1

2 4

2

b b acx

a

2

RADICALS Simplifying

1. Make a big radical & break the number into its prime factors 2. If variables, list them out 3. Look at the index to see what type of groups you're making 4. Pull out the groups & leave the leftovers under the radical

Adding & Subtracting

1. Simplify everything 2. Add/subtract the coefficients of the radicals with the same radicand

Multiplying & Dividing

1. Multiply/divide # by # & radical by radical 2. Simplify all radicals - reduce only the "whole" numbers 3. FOIL if there's an +/- sign

Rationalizing the Denominator (aka Get the Radical Out of the Denominator) 1. Multiply by a fancy one (denominator or conjugate) 2. Simplify radicals in numerator & find perfect square of the denominator then combine 3. Reduce only "whole" numbers at the end

Solving Radical Equations

1. Isolate the radical 2. Square both sides (may have to FOIL) 3. Solve for the variable 4. Check answers in the ORIGINAL problem – this is MANDATORY!

Examples

1. The expression 2 6

3 6

is equivalent to

(1) 6

3 (3) 2

(2) 6

3

(4) 2

2. What is the solution set of the equation 9 10 0x x ?

(1) {-1} (3) {10} (2) {9} (4) {10, -1}

3. Multiply: (2 3)(6 3) 4. Simplify: 8 643 324 p r

YOU CAN DO

THIS!!!

3

IMAGINARY & COMPLEX NUMBERS Simplifying Negatives Under the Radical

1. Pull out your "i" 2. Simplify the radical

Simplifying "i"s 1. Divide the exponent by 4 2. Look at the decimal 3. Remember your "cheer"

i -1 -i 1 .25 .5 .75 NO

**CAN ALSO USE iPart** Adding/Subtracting Imaginary Radicals

1. Pull out your "i" 2. Simplify & add/subtract the coefficients

Adding/Subtracting Imaginary #'s 1. Simplify all terms 2. Combine like terms

Multiplying Imaginary Radicals 1. Pull out your "i" 2. Multiply #'s and radicals 3. Simplify at the end

Multiplying Imaginary #'s 1. Multiply the coefficients 2, Add the exponents 3. Simplify the "i"

Dividing Imaginary Radicals

1. Pull out your "i" 2. Divide the #'s & radicals 3. Simplify at the end

Dividing Imaginary #'s 1. Divide the coefficients 2. Subtract the exponents 3. Simplify the "i"

Complex Numbers - When graphing: (3 + 2i) = (3, 2) Add/Subtract 1. Combine like terms 2. If graphing, make a vector

Complex Numbers - Multiplying 1. FOIL or use the calculator!! (a + bi mode)

**remember: i2 = -1**

Complex Numbers - Dividing 1. Multiply by a "fancy one" - conjugate 2. Simplify the numerator & denominator

Multiplicative Inverse 1. 1 over the given number 2. Multiply by a "fancy one" 3. Simplify the numerator & denominator

Examples 1. When expressed as a monomial in terms

of i, 2 32 5 8 is equivalent to

(1) 2 2i (3) 2 2i

(2) 2 2i (4) 18 2i

2. In a + bi form, the expression 1

7 4iis

equivalent to

(1) 7 4

65 65

i (3)

7 4

65 65

i

(2) 7 4

33 33

i (4)

7 4

33 33

i

4

3. What is the product of (2 – 5i) and its conjugate in simplest a + bi form?

4. The expression i3 + i(2 – i) is equivalent to (1) -1 + 3i (3) 1 – i (2) 1 + i (4) 1 + 3i

QUADRATICS

5

Examples: 1. The product of the roots for the quadratic equation 2x2 – 5x + 9 = 0 is

(1) 9

2 (3)

5

2

(2) 9 (4) 5

2. What is the nature of the roots of the quadratic whose equation is x2 = -18x + 81? (1) imaginary (2) real, irrational, and unequal (3) real, rational, and unequal (4) real, rational, and equal

