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HSPT Math : Algebra

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Example Questions

Example Question #84 : Equations

$6^{4}=$

Possible Answers:

1296

216

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 #281 : Algebra

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

Solve for .

3n+4=7

Possible Answers:

n=1

n=3

n=4

n=2

Correct answer:

n=1

Explanation:

3n+4=7

3n+4-4=7-4

3n=3

$\frac{3n}{3}=\frac{3}{3}$

n=1

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Example Question #282 : Algebra

Solve for .

$\frac{9}{x}=2$

Possible Answers:

x=4

x=3.5

x=5

x=4.5

Correct answer:

x=4.5

Explanation:

$\frac{9}{x}=2$

9=2x

$\frac{9}{2}=\frac{2x}{2}$

4.5=x

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Example Question #94 : Equations

Solve for .

3q-3=-6

Possible Answers:

q=-2

q=-1

q=2

q=1

Correct answer:

q=-1

Explanation:

3q-3=-6

3q-3+3=-6+3

3q=-3

$\frac{3q}{3}=\frac{-3}{3}$

q=-1

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Example Question #95 : Equations

Solve for :

5t - 17 = 78

Possible Answers:

t = 17

t = 19

t = 21

t = 16

Correct answer:

t = 19

Explanation:

5t - 17 = 78

5t - 17 + 17= 78+ 17

5t = 95

$5t \div 5 = 95 \div 5$

t = 19

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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 #97 : Equations

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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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #84 : Equations

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

Example Question #281 : Algebra

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

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

Example Question #282 : Algebra

Example Question #94 : Equations

Example Question #95 : Equations

Example Question #96 : Equations

Example Question #97 : Equations

All HSPT Math Resources

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