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HSPT Math : Concepts

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Example Questions

Example Question #96 : Equations

Solve for :

x (x-6) = 40

Possible Answers:

$x = -4 \textrm{ or }x = 10$

$x = 8 \textrm{ or }x = -5$

$x = -8 \textrm{ or }x = 5$

$x = 4 \textrm{ or }x = -10$

Correct answer:

$x = -4 \textrm{ or }x = 10$

Explanation:

Rewrite in standard form:

x (x-6) = 40

$x \cdot x-x \cdot 6 = 40$

$x ^{2}-6x = 40$

$x ^{2}-6x- 40 = 40 - 40$

$x ^{2}-6x- 40 = 0$

Factor the quadratic expression as (x + ?)(x + ?) , replacing the question marks with two integers whose product is and whose sum is . The integers are -10, 4 , so we write the equation as

(x -10)(x + 4) = 0

Set each linear binomial to 0 and solve:

$x - 10 = 0\Rightarrow x = 10$

$x + 4 = 0\Rightarrow x = -4$

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Example Question #901 : Concepts

Solve for :

-6x + 13 > 78

Possible Answers:

$x > 10 \frac{5}{6}$

$x < -10 \frac{5}{6}$

$x > -10 \frac{5}{6}$

$x < 10 \frac{5}{6}$

Correct answer:

$x < -10 \frac{5}{6}$

Explanation:

-6x + 13 > 78

-6x + 13 - 13 > 78- 13

-6x > 65

$-6x \div (-6) < 65 \div (-6)$

Note: switch the symbol when dividing by a negative number

$x < -10 \frac{5}{6}$

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Example Question #902 : Concepts

Solve for :

$- \frac{6}{5}y > -\frac{9}{20}$

Possible Answers:

$y> \frac{3}{8}$

$y< - \frac{3}{8}$

$y< \frac{3}{8}$

$y> - \frac{3}{8}$

Correct answer:

$y< \frac{3}{8}$

Explanation:

$- \frac{6}{5}y > -\frac{9}{20}$

$- \frac{5}{6} \left ( - \frac{6}{5} y \right )< - \frac{5}{6} \left ( -\frac{9}{20} \right )$

Note: switch the symbol when dividing by a negative number

$y< \frac{5}{6} \cdot \frac{9}{20}$

$y< \frac{1}{2} \cdot \frac{3}{4}$

$y< \frac{3}{8}$

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Example Question #903 : Concepts

Solve for :

6 (t - 0.13 ) = 9

Possible Answers:

t = 1.47

t = 1.63

t = 1.37

t = 1.52

Correct answer:

t = 1.63

Explanation:

Distribute, then solve:

6 (t - 0.13 ) = 9

$6 \cdot t - 6 \cdot 0.13 = 9$

6 t - 0.78 = 9

6 t - 0.78 + 0.78 = 9+ 0.78

6 t = 9.78

$6 t \div 6 = 9.78 \div 6$

t = 1.63

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Example Question #904 : Concepts

Solve for :

10 - 0.4t = 8.11

Possible Answers:

t = 45.275

t = 4.725

t = - 45.275

t = -4.725

Correct answer:

t = 4.725

Explanation:

10 - 0.4t = 8.11

10 - 0.4t - 10 = 8.11- 10

-0.4t = - ( 10.00 - 8.11 )

-0.4t = - 1.89

$0.4t \div 0.4 = - 1.89 \div \left ( -0.4 \right )$

$t = 1.89 \div 0.4$

Move each decimal point one digit right:

$t = 18.9 \div 4 = 4.725$

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Example Question #905 : Concepts

Give the solution set of the inequality:

4t + 9 < 35

Possible Answers:

$t < 6 \frac{1}{2}$

t < 13

t < 11

$t < 7 \frac{1}{2}$

Correct answer:

$t < 6 \frac{1}{2}$

Explanation:

4t + 9 < 35

4t + 9 -9 < 35-9

4t < 26

$4t \div 4 < 26 \div 4$

$t < 6 \frac{2}{4}$

$t < 6 \frac{1}{2}$

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Example Question #301 : Algebraic Concepts

f(x) = 50 - 4x

Evaluate f (10.5 )

Possible Answers:

Correct answer:

Explanation:

f(x) = 50 - 4x

$f(10.5) = 50 - 4 \cdot 10.5 = 50 - 42 = 8$

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Example Question #2422 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Define $f (x) = \frac{1}{2} x - 7$

Evaluate: f (12)

Possible Answers:

$2 \frac{1}{2}$

$6 \frac{1}{2}$

Correct answer:

Explanation:

$f (x) = \frac{1}{2} x - 7$

$f (12) = \frac{1}{2} \cdot 12 - 7$

f (12) =6- 7

f (12) =-1

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Example Question #907 : Concepts

Define $g (x) =\left ( x -6 \right )^{2}$

Evaluate g(8.7)

Possible Answers:

2.89

13.69

7.29

9.61

Correct answer:

7.29

Explanation:

$g (x) =\left ( x -6 \right )^{2}$

$g (8.7 ) =\left (8.7 -6 \right )^{2}$

$g (8.7 ) =2.7 ^{2}$

$g (8.7 ) =2.7 \cdot 2.7$

g (8.7 ) =7.29

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Example Question #908 : Concepts

Solve for :

0.7t + 0.23 = 0.3 t - 3.21

Possible Answers:

t = - 8.6

t = -7.45

t = -2.98

t = - 3.44

Correct answer:

t = - 8.6

Explanation:

0.7t + 0.23 = 0.3 t - 3.21

0.7t + 0.23 - 0.3t = 0.3 t - 3.21 - 0.3t

0.4t + 0.23 = - 3.21

0.4t + 0.23- 0.23 = - 3.21 - 0.23

0.4t = - 3.44

$0.4t \div 0.4 = - 3.44 \div 0.4$

$t = - 3.44 \div 0.4$

Move each decimal point one digit right:

$t = - 34.4 \div 4 = - 8.6$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #96 : Equations

Example Question #901 : Concepts

Example Question #902 : Concepts

Example Question #903 : Concepts

Example Question #904 : Concepts

Example Question #905 : Concepts

Example Question #301 : Algebraic Concepts

Example Question #2422 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #907 : Concepts

Example Question #908 : Concepts

All HSPT Math Resources

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