3. What is the quadratic equation whose roots are (2 – 4i) and (2 + 4i)?

4. Solve for x using the quadratic formula and leave your answer in simplest radical form.

x2 = -2x + 4

5. Solve x2 – 6x + 1 = 0 by completing the square. Express the result in simplest radical form.

6. What is the center and radius of the following circle?

x2 + y2 + 8x – 6y + 4 = 0

6

EQUATIONS & INEQUALITIES Solving Quadratic Inequalities - Algebraically

Set it equal to 0 and factor Put it on a number line – check “0” to

see which way to shade!

Solving Quadratic Inequalities - Graphically

If the inequality has a < or > symbol, you will need a dotted line to show that the points on those lines are not included in the solution set

If the inequality has a < or > symbol, you will need a solid line to show that the points on the line are included in the solution set.

You need to use a test point – usually (0, 0) if one is not given – to determine which way you are to shade (inside the parabola or outside the parabola)

Absolute Value Equations Isolate the absolute value Drop the absolute value and create 2

equations – one that’s set equal to the positive value, one that’s set equal to the negative value

Check all answers in your original equation

Absolute Value Equations When solving absolute value

inequalities, treat it just like an equation - the only difference is that the solution is not only one number, but a series of numbers

The solution will get graphed on a number line

Use test points to see which way you can shade – write the solution in notation form too!

Linear/Quadratic Systems

A linear equation will have variables with no exponents

A quadratic equation will have variables with squared exponents

The only way to solve a linear/quadratic system is substitution.

Linear/Circle Systems The linear equation will be the equation

without the exponents The equation of the circle will be the

equation with x2 and y2 The only way to solve a linear/circle

system is by substitution

7

Examples: 1. What is the solution of the inequality x2 – x – 6 < 0? (1) 3 2x x (3) 1 6x x

(2) 2 3x x (4) 3 2x x

2. What is the solution set of the equation 2 3 9x x ?

(1) {12} (3) {2, 12} (2) {2} (4) { }

3. Solve the absolute value inequality, graph the solution set, and write the solution set.

2 3 5x

4. Solve the following system of equation algebraically and leave your answer in simplest radical form.

2x2 + x + 1 = y y = x + 7

8

RATIONAL EXPRESSIONS Undefined

To see when a fraction is undefined we set the denominator equal to 0

Remember to factor if you are given a squared term!

Simplifying Make sure that you factor first, then

reduce!!

Multiplying & Dividing Rational Expressions

Make sure that you factor first, and then reduce!!

When you divide, keep the first fraction, change the division sign to multiplication, & flip the second fraction. Then keep going as if you were multiplying!

Adding & Subtracting Rational Expressions When adding & subtracting fractions, you

need a common denominator Here’s what we always need to ask

ourselves: CAN WE FACTOR THE DENOMINATOR?

Complex Fractions Remember that fractions are really a

big division problem Rewrite the problem as a division

problem before factoring and reducing!

Rational Equations Either cross multiply or get a common

denominator then ignore the denominator, and solve the numerator!

Remember to check your answer in the original problem!

Rational Inequalities Write the inequality as an equation and

solve. Determine any values that make the

denominator equal 0 (undefined). Make each of the critical values from

steps 1 and 2 on a number line. Select a test point in each interval –

check to see if the chosen test points satisfy the inequality.

Mark the number line to reflect the values and intervals that work.

Write your answer in set notation.

Multiply the denominators

Factor the denominators & take

your bits & pieces

Try to remain calm…we’ll get

through this together!

9

Examples: 1. If the length of a rectangular garden is

represented by 2

2

2

2 15

x x

x x

and its width is

represented by2 6

2 4

x

x

, which expression

represents the area of the garden?

(1) x (3) 2 2

2( 5)

x x

x

(2) x + 5 (4) 5

x

x

2. For which value of m is the expression 15

3

2m n

m undefined?

