HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #272 : Algebra

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

What is \displaystyle x ?

Possible Answers:

\displaystyle x=8^{\circ }

\displaystyle x=67^{\circ }

\displaystyle x=97^{\circ }

\displaystyle x=164^{\circ }

\displaystyle x=82^{\circ }

Correct answer:

\displaystyle x=82^{\circ }

Explanation:

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

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

\displaystyle x + x + 84 + 97 + 15 = 360

\displaystyle 2x + 196 = 360

\displaystyle 2x + 196 -196 = 360-196

\displaystyle 2x = 164

\displaystyle 2x \div 2= 164 \div 2

\displaystyle x=82^{\circ }

Example Question #81 : Equations

Solve for \displaystyle x:

\displaystyle x - 7.2 = -1.3

Possible Answers:

\displaystyle x = -8.5

\displaystyle x = -6.5

\displaystyle x = -5.9

\displaystyle x = 5.9

\displaystyle x = 6.5

Correct answer:

\displaystyle x = 5.9

Explanation:

\displaystyle x - 7.2 = -1.3

\displaystyle x - 7.2 + 7.2 = -1.3+ 7.2

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

Example Question #274 : Algebra

Solve for \displaystyle t:

\displaystyle t + 5.9 = 2.6

Possible Answers:

\displaystyle t = 3.3

\displaystyle t = -8.5

\displaystyle t = -3.3

\displaystyle t = 2.7

\displaystyle t = -2.7

Correct answer:

\displaystyle t = -3.3

Explanation:

\displaystyle t + 5.9 = 2.6

\displaystyle t + 5.9 -5.9 = 2.6-5.9

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

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

Solve for \displaystyle t:

\displaystyle 8t - 12 = 3t - 43

Possible Answers:

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

\displaystyle t = -11

\displaystyle t = 11

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

The equation has no solution.

Correct answer:

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

Explanation:

\displaystyle 8t - 12 = 3t - 43

\displaystyle 8t -3t - 12 = 3t -3t - 43

\displaystyle (8 -3)t - 12 = - 43

\displaystyle 5t - 12 = - 43

\displaystyle 5t - 12+12 = - 43+12

\displaystyle 5t = - (43 - 12)

\displaystyle 5t = - 31

\displaystyle 5t \div 5 = - 31 \div 5

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

Example Question #82 : Equations

\displaystyle 2^{2}+6=

Possible Answers:

\displaystyle 6

\displaystyle 10

\displaystyle 8

\displaystyle 4

Correct answer:

\displaystyle 10

Explanation:

Solve the exponents:

\displaystyle 2^{2}=4

Then solve:

\displaystyle 4+6=10

Answer: \displaystyle 10

Example Question #1 : Expressions & Equations

\displaystyle 5^{4}=

Possible Answers:

\displaystyle 20

\displaystyle 25

\displaystyle 625

\displaystyle 125

Correct answer:

\displaystyle 625

Explanation:

Multiply: \displaystyle 5\cdot 5\cdot 5\cdot 5=625

Answer: \displaystyle 625

Example Question #1 : Expressions & Equations

\displaystyle 6^{4}=

Possible Answers:

\displaystyle 1296

\displaystyle 36

\displaystyle 24

\displaystyle 216

Correct answer:

\displaystyle 1296

Explanation:

Multiply:

\displaystyle 6\cdot 6\cdot 6\cdot 6=1296

Answer: \displaystyle 1296

Example Question #1 : Expressions & Equations

\displaystyle 9^{3=}

Possible Answers:

\displaystyle 729

\displaystyle 243

\displaystyle 27

\displaystyle 81

Correct answer:

\displaystyle 729

Explanation:

Multiply:

\displaystyle 9\cdot 9\cdot 9=729

Answer: \displaystyle 729

Example Question #83 : Equations

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

Possible Answers:

\displaystyle 8

\displaystyle 4

\displaystyle 7

\displaystyle 6

\displaystyle 5

Correct answer:

\displaystyle 7

Explanation:

\displaystyle 2+4(x-1)=26

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

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

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

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

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

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

Again combine like terms and rewrite equation \displaystyle 4x=28

Divide by 4 on both sides of the equation 

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

\displaystyle x=7

 

Example Question #1481 : Hspt Mathematics

Simplify:

\displaystyle (3^2)^8=

Possible Answers:

\displaystyle 3

Correct answer:

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.

\displaystyle (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 \displaystyle 4\times 4 which is \displaystyle 16. 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 \displaystyle (2) times the other exponent \displaystyle (2)\displaystyle =4.

Looks like this 

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

Or the same thing as saying

\displaystyle 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. \displaystyle 2\times 8=16

So as the question asks us to simplify we just need to put 

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