Final Review

Statistics

100

A sample is collected by picking names from a hat. What sampling strategy is this?

simple random sampling

200

Explain how to find the IQR from a cumulative frequency table. (You can sketch a pic if it helps.)

Q3: Find 3/4 of the total, then find corresponding x-value

Q1: Find 1/4 of the total, then find corresponding x-value

Subtract Q3 – Q1

300

A data set has a variance of 32. All values are multiplied by 6. What is the new variance of the data set?

1152

400

The number of students in 5 different classes are: 23, 25, 31, 32, 38. What is the smallest number of students that would not be considered an outlier?

8

500

Calculate the mean of the frequency table by hand.

x freq

3   12

5   7

7   6

9   10

5.8

Functions

100

Find the inverse of the function f(x) = 4x³ – 11

cube root((x+11)/4)

200

f(x) = x – 3

g(x) = x² – 7

Find g(f(x)).

g(f(x)) = x² – 6x + 2

300

State the domain and range of the function y = –x² + 8.

D: (–inf, inf)

R: (-inf, 8]

400

The height (in meters) of a projectile is modeled by the function H(t) = –t² + 80t + 5, where t is time in seconds. How long does it take for the projectile to reach a height of 1000 meters?

(Hint: Solve by graphing.)

15.4 seconds

500

The function y = g(x) contains the point (4,3). Find the corresponding point on the function y = 4g(2x) – 7.

(2, 5)

Logs

100

Evaluate: log₄(8) + log₄(2)

2

200

Simplify completely: log₂(4^x/8^y)

2x – 3y

300

Solve for x:

3ln(x) = 1 – ln(4)

0.879

400

Sketch a graph of y = log₂(x + 3). Label the asymptote and at least one point.

Asymptote at x = –3.

Points at (-2, 0), (-1, 1), (1, 2), etc.

500

Solve for x.

3(7)^1.5x – 2 = 8

0.412

Calculus

100

f(x) = 6x⁴ – 5x³ + 12x² – 8x + 6

Find f'(x).

f'(x) = 24x³ – 15x² + 24x – 8

200

f(x) = 5/x⁴ + 2e^x

Find f'(x).

f'(x) = –20x^–5 + 2e^x

300

Find the tangent line to the graph of y = 10x – 3x² + 1 at x = 3.

y = –8x + 28

400

NO CALC. Find the coordinates of the maximum of the function y = –x² + 8x + 2.

(4, 18)

500

At what x-values does the function y = 1/3x³ – 3x² – 7x + 5 have horizontal tangent lines?

x = –1 and x = 7

Grab Bag

100

Find the sum to infinity of the sequence 200, 160, 128, ...

1000

200

Write down the horizontal and vertical asymptotes of the function y = (4x – 5)/(2x + 6).

HA: y = 2

VA: x = –3

300

For what values of p does the equation px² – 6x + 1 = 0 have no real roots?

p > 9

400

Rewrite the equation y = 2x² + 8x – 5 in the form y = a(x – h)² + k.

y = 2(x + 2)² – 13

500

Find the area of a triangle with side lengths 6, 7, and 11.

19.0