Quadratic functions
Cubic functions
Probability
Sequences
Linear and Absolute value functions
100

Find the vertex of the quadratic function:

y=x^2−4x+3y

(2,−1)

100

Evaluate the function when x=2

f(x)=x^3−2x^2+3

f(2)=3

100

A fair six-sided die is rolled once. What is the probability of rolling a 4?

P(4)=1/6

100

Find the next term in the sequence:

2, 5, 8, 11, …

+3 

Next term:14

100

Find the slope of the line:

y=3x+5

So the slope is:

3

200

Solve the quadratic equation:

x^2−5x+6=0 

x=2orx=3

200

Solve:

x^3−8=0

x=2

200

A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?

P(blue)=2/10=1/5

200

Find the 10th term of the arithmetic sequence:

4, 7, 10, 13, …

an=a1+(n−1)d

First term:

a1=4

Common difference:

d=3

Term number:

n=10

So the 10th term is:

31

200

Write the equation of the line with slope 2 and y-intercept −1

y=2x−1

300

Solve:

2x2+3x−2=0


x=1/2orx=−2  

300

Factor completely:

x^3−6x^2+11x−6 

(x−1)(x−2)(x−3)

300

A coin is flipped twice. What is the probability of getting two heads?

P(two heads)=1/2×1/2 =1/4=

300

Find the 6th term of the geometric sequence:

3, 6, 12, 24, …

an=a1r^n−1

First term:

a1=3

Common ratio:

r=2

So the 6th term is:

96

300

Find the slope of the line passing through:

(2,5)and(6,13)

So the slope is:

2

400

For the function

y=−x^2+6x−5

find:

  1. Vertex
  2. Axis of symmetry
  3. Maximum or minimum value

vertex=(3,4)

axis of symmetry=x=3

maximum=4

400

For the function

y=x^3−3x^2−9x+27

find:

  1. The x-intercepts
  2. The y-intercept

x-intercepts:(−3,0),(3,0) 

y-intercept:

(0,27)


400

A card is drawn from a standard deck of 52 cards. Given that the card is a face card, what is the probability that it is a king?

P(king | face card)=4/12 =1/3

400

Find the sum of the first 20 terms of the arithmetic sequence:

5, 8, 11, 14, …

Sn=n/2(a1+an)

the sum is:

670

400

For the function

y=−2x+4y

find:

  1. The slope
  2. The y-intercept
  3. The x-intercept

slope:m=−2 

y-intercept:(0,4)

x-intercept:

(2,0)

500

A ball is thrown upward from a height of 5 meters with an initial velocity of 20 m/s. Its height is modeled by

h(t)=−5t^2+20t+5 

  1. When does the ball reach maximum height?
  2. What is the maximum height?
  3. When does the ball hit the ground?

The ball reaches maximum height after:2 seconds

Maximum height:25 meters

Positive solution:t≈4.24 seconds 

500

The volume of a box is modeled by

V(x)=x(12−2x)(10−2x)

where x is the size of squares cut from each corner.

  1. Expand the cubic function.
  2. Find the volume when x=2.
  3. Determine the reasonable domain for x.

V(x)=4x3−44x2+120x 

Volume:

96 cubic units

domain:0<x<5

500

A box contains:

  • 4 red balls
  • 5 blue balls
  • 3 green balls

Two balls are drawn without replacement.

What is the probability that both balls are blue?

5/33

500

A sequence is defined recursively by:

a1=2

an=3an−1+1

Find:

  1. The first five terms
  2. The value of a6

First five terms:

2, 7, 22, 67, 202

Final answer:

a6=607

500

A taxi company charges a $4 starting fee plus $3 per mile traveled.

  1. Write a linear function for the total cost.
  2. Find the cost of traveling 10 miles.
  3. How many miles can someone travel for $40?

C(x)=3x+4 

Cost:

$34

So the person can travel:

12 miles

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