End of Year Math

Factoring

100

Factor: (X²-9)

(X-3)(X+3)   or    (X+3)(X-3)

200

Factor: 15x²+14x-8

(5x-2)(3x+4)

300

Factor:(x³+64)

(x+4)(x²-4x+16)

400

Factor: 24x²y+34xy+12y

2y(3x+2y)(4x+3)

500

Factor the Polynomial in Quadratic Form:

x⁴+x²-2

(x²+2)(x-1)(x+1)

Trigonometry

100

What is the ratio for Sin, Cos, and Tan?

Sin: Opposite/Hypotenuse

Cos: Adjacent/Hypotenuse 

Tan: Opposite/Adjacent

200

What are the ratios for csc,sec, and cot?

csc: Hypotenuse/Opposite

sec: Hypotenuse/Adjacent

cot: Adjacent/Opposite

300

Find the area of the triangle:

(round to the nearest tenth)

B=72(degrees)

a=105

c=64

Area= 3195.6

400

Find the area of the triangle having sides of lengths 

a=29.7ft, b=42.3ft, and c=38.4ft

(round to the nearest hundredth)

Area=552.32ft²

500

Determine whether the given information results in one, two or no triangles.

a=3

b=2

A=50(degrees)

One oblique triangle

Arithmetic/Geometric

100

Is this sequence Arithmetic or Geometric?

58,65,72,79,86,93

Arithmetic

200

Find the sixtieth term of sequence which has

a₁=-12

d=-2.7

a₆₀=-171.3

300

Find the sixty-third term of 7,10,13...

a₆₃=193

400

Write an explicit rule for the n^th term. Then find a₇.

a₁=10;r=1/2

Rule: a₇=10(1/2)^7-1

a₇=5/32

500

Write an explicit rule for the n^th term of the geometric sequence.

a₄=12, r=2

a_n=3\2(2)^n-1

Compositions

100

Solve. f(g(2))

f(x)=x+3

g(x)=4x

f(g(2))=11

200

Solve. f(m(11))

f(x)=1/3x+2

m(x)=3x-6

f(m(11))=11

300

Solve: f(g(x))

f(x)=2x+3

g(x)=-x²+5

f(g(x))=-2x²+13

400

Solve: g(f(x))

g(x)=-x²+5

f(x)=2x+3

g(f(x))=-4x²-12x-4

500

Solve: f(g(x))

f(x)=3x+5

g(x)=4x+6

f(g(x))=12x+23

Misc.

100

Is the following sequence Arithmetic or Geometric?

2,16,128,1024,8192

Geometric

200

What are the solutions for the following equation?(x-3)(x+5)(x-9)

x=3

x=-5

x=9

300

What does pi/6 equal in degrees?

30 degrees

400

Factor:

12x²-13x+3

(1/3,3/4)

500

Solve:

x/x+3=8/x+6

x=4

x=-6