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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 #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar \frac{1}{2} = -1$ , evaluate .

Possible Answers:

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

a = -3

a = 3

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

Correct answer:

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

Explanation:

$a \bigstar b = \frac{a+b}{ab}$

$a \bigstar \frac{1}{2} = \frac{a+ \frac{1}{2} }{a \cdot \frac{1}{2} } = \frac{\frac{2a}{2}+ \frac{1}{2} }{ \frac{a}{2} } = \frac{\frac{2a+1}{2} }{ \frac{a}{2} }$

Equivalently

$a \bigstar \frac{1}{2} = \frac{2a+1}{2} \div \frac{a}{2} = \frac{2a+1}{2} \cdot \frac{2}{a} = \frac{2a+1}{a}$

$a \bigstar \frac{1}{2} = -1$ , so set this equal to :

$\frac{2a+1}{a} = -1$

$\frac{2a+1}{a} \cdot a = -1 \cdot a$

2a+1 = -a

2a+1 + a - 1 = -a + a - 1

3a= - 1

$3a\div 3 = - 1 \div 3$

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

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Example Question #3 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar 0.5 = 0.1$ , then evaluate .

Possible Answers:

$a = \frac{ 19} {10}$

$a = - \frac{10}{19}$

$a = - \frac{ 19} {10}$

$a = \frac{10}{19}$

Correct answer:

$a = - \frac{10}{19}$

Explanation:

$a \bigstar b = \frac{a+b}{ab}$ ,

$a \bigstar 0.5 = \frac{a+0.5 }{a \cdot 0.5 } = \frac{a+0.5 }{0.5a }$

Set this equal to 0.1:

$\frac{a+0.5 }{0.5a } = 0.1$

$\frac{a+0.5 }{0.5a } \cdot 0.5 a = 0.1 \cdot 0.5 a$

a+0.5 = 0.05 a

$(a+0.5) \cdot 100 = 0.05 a \cdot 100$

$a \cdot 100 +0.5 \cdot 100 = 5 a$

100a +5 0= 5 a

100a +50 - 100a = 5 a - 100a

50 = -95a

$50 \div (-95) = -95a \div (-95)$

$a = -\frac{50}{95} = - \frac{10}{19}$

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Example Question #1166 : Concepts

is a number less than 36.

Which of the following gives a solution of the equation

|x- 17 | + K = 36

in terms of ?

Possible Answers:

x = -53 - K

x = 19 - K

x = 53 - K

x = -19 - K

Correct answer:

x = 53 - K

Explanation:

|x- 17 | + K = 36 ,

|x- 17 | + K - K = 36 - K

|x- 17 | = 36 - K

Since K < 36 , 36 - K > 0 , so solutions exist. One of the following two situations occurs:

x- 17 = 36 - K

x- 17 + 17 = 36 - K + 17

x = 53 - K

-(x- 17 )= 36 - K

-x+ 17 = 36 - K

-x+ 17 - 17 = 36 - K - 17

-x = 19 - K

-(-x )= -(19 - K)

x = K - 19

Of these two, only x = 53 - K is among the choices, so it is the correct choice.

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Example Question #1164 : Concepts

If L < 32 , then which of the following is equivalent to the expression | L - 32 | + 12 ?

Possible Answers:

20+L

44 + L

44 - L

20-L

Correct answer:

44 - L

Explanation:

If L < 32 , then L - 32 < 0 , so

| L - 32 | + 12

= -(L - 32 )+ 12

= - L + 32 + 12

= - L + 44

= 44 - L

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Example Question #552 : Algebra

If L > 47 , then which of the following is equivalent to the expression | L - 47 | - 32 ?

Possible Answers:

L - 79

L - 15

- L + 79

- L + 15

Correct answer:

L - 79

Explanation:

If L > 47 , then L - 47 > 0 , so

| L - 47 | - 32

= L - 47 - 32

= L - 79

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Example Question #1761 : Hspt Mathematics

If 4< X< 12 , then

|X - 12| + |X- 4|

can be rewritten as which of the following?

Possible Answers:

2X-16

-2X + 16

Correct answer:

Explanation:

If X > 4 , then

X - 4 >0 , so

|X- 4| = X-4 .

If X< 12 , then

X - 12 < 0 , so

|X- 12| = -(X-12)= -X + 12

|X - 12| + |X- 4|

= X-4 + (-X + 12)

= X-X -4 + 12

= 8

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Example Question #1762 : Hspt Mathematics

If X< 4 , then

|X - 12| + |X- 4|

can be rewritten as which of the following?

Possible Answers:

-2X + 16

2X-16

Correct answer:

-2X + 16

Explanation:

If X < 4 , then

X - 4 < 0 , so

|X- 4| = -(X-4)= -X + 4 .

Also,

X - 12 < 4 - 12 = -8 < 0 , so

|X- 12| = -(X-12)= -X + 12

Therefore,

|X - 12| + |X- 4|

= (-X + 4)+ (-X + 12)

= -2X + 16

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Example Question #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

$a \bigstar (-1) = 1$ . What is the value of ?

Possible Answers:

a= -2

a= 2

$a = \frac{1}{2}$

$a = - \frac{1}{2}$

Correct answer:

$a = \frac{1}{2}$

Explanation:

$a \bigstar b = \frac{a+b}{ab}$

and

$a \bigstar (-1) = 1$

$\frac{a+(-1)}{a(-1)}=1$

$\frac{a-1}{-a} = 1$

$\frac{a-1}{-a} \cdot (-a) = 1 \cdot (-a)$

a- 1 = -a

a- 1 + a +1 = -a + a +1

2a= 1

$2a \div 2 = 1 \div 2$

$a = \frac{1}{2}$

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Example Question #1763 : Hspt Mathematics

Solve for :

4x+6=30

Possible Answers:

x=6

x=20

x=9

x=30

Correct answer:

x=6

Explanation:

The first step to solve for is to undue the by subtracting it from both sides of the equation.

This results in having

4x=24 .

Then you must undue 4*x by dividing by on each side resulting in an answer of

24/4=6 .

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Example Question #5 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{ab}{a+b}$

$a \bigstar 1= -1$ . What is the value of ?

Possible Answers:

a = -0.5

a = -2

No real value of makes this true.

a = -1

Correct answer:

a = -0.5

Explanation:

$a \bigstar b = \frac{ab}{a+b}$ , so

$a \bigstar 1 = \frac{a \cdot 1 }{a+1} = \frac{a }{a+1}$

Set this equal to :

$\frac{a }{a+1} = -1$

$\frac{a }{a+1} \cdot (a+1) = -1 \cdot (a+1)$

a = -a - 1

a + a = -a - 1 + a

2a = - 1

$2a \div 2= - 1 \div 2$

a = -0.5

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #3 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #1166 : Concepts

Example Question #1164 : Concepts

Example Question #552 : Algebra

Example Question #1761 : Hspt Mathematics

Example Question #1762 : Hspt Mathematics

Example Question #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #1763 : Hspt Mathematics

Example Question #5 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

All HSPT Math Resources

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