = 360-196

2x = 164

$2x \div 2= 164 \div 2$

$x=82^{\circ }$

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Example Question #81 : Equations

Solve for :

x - 7.2 = -1.3

Possible Answers:

x = -5.9

x = 5.9

x = 6.5

x = -6.5

x = -8.5

Correct answer:

x = 5.9

Explanation:

x - 7.2 = -1.3

x - 7.2 + 7.2 = -1.3+ 7.2

$x = -1.3+ 7.2 =+\left ( 7.2 - 1.3 \right ) = 5.9$

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Example Question #2401 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for :

t + 5.9 = 2.6

Possible Answers:

t = -8.5

t = -2.7

t = 3.3

t = -3.3

t = 2.7

Correct answer:

t = -3.3

Explanation:

t + 5.9 = 2.6

t + 5.9 -5.9 = 2.6-5.9

t = 2.6-5.9 = 2.6 + (-5.9) = - (5.9 - 2.6) = -3.3

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Example Question #291 : Algebraic Concepts

Solve for :

8t - 12 = 3t - 43

Possible Answers:

$t = 6 \frac{1}{5}$

t = 11

$t = -6 \frac{1}{5}$

The equation has no solution.

t = -11

Correct answer:

$t = -6 \frac{1}{5}$

Explanation:

8t - 12 = 3t - 43

8t -3t - 12 = 3t -3t - 43

(8 -3)t - 12 = - 43

5t - 12 = - 43

5t - 12+12 = - 43+12

5t = - (43 - 12)

5t = - 31

$5t \div 5 = - 31 \div 5$

$t = -6 \frac{1}{5}$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #71 : Equations

Example Question #77 : How To Find The Solution To An Equation

Example Question #882 : Concepts

Example Question #881 : Concepts

Example Question #80 : How To Find The Solution To An Equation

Example Question #81 : How To Find The Solution To An Equation

Example Question #82 : How To Find The Solution To An Equation

Example Question #81 : Equations

Example Question #2401 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #291 : Algebraic Concepts

All HSPT Math Resources

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