(1) 1 (3) 3 (2) 0 (4) -3

3. What is the value of x in the equation

?262

xx

(1) 12 (3) 3

(2) 8 (4) 4

1

4. Simplify and leave your answer in simplest form.

2

2

6 16

64

x x

x

5. Simplify the following complex fraction.

2 2

1 1

1 1x y

x y

6. Divide and leave your answer in simplest form.

2

2

6 9 3 9

9 3

y y y

y y

10

RELATIONS & FUNCTIONS Topic Good Things To Know

Relations & Functions

Functions _____ value cannot repeat ____________

line test

One to One Function _____ and _____ cannot repeat

must pass _______________ and ______________ line test

Onto Function all values of the _____________ are used

Domain &

Range

Domain ____ values

Fractions denominators ______

Radical cannot be ___________ > 0

Fraction with Radical in Denominator denominator

must be > ____

Range _____ values

Graph to see what values are in the range

Transformations

Moving UP or DOWN

UP _______________

DOWN _____________

Moving LEFT or RIGHT

LEFT _______________

RIGHT _______________

Reflecting in X-AXIS or Y-AXIS

X-AXIS ______________

Y-AXIS ______________

Function Notation &

Compositions of

Functions

f(x), g(x), h(x), etc – another way to write “y = “

Whatever value is inside the parentheses will replace the

x in the given function

Inverse Functions

When given points, _________________________________

When given an equation, switch ______ and ______, then

solve for ________

To justify a composition f(f-1(x)) = f-1(f(x)) = x

Direct & Inverse Variation

DIRECT VARIATION set up a ______________________

INVERSE VARIATION set up _______________________

11

Examples: 1. The function g(x) is defined as g(x) = 5 – 6x with the domain -4 < x < 2. What is the least element in the range? (1) 29 (3) -7 (2) 5 (4) -4

2. What is the domain of ( ) 5f x x ? (1) , 5x (3) , 5x

(2) , 0x (4) , 5x

3. Which of the following relations would not be considered a function? (1) f(x) = {(-4, 2), (1, 0), (9, 7)} (2) g(x) = {(4, -2), (-4, 0), (-9, -7)} (3) h(x) = {(2, -4), (2, 1), (7, 2)} (4) j(x) = {(-2, 4), (0, -1), (-7, -9)}

4. Which equation defines a relation that is not a function? (1) y = 3 – 2x (3) y = x2 + 4x + 6 (2) x2+ y2 = 16 (4) y = -5

5. If f(x) = 3x – 4, and g(x) = x2 – 4x, what is the value of g(f(x))?

6. What is the inverse of the function f(x) = 5 – 2x?

7. The frequency of a radio wave is varied inversely to the wave length. If the wave of 300 meters has a frequency of 1,500 kilocycles per second, what is the length, in meters of a wave with a frequency of 1,000 kilocycles per second?

8. If y = f(x) is shifted five units right and reflected over the x-axis, which of the following equations would represent that transformation? (1) y = -f(x) + 5 (3) y = -f(x) – 5 (2) y = -f(x + 5) (4) y = -f(x – 5)

12

CIRCLES Center-Radius Form Centered at the Origin Centered at (h, k) x2 + y2 = r2 (x – h)2 + (y – k)2 = r2

Standard Form x2 + y2 + ax + by + c = 0 complete the square to get from standard form into center-radius form Examples: 1. Determine the center and radius of the circle whose equation is:

x2 + y2 – 2x – 8y + 1= 0

2. What is the equation of the circle below that passes through the point (0, -1)?

13

EXPONENTS

Name of Law Explanation of Law Example

Multiplication Law

Add the exponents

5 9 453 5 15x x x

Division Law

Subtract the exponents

84

4

84

2

xx

x

Power Law

Multiply the exponents

46 242 16x x

Negative

Exponent Law

To make the negative exponent positive, move it from the numerator to

the denominator (or vice versa)

5 2 22 7

3 9 7

10 55

2

x y xx y

x y y

Power of Zero

Law

Anything to the 0 power equals 1

80

81

xx

x

Fractional Exponent

Law

The denominator becomes the index!

