Math Summary

Linear Systems

100

What does "P.O.I" stand for?

Point of Intersection

200

What are the 2 ways you can use to solve a linear system?

Substitution and Elimination

300

Translate this sentence into an equation:

Brad has 8 more fidgets than Samantha. Together, they have 23 fidgets. 

x + (x+8) = 23

400

Solve:

y + 3x = 6

y = 2x + 1

x = 1

y= 3

500

Solve:

Gregory works half as many hours per

week as Paul. Between the two, they work

a total of 48 hours one week. How many hours did they each work?

Gregory works 16 hours and Paul works 32 hours

Quadratic Expressions and Relations

100

What method can be used for factoring?

FOIL

200

Expand and Simplify:

(y+5)(y+9)

y² + 14y + 45

300

Factor:

x² - 49

(x-7) (x+7)

400

Common Factor:

9m⁴n²p⁵ - 9m³n³p³ + 27m²n⁴p⁴

= 9m²n²p³ (m²p² - mn + 3n²p)

500

Factor fully:

10e² + 31e + 3

(10e + 1) (e + 3)

Quadratic Equations

100

What is "CTS" method?

Completing the Square

200

How do "h" and "k" affect a parabola?

"h" represents the horizontal shift and "k" represents the vertical shift.

300

State an equation for:

a parabola that is reflected in the x-axis, is stretched by a factor of 5, is shifted 5 units to the right, and down 2 units.

y = -5(x - 5)² - 2

400

rewrite in form "y = a(x - h)² + k" form:

y = x² + 8x - 7

y = (x + 4)² - 23

500

Find the x values

2x² - 22x + 48 = 0

x₁ = 8

x₂ = 3

Trigonometry

100

TRUE OR FALSE:

Similar triangles have the same angles and sides. 

False! Similar triangles have the same angles BUT not the same sides, they are just the same ratios.

200

What are the three ratios?

SOH, CAH, TOA

300

Solve:

cos X = 0.84562

X = 32.26

400

When is the cosine law used?

1. There is a contained angle 

2. All 3 side lengths are given

500

Find side b using the given information:

Angle A = 74^o

Angle B = 45^o

Side a = 25 cm

Side c = 18 cm

18.3 cm