Math II Spring Final Review

Triangle Similarity

100

Find the value of x.

20/25=(2x+2)/(4x-23)

x=17

200

The ratio of two complementary angles is 3:7. Find the measure of the smaller angle.

27°

300

The ratio of the measures of the angles in a triangle is 8:3:4. Find the measure of the largest angle.

96°

400

The ratio of the measures of the sides of a triangle is 2:8:9. If the perimeter of the triangle is 76 inches, find the length of the longest side.

36in

500

The ratio of two supplementary angles is 4:1. Find the measure of the larger angle. 

144°

Right Triangles and Trigonometry

100

The legs of a right triangle are 8 and 13. Use the Pythagorean Theorem to calculate the hypotenuse. Round to the nearest tenth.

15.3

200

What are the sides of a 45°-45°-90° triangle?

Leg=x

Hypotenuse=x√2

300

What are the sides of a 30°-60°-90° Triangle?

Short Leg=x

Long Leg=x√3

Hypotenuse=2x

400

Jake leaned a 12-foot ladder against his house. If the angle formed by the ladder and the ground is 68°, how far from the base of the house did he place the ladder?

x=4.5ft

500

Ryan is flying a kite and lets off 275 feet of string. If the kite is 150 feet above ground and assuming the string is straight, what angle does the string make with the ground?

x=33.1°

Absolute Value and Piecewise Functions

100

Solve the equation for x.

-5|-3+x|=-25

x={-2,8}

200

Describe the transformations of the absolute value equation. 

y=3|x+1|-4

Stretch by 3, Left 1, Down 4

300

Writing an absolute value equation based on the transformations. Shrinks by 1/2, right 6, up 7

y=1/2|x-6|+7

400

Evaluate the piecewise function at x=-3.

f(x)=-x, x<-3

x-2, -3≤x<3

x-3, x≥3

f(-3)=-5

500

Evaluate the piecewise function at x=6.

f(x)=-x, x<-3

x-2, -3≤x<3

x-3, x≥3

f(6)=3

Polynomials Part I

100

Add the polynomials. Answer in standard form.

(5w³-w+2w²+4)+(3w²+1-4w)

5w³+5w²-5w+5

200

Divide the Polynomial by the Monomial.

(12r³s⁵-18r²s²+3rs)/(3rs)

4r²s⁴-6rs+1

300

Factor the Polynomial by GFC:

18x²yz-24xz²+36yz³

6z(3x²y-4xz+6yz²)

400

Describe the Transformations of the Function:

y=3(x-6)²-2

Vertical Stretch by 3, Right 6, Down 2

500

Write a Quadratic Function based on the Transformations. Reflected over the x-axis, then translated 4 units left and 1 unit down

y=-(x+4)²-1

Polynomials Part II

100

Solve by Factoring:

x²-6x-40=0

x={-4,10}

200

Solve by Factoring:

4x²+5x+1=0

x={-1,-1/4}

300

Solve by Taking Square Roots:

4x²-1=48

x={-7/2,7/2}

400

Solve by using the Quadratic Formula:

-x²+4x=9

x={}

500

Solve by Completing the Square:

x²-18x+65=0

x={5,13}