37 37x x

25 2 5x x

Steps to Solve Equations with Fractional & Negative Exponents

1. Isolate the variable with the exponent 2. To solve for the variable, raise both sides of the equation to the reciprocal power.

In order to solve an exponential equation, you must have the same base If the bases are the same, we set the exponents equal to each other and solve for the

variable. If the bases are not the same, force them to be the same usually look for bases of 2, 3,

5, or 7

Growth/Decay

y = abx

Compounding Interest

1nt

rA P

n

Continuous Growth/Decay

rtA Pe

14

Examples:

1. Which of the following is equivalent to1

81x ?

(1) 3-4x (3) 3-4 (2) 34 (4) 34x

2. The expression 22 4

3 5

2

2

a b

a b is equivalent to

(1) ab3 (3) 2a

b

(2) 32b

a (4) 2ab13

3. What is the value of x in the

equation 2 116

8

xx

?

(1) 1 (3) 7

8

(2) -2 (4) 8

7

4. Given the equation y = abx, if the equation models exponential growth, the value of b must be greater than

(1) 1 (3) 0 (2) -1 (4) 2

5. Solve for x:

3

227 4 68x

6. Andrew received a $3,200 bonus at work. He invested his money in a savings account that was making 4.5% interest that was compounded monthly. Using the equaition

1nt

rA P

n

, where A is the value of the

investment after t years, P is the principal invested, r is the interest rate, and n is the number of times per year it was compounded, determine, to the nearest cent, how much money Andrew would have after 6 years.

15

“Circle the base to finish the race” “Log = Exponent”

LOGARITHMS Log Rules

Exponential Rule Log Rule Example

Product

(xm)(xn) = xm + n

Log mn = Log m + Log n

Log 5(4) = Log 5 + Log 4

Quotient

mm n

n

xx

x

Log m

n = Log m – Log n Log

5

2 = Log 5 – Log 2

Power

(xm)n = xmn

Log mn = n Log m

Log x2 = 2 Log x

Logs to Exponentials and Exponentials to Logs

ba = c log b c = a

Common Logs * Base of 10 * Log x = Log 10 x * Use 10x to solve

Natural Logs * Base of e * Ln x = Ln e x *Use ex to solve

Change of Base Formula log

loglogx

yy

x

Good Logs to Know Log 1 = 0 Ln e = 1 Log 10 = 1 Ln 1 = 0 Log 100 = 2

16

Examples:

1. The expression 1

log 3log3

a b is equivalent

to

(1) 3

3log

a

b (3) 33log a b

(2) 3

log3

a

b (4) 3

log3

a

b

2. If log 3 = x and log 5 = y, which of the following could represent log 45? (1) 2x + y (3) x2 + y (2) 2xy (4) x2y

3. The expression 2 3

logx y

zis equivalent to

(1) (2 log x + 3 log y) + 1

2log z

(2) (2 log x + 3 log y) - 1

2log z

(3) (log 2x + log 3y) – log 1

2z

(4) 2 312

x y

z

4. Solve for x: log (x – 1) + log (2x – 3) = 1

5. Mouthwash manufacturers are constantly testing various chemicals on bacteria that thrive on human saliva. The death of the bacteria exposed to Antigen 223 can be represented by the function P(t) = 2,000e-0.37t where P(t) represents the number of bacteria from a population of 2,000 surviving after t minutes.

a) Determine the number of bacteria surviving 3 minutes after exposure to Antigen 223.

b) Using logarithm, determine the number of minutes, to the nearest tenth of a minute, necessary to kill 1500 bacteria.

