A2 Review for final

Linear Systems

100

Solve the system using substitution: 

2m+4n=10

3m+5n=11

(-3,4)

200

Solve the system using elimination:

2r+s=3

4r-s=9

(2,-1)

300

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 3 vans and 9 buses with 270 students.  High School B rented and filled 9 vans and 11 buses with 410 students.  Every van had the same number of students in it as did the buses.  How many students can a van carry?  How many students can a bus carry?

Van: 15

Bus: 25

400

A plane traveled 980 miles each way to Berlin and back.  The trip there was with the wind.  It took 5 hours.  The trip back was into the wind.  The trip back took 7 hours.  Find the speed of the plane in still air and the speed of the wind.

plane: 168 mph, wind: 28 mph

500

[-x - 5y + z = 7]

[-4x - 5y + z = 4]

[-x + 5y + 3z = -17]

(1,-2,-2)

Quadratic Functions

100

Describe how the graph was translated from y=x²

y=2(x+7)² -8

Stretch by 2

Left 7

Down 8

200

Identify vertex, axis of symmetry, max/min and range. 

y=-x²+2x+1

Vertex: (1,2)

Axis of symmetry: at x=1

Minimum: 1

Range: y≤2

300

Write the function in vertex form:

f(x)=2x²-5x+12

f(x)=2(x-5/4)²+71/8

400

Factor the expression:

2x²-19x+24

(x-8)(2x-3)

500

Find all solutions 

x²-2x+2=0

1±i

Radical Functions

100

Simplify

-5sqrt(10m)x3sqrt(12m²)

-30msqrt(30m)

200

Simplify 

-sqrt(2)-sqrt(3)-2sqrt(3)

-2sqrt(2)-3sqrt(3)

300

Rationalize the denominator

sqrt(3xy²)/sqrt(5xy³)

sqrt(15y)/5y

400

FREE POINTS 

+20

500

Simplify

3^1/4x27^1/4

3

Exponential and Logarithmic Functions

100

Determine whether a function represents exponential growth or decay. Find the y-intercept.

y=0.8(1/8)^x

Decay and 0.8

200

A population of 120,000 grows 1.2% per year for 15 years

143,512

300

Condense

4logm-logn

log(m⁴/n)

400

Write each equation in logarithmic form 

625=5⁴

log (base 5) of 625=4

500

Solve

log(5)-log(2x)=1

1/4

Rational Functions

100

The number of buckets of paint n needed to paint a fence varies directly with the total area a of the fence and inversely with the amount of paint p in a bucket. It takes three 1-gallon buckets of paint to paint 72 square feet of fence. How many 1-gallon buckets will be needed to paint 90 square feet of fence???

4 buckets

200

Find the vertical asymptotes and holes for the graph 

y=(x+3)(x-2)/(x-2)(x+1)

VA at x=-1 and hole at x=2

300

Find the horizontal asymptote: 

y=5x³+2x/2x⁵-4x³

at y=0

400

Multiply and state restricted values

2x+12/3x-9 x 6-2x//3x+8

-4(x+6)/3(3x+8)

x cannot equal 3 or -8/3

500

Solve

2/y + 1/2 =5/2y

1