MATH HL

Statistics

100

Define Census, Sample and Survey

Census: The collection of information from the whole population

Sample: A subset of the population which should be chosen at random to avoid bias

Survey: The collection of information from a sample.

200

Draw a Negatively Skewed Graph

The data is stretched out across the left side.

300

Abe borrowed $16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1¹/₂ years?

$18522

400

1. What was the highest score on the test?

2. What percent of the class scored above a 72?

3. What was the median score on the test?

4. What percent of the class scored between 88 and 96?

1. 102

2. 75%

3. 88

4. 25%

500

Without using your calculator find the standard deviation for the following data set (Round to 3 sig fig)

2.4, 3.4, 3.6, 3.8, 3.8, 4.0, 4.9

0.691

Calculus

100

What is a Stationary Point.

A point where the derivative of f(x) is equal to 0

200

What is the derivative of F(x) = 6x³ - 5x² + 2x - 3

F^'(x) = 18x² - 10x + 2

300

Evaluate

lim_{x --> 1} = (7x² - 4x - 3) / (3x² - 4x + 1)

lim_{x --> 1} = 5

400

A curve has the equation y = x² - 4x + 21

Find dy/dx

Find the Minimum point's position

dy/dx = 2x - 4

When x = 2, a Minimum Point occurs at (2,17)

500

Consider f(x) = 2x + (2 / x)

a) Find F^'(x)

b) Draw a Sign Diagram for F^'(x)

c) Find the position and nature of any stationary points

d) use technology to help sketch the graph F(x)

a) F^'(x) = 2 - (2 / x²)

b) Check Diagram

c) Maximum Turning Point at (-1, -4), Minimum Turning Point at (1, 4)

d) Check Graph

Logarithms

100

What is the formula for a logarithm?

log_b(b^x) = x

200

What are all the rules of Exponents and Logs?

a^x * a^y = a^{x + y}

a^x / a^y = a^{x - y}

(a^x)ⁿ = a^{x * y}

a^-x = 1/a^x

x⁰ = 1

log_ax + log_ay = log_a(xy)

log_ax - log_ay = log_a(x/y)

log_axⁿ = nlog_ax

300

Solve 

log₄(v + 8) = log₄(-4v - 2)

-2

400

Expand

log₃(z((3sqrt)xy)

log₃z + (log₃x / 3) + (log₃y / 3)

500

Solve the Following

1.) log₉3x + log₉2 = 2

2.) log₃4 + log₃2x = log₃56

3.) 5^2p = 5^{3p + 1}

1.) 27/2

2.) 7

3.) -1

Unit Circle

100

Draw and Label a Unit Circle using Radians, and mark which quadrants each value (Cosine, Sine, Tangent) are positive in.

0/2pi, pi/2, pi, 3pi/2

All, Sine, Tangent, Cosine

200

Draw the Ratio Triangles for the Unit Circle

45,90,45   >    1, 1, sqrt2

60,60,30/30    >   2,2,1/1,sqrt3

300

Find all possible values for Sinx= 1/2

for 0 < x < 2pi

pi/6, 5pi/6, 7pi/6, 11pi/6

400

Without Using A Calculator Simplify the following

2tan(-5pi/4) - sin(3pi/2)

-1

500

Find the exact values for Sinx and Cosx given that

Tanx = -12/5 

3pi/2 < x < 2pi

Sinx = -12/13

Cosx = 5/13

Trigonometric Functions

100

What is the equation for finding the Period?

2pi/b

200

Find the Amplitude and Period of 

y = 5cos2x + 3

Period = pi

Amplitude = |5|

300

Sketch the graph for 0 < x < 4pi

y = 2sin(1/2)x + 5

Check Graph

400

Solve 2cos²x + cosx - 1 = 0

pi/3, pi, 5pi/3

500

(DOUBLE POINTS)

Hyun Joo is riding a ferris wheel. 

H(t) = −10cos((2pi/150)t) + 10 

models her height m above the ground, t seconds after the ride starts. Here, t is entered in radians.

a) Sketch the graph

b) When does Hyun Joo First reach a height of 16 meters?

c) At which times is Hyun Joo at 0 meters

 (When 0 < t < 225)

a) Check Graph

b) 52.862

c) 0, 150