17

TRIG. FUNCTIONS 3 Basic Trig. Functions

Always remember SOH CAH TOA to determine the 3 basic trig. functions

sin __________ cos __________ tan __________

Good Things to Know With the Coordinate Axes P(x, y) P( , ) x =_____________ y = _____________ tan = __________ = __________

x

y

Co-Terminal Angles Add ______ if original angle

was negative Subtract ______ if original

angle was positive

Quadrantal Angles Angles that lie on the

quadrants 00, 900, 1800, 2700, 3600

*00 300 450 600 *900 *1800 *2700

sin

cos

tan

Reciprocal Functions csc = _________ = _________ sec = _________ = _________ cot = _________ = _________

ARC LENGTH

DEGREES RADIANS Multiply by

RADIANS DEGREES Substitute _____ in

for_____

If there’s no ____,

multiply by _____

Cofunctions Cofunctions are equivalent

if the angles are complementary

sin _______ tan _______ sec _______

18

Examples: 1. A circle has a radius of 4 inches. In inches, what is the length of the arc intercepted by a central angle of 2 radians?

(1) 2 (3) 8 (2) 2 (4) 8

2. The expression csc

sec

is equivalent to

(1) sin (3) sin

cos

(2) cos (4) cos

sin

3. What is the number of degrees in an angle

whose radian measure is 11

12

?

(1) 1500 (3) 3300 (2) 1650 (4) 5180

4. The coordinates of a point on the unit circle

are3 1

,2 2

. If the terminal side of an

angle in standard position passes through the given point, what is the measure of ? (1) 2400 (3) 2250 (2) 2330 (4) 2100

5. What is 2350 expressed in radian measure?

(1) 235 (3) 47

36

(2) 235

(4)

36

47

6. Find the exact value of (sin 2250)(cos 3000).

TRIG. GRAPHS

Each value of a trig. function represents something important to graphing:

y = a sin bx + d

“a” – the amplitude tells us how far above and below the midline the graph will reach – a negative “a” value will reflect the graph over the x-axis

“b” – the frequency tells us how many curves we will see between 0 and 2 - the period 2

b

is based off of the frequency and tells us how it will take before we see one full

trig. curve “d” – the midline tells us the line of horizontal symmetry – this line cuts the graph in half

horizontally – this will move the entire trig. graph up (positive midline value) or down (negative midline value)

amplitude frequency

midline

19

2

-3

3

Examples: 1. What is the amplitude of the graph whose equation is y = -2 sin 4x? (1) (2) 2 (3) -2 (4) 4

2. If the period of a cosine curve is , what is the frequency?

(1) 2 (3) 2

(2) 2 (4) 1

2

3. Which is an equation of the graph shown below?

(1) 1

3cos2

y x (3) y = -3 sin 2x

(2) y = 3 sin 2x (4) y = 3 cos 2x

4. What is the minimum value of the range of y = 3 + 2 sin x? (1) 1 (2) 0 (3) -1 (4) -5

5. As increases from 2

to

3

2

, the value of

sin will (1) increase only (3) increase then decrease (2) decrease only (4) decrease then increase

6. What is the frequency of the graph of the

equation 1

2cos 72

y x ?

(1) 2 (3) -2

(2) 1

2 (4) 2

20

TRIG. IDENTITIES These Identities You NEED To Memorize

Reciprocals Quotients Pythagorean

These Identities Are On The Reference Sheet

SUM AND DIFFERENCE IDENTITIES Identities of the SUM of 2 Angles Identities of the DIFFERENCE of 2 Angles

1. sin (A + B) = sin A cos B + cos A sin B

2. cos (A + B) = cos A cos B – sin A sin B

3. tan tantan

1 tan tan

A BA B

A B

1. sin (A – B) = sin A cos B – cos A sin B

2. cos (A – B) = cos A cos B + sin A sin B

3. tan tantan

1 tan tan

A BA B

A B

DOUBLE ANGLE IDENTITIES Sin 2A Cos 2A Tan 2A

1. sin 2A = 2 sin A cos A 1. cos 2A = cos2A – sin2A 2. cos 2A = 2 cos2A – 1 3. cos 2A = 1 – 2sin2A

