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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 #2529 : Isee Middle Level (Grades 7 8) Mathematics Achievement

For what values of is the following expression undefined?

$\frac{x-1}{x^2+1}$

Assume is a real number.

Possible Answers:

x=0

x=-1

The expression is defined for all real values of

x=1

$x=1\ and\ x=-1$

Correct answer:

The expression is defined for all real values of

Explanation:

The expression would be undefined for the values of that yield a denominator of zero:

$\frac{x-1}{x^2+1}$

x^2+1=0

Solve for .

x^2+1-1=0-1

x^2=-1

No real numbers satistfy this equation, since x^2 will never be a negative number. Hence, the expression is defined for all real values of because the denominator can never be equal to zero.

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Example Question #400 : Algebra

For what values of the following expression is undefined?

$\frac{2x+3}{x^2-4}$

Assume is a real number.

Possible Answers:

x=-2

$x=\pm 2$

The expression is defined for all real values of

$x=-\frac{3}{2}$

x=2

Correct answer:

$x=\pm 2$

Explanation:

The expression would be undefined for the values of that yield a denominator of zero:

$\frac{2x+3}{x^2-4}$

x^2-4=0

Solve the equation to find the value of :

x^2-4+4=0+4

x^2=4

$x=\pm2$

That means the denominator would be equal to zero if x=2 or x=-2 .

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Example Question #204 : How To Find The Solution To An Equation

For what values of the following expression is undefined?

$\frac{2x-1}{-x^2-4}$

Assume is a real number.

Possible Answers:

The expression is defined for all real values of

x=-2

$x=\pm 2$

x=2

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

Correct answer:

The expression is defined for all real values of

Explanation:

The expression would be undefined for the values of that yield a denominator of zero:

$\frac{2x-1}{-x^2-4}$

-x^2-4=0

Solve for the value of

-x^2-4+4=0+4

-x^2=4

x^2=-4

No real numbers satistfy this equation, since x^2

will never be a negative number. Hence, the expression is defined for all real values of

because the denominator can never be equal to zero.

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Example Question #208 : How To Find The Solution To An Equation

Solve for :

(2x+1)^2=4x(x-1)

Possible Answers:

$x=\frac{1}{4}$

$x=-\frac{1}{8}$

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

$x=\frac{1}{8}$

$x=-\frac{1}{4}$

Correct answer:

$x=-\frac{1}{8}$

Explanation:

First we should expand both sides of the equation; for the left side we can use the binominal square pattern and for the right side we can use distribution:

(2x+1)^2=4x(x-1)

4x^2+(2)(2x)(1)+1^2=(4x)(x)-(4x)(1)

4x^2+4x+1=4x^2-4x

Now that both sides of the equation have been expanded, we can begin to simplify.

4x^2+4x+1-4x^2=4x^2-4x-4x^2

4x+1=-4x

1=-4x-4x

1=-8x

$\frac{1}{-8}=x$

The answer is $x=-\frac{1}{8}$ .

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Example Question #2531 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for n:

8n=64

Possible Answers:

$\frac{1}{8}$

Correct answer:

Explanation:

Divide each side by 8:

$8n\div 8=64\div 8$

n=8

Answer:

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Example Question #2532 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for p:

8p=88

Possible Answers:

Correct answer:

Explanation:

Divide each side by 8:

$8p\div 8=88\div 8$

p=11

Answer:

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Example Question #2533 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for s:

13s=104

Possible Answers:

Correct answer:

Explanation:

Divide each side by 13:

$13s\div 13=104\div 13$

s=8

Answer:

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Example Question #2533 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for m:

33m=264

Possible Answers:

Correct answer:

Explanation:

Divide each side by 33:

$33m\div 33=264\div 33$

m=33

Answer:

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Example Question #1015 : Concepts

Solve for :

3n=57

Possible Answers:

Correct answer:

Explanation:

To solve divide each side by :

$3n\div 3=57\div 3$

n=19

Answer:

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Example Question #1014 : Concepts

Solve for :

8q=80

Possible Answers:

Correct answer:

Explanation:

To solve divide each side by :

$8q\div 8=80\div 8$

q=10

Answer:

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #2529 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #400 : Algebra

Example Question #204 : How To Find The Solution To An Equation

Example Question #208 : How To Find The Solution To An Equation

Example Question #2531 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2532 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2533 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2533 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1015 : Concepts

Example Question #1014 : Concepts

All HSPT Math Resources

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