Math Project

Factoring Completely

100

x⁴-81

(x²+9)(x+3)(x-3)

200

2x⁴-18y²

2(x²+3y)(x²-3y)

300

x³-13x²-30x

x(x+2)(x-15)

400

4x³-49x

x(2x+7)(2x-7)

500

4x²+2x-42

2(2x+7)(x-3)

Sequences

100

Write the explicit and recursive formula using:

6,13,20,27,...

Explicit: a_n=7n-1

Recursive: a₁=6, a_n=a_n-1+7

200

Write the explicit and recursive formula using:

3,-18,108,...

Explicit: r=-6, a_n=3(-6)^n-1

Recursive: a₁=3, a_n=a_n-1(-6)

300

Write the explicit and recursive formula using:

4, 16x, 64x²,...

Explicit: r=4x, a_n=4(4x)^n-1

Recursive: a₁=4, a_n=a_n-1(4x)

400

Write the geometric explicit formula using:

a₁=31 and a₄=1984

r=4, a_n=31(4)^n-1

500

Write the geometric explicit formula formula using:

a₁=43 and a₅=688

r=2, a_n=43(2)^n-1

Literal Equations

100

Solve for b:

7a-b=2c

b=7a-2c

200

Solve for r:

I=Prt

I/(Pt)

300

Solve for h:

A=1/2bh

h=2A/b

400

Solve for n:

S=180(n-2)

S/180+2

500

Solve for c:

5c+2m=3p

c=(3p-2m)/5

Quadratics

100

State the vertex of:

f(x)=(x-2)²+4

(2,4)

200

Determine how long it takes the ball to hit the ground using:
h(t) =-8t² + 2t + 3

0.75 seconds

300

Determine how long it takes the ball to reach its max height using:

f(x)=-x²+7x+3

3.5 seconds

400

Determine how long it takes the ball to reach its max height using:

h(t) = -2t² + 8t + 5

2 seconds

500

Determine how long it takes the ball to hit the ground using:

h(t)=-16t²+64t+80

5 seconds

WEOL

100

WEOL that has a slope of 2/3 and goes through (3,9)

y=2/3x+7

200

WEOL that goes through (4,3) and (8,11)

y=2x-5

300

WEOL that is parallel to y=5/8x+6

y=5/8x+2 (answers will vary)

400

WEOL that is perpendicular to y=-4/3x-7 and goes through (16,1)

y=3/4x-11

500

WEOL that is perpendicular to y=4x-5 and goes through (15,13)

y=-1/4x+67/4