Math 8 ACAP Review

Pythagorean Theorem

100

What is the hypotenuse of the right triangle if its two legs are 12 inches and 9 inches?

15 inches

200

What is the hypotenuse of the right triangle if its two legs are 5 inches and 12 inches?

13 inches

300

What is the hypotenuse of the right triangle if its two legs are 7 feet and 24 feet?

25 feet

400

What is the value of the missing leg if one leg is 15 meters and the hypotenuse is 39 meters?

36 meters

500

A 34 feet ladder is leaning against a window that is 30 feet high. How far away is the base of the ladder from the base of the building?

16 feet

Systems of Equations

100

Find the solution to the following system of equations. 

Equation 1: x = 5

Equation 2: y= 2x+14

(5, 24)

200

Find the solution to the following system of equations. 

Equation 1: y = 20

Equation 2: y= 2x+14

(3, 20)

300

Find the solution to the following system of equations. 

Equation 1: y= 3x -5

Equation 2: y= 4x+1

(-6, -23)

400

Find the solution to the following system of equations. 

Equation 1: y= -2x +5

Equation 2: y= 4x+23

(-3, 11)

500

A brother is 9 years older than his sister. Their total age is 53. How old is each sibling?

Brother is 31. Sister is 22. 

Exponent Rules

100

Simplify the following expression

x⁶ / x² 

x⁴

200

Simplify the following expression

(x⁵ y³ )(x² y⁷ )      

x⁷ y¹⁰  

300

Simplify the following expressions

(x⁴ )³ / (x^-2 )⁶      

x²⁴

400

Simplify the following expression

(x⁸ y² )^-3 / (x^-3 y^-4 )²           

 y² /x¹⁸  

500

Simplify the following expression

(x⁵ y¹² z⁴ )/(x^-3 y⁸ z^-2 )                  

x⁸ z⁶ /y⁴        

Evaluating Functions

100

Evaluate the following

f(x) = 4x - 12

f(6) =

f(6)=12

200

Evaluate the following

g(x) = -2x +10

g(-5) =

g(-5)=20

300

Evaluate the following

h(x) = 2x² - 4x + 10  

h(-1) =

h(-1)=16

400

What is x if 

f(x) = 4x - 12 

and

f(x) = 8

x=5

500

What is the value of x if

d(x) = -3x +9

and

d(x) = 18

x = -3

Identifying Slope

100

What is the slope of the line below?

y = 2/3 x + 12

2/3

200

What is the slope of the line below?

2y = 3x +6

3/2

300

What is the slope between the points 

(3, 2) and (6, 7)?

5/3

400

What is the slope between the points 

(-6, -7) and (4, 1)?

4/5

500

What is the slope of the line below?

4x + 8y = 24

-1/2