1. 2

2 tantan 2

1 tan

AA

A

HALF ANGLE IDENTITIES

1 1 cossin

2 2

AA

1 1 coscos

2 2

AA

1 1 costan

2 1 cos

AA

A

21

Examples:

1. If 12

sin13

x , 3

cos5

y , and x and y are acute

angles, the value of cos(x + y) is

(1) 21

65 (2)

63

65 (3)

14

65 (4)

33

65

2. The expression csc

cot

is equivalent to

(1) sin (2) cos (3) sec (4) tan

3. If 7

sin25

x and x is in quadrant IV, then

cos 2x equals

(1) 48

25 (2)

527

625 (3)

14

25 (4)

134

625

4. If 5

cos3

A and angle A is in quadrant I,

what is the value of cos2A?

5. Prove:

2 2 2csc 1 sin cot 6. Cos 700 cos 400 – sin 700 sin 400 is equivalent to (1) cos 300 (3) cos 1100 (2) cos 700 (4) sin 700

7. The expression 2

sin 2

sin

is equivalent to

(1) 2

sin (3) 2 cot

(2) 2 cos (4) 2 tan

8. If 8

cos17

A and 2700 < A < 3600, what is the

value of tan 2A?

22

23

Examples: 1. What value of x in the interval 900 < x < 1800 satisfies the equation 2sin sin 0x x ? (1) 900 (2) 1200 (3) 1350 (4) 1800

2. Which of the following is not a solution to the equation 2 cos x – 1 = sec x? (1) 00 (2) 1200 (3) 1800 (4) 2400

3. Solve for the exact value of x in the interval 00 < x < 3600.

4csc 5 3csc 4x x

4. Solve the equation below for all values of x in the interval 00 < x < 3600. Round your answer to the nearest degree.

22sin 5cos 4x x

5. Solve for the exact value of x in the interval 00 < x < 2 .

22cos cosx x

6. Solve for the exact value of x in the interval 00 < x < 3600. Round to the nearest tenth of a degree.

25cos 3

cosx

x

24

25

Examples: 1. You must cut a triangle out of a sheet of paper. The only requirements you must follow are that one of the angles must be 60º, the side opposite the 60º angle must be 40 centimeters, and one of the other sides must be 15 centimeters. How many different triangles can you make? (1) 1 (3) 3 (2) 2 (4) 0

2. A garden is in the shape of an equilateral triangle and has sides whose lengths of 10 meters. What is the area of the garden? (1) 25m2 (3) 43m2 (2) 50m2 (4) 87m2

3. In ABC , if AC = 12, BC = 11 and mA = 300, then ABC could be (1) an obtuse triangle only (2) an acute triangle only (3) a right triangle only (4) either an obtuse triangle or an acute triangle

4. While sailing a boat offshore, Donna sees a lighthouse and calculates that the angle of elevation to the top of the lighthouse is 30. When she sails her boat 700 feet closer to the lighthouse, she fins that the angle of elevation is now 50. How tall, to the nearest tenth of a foot, is the lighthouse?

