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HSPT Math : HSPT Mathematics

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 #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:

$x=164^{\circ }$

$x=82^{\circ }$

$x=97^{\circ }$

$x=8^{\circ }$

$x=67^{\circ }$

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 #883 : Concepts

Solve for :

x - 7.2 = -1.3

Possible Answers:

x = -5.9

x = 6.5

x = 5.9

x = -8.5

x = -6.5

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 #84 : How To Find The Solution To An Equation

Solve for :

t + 5.9 = 2.6

Possible Answers:

t = -3.3

t = 3.3

t = -2.7

t = -8.5

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 #85 : How To Find The Solution To An Equation

Solve for :

8t - 12 = 3t - 43

Possible Answers:

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

t = -11

t = 11

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

The equation has no solution.

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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Example Question #891 : Concepts

$2^{2}+6=$

Possible Answers:

Correct answer:

Explanation:

Solve the exponents:

$2^{2}=4$

Then solve:

4+6=10

Answer:

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Example Question #1 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

$5^{4}=$

Possible Answers:

125

625

Correct answer:

625

Explanation:

Multiply: $5\cdot 5\cdot 5\cdot 5=625$

Answer: 625

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Example Question #1 : Expressions & Equations

$6^{4}=$

Possible Answers:

216

1296

Correct answer:

1296

Explanation:

Multiply:

$6\cdot 6\cdot 6\cdot 6=1296$

Answer: 1296

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Example Question #2 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

$9^{3=}$

Possible Answers:

729

243

Correct answer:

729

Explanation:

Multiply:

$9\cdot 9\cdot 9=729$

Answer: 729

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Example Question #892 : Concepts

Solve for : 2+ 4(x-1)=26

Possible Answers:

Correct answer:

Explanation:

2+4(x-1)=26

By using order of operations we must first multiply by using the distributive property

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

This gives us: 2+ 4x-4=26

Next we must combine like terms: 2-4=-2

Rewrite the equation after combining like terms: 4x-2=26

Add a positive 2 to both sides of the equation. 4x-2+2=26+2

Again combine like terms and rewrite equation 4x=28

Divide by 4 on both sides of the equation

$\frac{4x}{4}=\frac{28}{4}$

x=7

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Example Question #91 : How To Find The Solution To An Equation

Simplify:

(3^2)^8=

Possible Answers:

3^1^0

3^1^8

3^1^6

3^4^8

Correct answer:

3^1^6

Explanation:

When we have an exponent raised to an exponent, our rule is to multiply the exponent by the exponent. Lets look at an easier problem to show this rule.

(2^2)^2

In this problem it is saying two squared, times two squared correct? (Yes)

So what is 2 squared? (4), what is 2 squared again? (4).

So this problem is saying $4\times 4$ which is . This is one way we can do the equation. Another is a rule that was mentioned before. When we have an exponent raised by an exponent *only in these cases* we can multiply the exponents by each other.

So in our easier example the exponent (2) times the other exponent (2) .

Looks like this

$2^{2\times 2}= 2^4$

Or the same thing as saying

$2\times 2\times 2\times 2=16$ . Either way we get the same answer!

Returning back to the original problem. We have the exponent 2 raised to the exponent 8. We can multiply them by each other in this case. $2\times 8=16$

So as the question asks us to simplify we just need to put 3^1^6

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

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

Example Question #883 : Concepts

Example Question #84 : How To Find The Solution To An Equation

Example Question #85 : How To Find The Solution To An Equation

Example Question #891 : Concepts

Example Question #1 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #1 : Expressions & Equations

Example Question #2 : Write And Evaluate Numerical Expressions With Exponents: Ccss.Math.Content.6.Ee.A.1

Example Question #892 : Concepts

Example Question #91 : How To Find The Solution To An Equation

All HSPT Math Resources

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