MATH CULMINATING

Linear Systems

100

What are the three main methods for solving linear patterns?

Graphing 

Substitution

Elimination

200

What is it called when there's infinite amount of solutions on a graph

Parallel & Coincident

300

What is y=mx+b used for?

To find the equation of the line

400

determine whether equation has one solution, no solutions, or infinitely many solutions

3𝑥−𝑦=0 

6𝑥−2𝑦=3

This equation have NO solutions

500

Find the point of intersection

2𝑥+5𝑦=−20

5𝑥−3𝑦=−15

x= -4.2  y= -2.2

POI: (-4.2,-2.2)

Quadratic Expressions and Relations

100

Put the following algebraic expressions into descending order

- m² + 2m³ + 8m + 9m⁵

9m⁵  + 2m³ + (- m²) + 8m

200

Solve by foil

(x + 3)(x - 5)

= x² + 5x + 6

300

factor the following 

5x + x² - 36

Hint: use factoring for easy trinomials

(x - a)(x + 4)

400

Solve by factoring 

- 12 + 26x + 16x²

Hint: Use factoring for hard trinomials 

2(8x-3)(x=2)

500

Factor perfect square trinomial

81m² - 90m + 25

(9) (5) (2) = 90 

=(9m - 5)²

Quadratics Equations

100

If the parabola opens the vertex is a _____ point

Min

200

The quadratic function can be written in three forms, what are they?

Standard, intercept,  and vertex

300

Find the vertex that belongs to:

y = (x + 3)² - 4

(-3,-4)

400

find the equation of  the parabola

V= (3,8)

P= (0,-1)

Y= -1 (x - 3)² + 8

500

Solve by completing the square 

- 5x² + 20x + 2

= -5 (x - 2)² + 22

(2, 22)

Trigonometry

100

There are 3 ways to prove triangles are similar, what are they?

Angle Angle similarity (2 angles are equal)

Side Side Side similarity (all ratios of sides are equal)

Side Angle Side similarity (2 ratios of sides and 1 angle are equal)

200

What are you looking for when you have the opposite and hypotenuse of a right triangle?

sinθ = opp / hyp

300

Calculate the trig ratio 

tan50°

= 1.19

400

Using sine law find the measure of angle R.

R = 67.15°

500

Find the length of side x by using cosine law

x = 8.58

8.6 if rounded 

Analytic Geometry

100

When finding the midpoint of a line segment what is the formula you use?

200

Determine at least one of what these line segments mean

Median of a triangle

Altitude of a Triangle

Right Bisector of a Triangle

A median of a triangle is the line segment that joins a vertex to the midpoint of the opposite side.

An altitude of a triangle is a line segment from a vertex of a triangle to the opposite side.

The right bisector of a triangle is the line that passes through the midpoint of a line segment and intersects it at 90° angle.

300

When finding the length of a line segment you first create a right triangle to find it, how is it constructed?

construct a right-angle triangle using the rise and run of the line segment. The
run is the difference in the 𝑥-coordinates, while the rise is the difference in the 𝑦-coordinates.

400

Find the midpoint of the line segment

A(5,7) and B(3,9)

= ( 4 , 8 )

500

∆DEF has vertices D(2,5), E(−6, −1) and F(10, −1).

The median from vertex D = (-1 , 2)

Find the equation for the altitude from vertex D

y = 1x + 3