26

SERIES & SEQUENCES Arithmetic Sequences

To Find the Nth Term *To Find the Sum of N Terms Geometric Sequences

To Find the Nth Term *To Find the Sum of N Terms Examples:

1. The value of the expression 2

2

0

2 2n

n

n

(1) 12 (2) 22 (3) 24 (4) 26

2. Which expression represents the sum of the sequence 3, 5, 7, 9, 11?

(1) 5

1

2 1n

n

(3) 5

1

3 1n

n

(2) 5

1

3n

n (4)

5

1

1n

n

3. What is the fifteenth term of the sequence 5, -10, 20, -40, 80…? (1) -163,840 (3) -81,920 (2) 81,920 (4) 327,680

4. Find the first four terms of the recursive sequence defined below.

a1= -4 an = 2an-1 – 2n

27

ONE VARIABLE STATISTICS **REMEMBER THAT EACH PART OF THE NORMAL CURVE REPRESENTS .5 STANDARD DEVIATIONS FROM THE MEAN**

Measures of Central Tendency

Mean average - x Median middle number – numbers

must be in order Mode number that appears most

often

Measures of Dispersion Range biggest # - smallest # Interquartile Range Q3 – Q1 Variance (standard deviation)2 Standard Deviation variance

28

Examples: 1. A new survey is designed to collect data based on the number of miles people drive each month. Which of the following groups would create the least bias in conducting the survey? (1) All students who attend the local high school (2) People at a senior citizens center (3) People entering the mall (4) People riding the subway

2. The Write-O Pen company manufactures pens that have a mean life time of 200 pages with a standard deviation of 12 pages. Approximately what percentage of the pens last between 182 and 212 pages?

3. In a normal distribution, 2 50x and 2 10x when x is the mean and is the

standard deviation. What is the mean?

4. On a standardized test with normal distribution, the mean is 85 and the standard deviation is 6. If 1400 students took the test, approximately how many students would be expected to score between 79 and 97?

29

PROBABILITY PERMUTATIONS COMBINATIONS

Order matters Key words arrangement/arrange,

filling specific roles (president, vp, secretary or 1st, 2nd, 3rd place), ordering/order, license plates, telephone numbers, or making “words”

Open up spots to fill, then multiply

Repeated “letters”

total number !

repeated letters !

Order does not matter Key words committees, chose,

chosen, groups, team, gather, or assemble/assembly

Make a have/want chart

30

Bernoulli Trials “Exactly” Probability

(haveCwant)(swant)(fhave-want)

“AT MOST” PROBABILITY “AT LEAST” PROBABILITY consider all the probabilities equal to

or less than the given probability

(ex.) Mrs. Pace had a class of 10 students. She was to choose AT MOST 7 students to attend a trip. How many students could she have sent? 7, 6, 5, 4, 3, 2, 1, or 0

consider all the probabilities equal to

or more than the given probability

(ex.) Mrs. Pace had a class of 10 students. She was to choose AT LEAST 7 students to attend a trip. How many students could she have sent? 7, 8, 9, or 10

Binomial Expansion

Used like FOIL, but with exponents greater than 2 (x + 4)6 On the reference sheet:

Examples: 1. A family with 6 children is selected at random for a study. What is the probability that the family will have at most 2 girls?

2. What is the third term in the expansion of (x – 2)7?

3. In one state, a license plate consists of three letters followed by two digits. If no letter or digit can be repeated, how many different license plates are possible?

4. In a group of 8 students, three are female and five are male. What is the probability that two females and one male will be chosen to work on a subcommittee?

Probability of success Probability of failure (1 – prob. of success)

31

TWO VARIABLE STATISTICS Regressions

Correlation coefficient (r) how close to the “line” of best fit will the data lie – closest to +1 or -1 is the “best” fit line

Linear regressions (LinReg), exponential regressions (ExpReg), logarithmic regressions (LnReg), power regressions (PwrReg), cubic regressions (CubicReg) and quadratic regressions (QuadReg) Linear Logarithmic Exponential

y = ax + b y = a + blnx y =abx

Power Cubic Quadratic y = axb y = ax3 + bx2 + cx + d y = ax2 + bx + c Example: The accompanying table shows the enrollment of a preschool from 1980 through 2000.

a) Write a linear regression equation to model this data.

b) How many students did they have in 1998?

c) In what year did enrollment reach 50 students?

BRING ON THE REGENTS

EXAM… GO ON…BRING IT!