Maths B Notes - Term 4

8/8/2019 Maths B Notes - Term 4

1/5

Maths Study Sheet Term 4

Q1 - Trapezoid and Rectangle Area by

Approximation

Ex. 7A (pp217); Plus worksheet. (ONLY ONE

QUESTION ON THIS ON THE TEST WOO)

Rules:

Rectangle: LxW

Trapezoid:

x h (a+b) Just need to know this one

Triangle:

x b x h

Step 1: Sketch the graph. If number of trapeziums

to use is not specified, four or five is a good

number to use. Six if youre feeling energetic on

an M&P question.

Step 2: Work out the area of each trapezoid, then

total the area. The totalling can be done by the

FML rule, where:

A = (First + 2(Middle) + Last)Here is a worked example from the book:

Remember that the more

trapezoids you use, the

more accurate it will be. It

is also best to learn the

trapezoid rule because it

works for rectangles too.

Whats going to be on the Test:

K&P E & D Standard

1. Integration Using calculatorand trapezoid rule.

2. Normal distribution Using thecalculator, finding x values.

3. Normal distribution finding Zscores.

D & C Standard

4. PDF: Graph, area, comment.Eg. Is a PDF because it is equal

to 1

5. Cumulative Standard Normtable: Given Z, find probability

scores.

6. Cumulative Standard Normtable: Given probability, find Zscore.

C & B Standard

7. PDF: Finding unknowns, simplefunction.

8. Area between two curves.(Speed, Velocity and

Displacement)

9. Normal approximation toBinomial. (Use three tests)

B & A Standard

10.Harder cumulative standardnorm table findingprobabilities and Z scores.

11.Application of normaldistribution.

12.Application of normaldistribution.

13.PDF: Finding unknowns,reciprocal functions.

MAPS

14. Integration substitution.(Finding the + c, maybe?)

15.Normal distribution usingtables.

16.Application of normal dist,complex.

Test is on

Wednesday

8.35 10.35

Q8. This will be a Speed Velocity Displacement question,

so make sure you know their relationships :D


2/5

Q7 Example for PDF Functions.

Working backwards to find k:

Step 1: Write down the formula given in

integration form, making it equal to 1.

(Because its a PDF)

Step 2: Integrate; replacing the xs with the

domain numbers, and solve to find k.

Q8; Integration between Curves:

Ex. 8D (We have already done this; but just

if you want to practice one or two)

Step 1: Find points of intersection

(Algebraically or using calc. See calc

tutorial on last page for how to do this)

Step 2: Integrate both functions betweenthe intersections;

Step 3: Minus the top function from the

bottom.

See example below:

Note that a graph is drawn with X-

intercepts labelled, and the area shaded.

To find the X-intercepts manually, make

each function equal each other, solving for

X. Dont forget that area below the X-axis

is negative.(Possibly Q14?) M&P Example of Integrating

between curves:

WE 13 from 8DThese mother functions have the two curves

crossing over one another, so that half is

above the lower, and half the lower is above

the higher. This means that youll have to

work each area out separately and add them

together. WOOT

Q4, 7, 13, 17. PDF Functions.

This is just what weve been doing with integration

between two points. It becomes a PDF when the area

is equal to one.

Step 1: Graph the function given and shade the area

wanted. Make a table of the domain.

Step 2: Integrate between the domain, and write a

sentence to say whether it is a PDF or not.

This example would be for Q4. Note there are onlypractices for this in the worksheet 1, nothing in the

textbookie. .


3/5

Hard PDF Questions 13 and 17.

Q13 is a Reciprocal PDF function, meaning that youll need to know how to integrate different sorts of

fractions. Im betting that Q17 will also be a trigonometry PDF featuring sine or cos. So here are

integration examples of how to tackle them, and you just have to use these techniques in conjunction with

integration between two points. So, if the x is on the denominator and is to the power of something, you

can just re-arrange the function and bring it to a negative exponent. If it doesnt on the other hand, this

doesnt work and you end up bringing it to the power of zero which doesnt work. SO WE MUST TURN TO

LOGS... See textbookie examples below. Page 226 if youre interested.

STUDY TIP: Dont get distracted by your CUTE

WIDDLE PUPPY WUPPY thats underneath your

desk. I mean, I wouldnt get distracted.

Q2, 3, 5, 6, 9, 10, 11, 12, 15,16.

Cumulative Standard Norm Table (Over half the exam!)

Q2: See calc tutorials on last page;

Q3: Finding Z scores:

Just use this rule Easy Peasy.

Z =

Q5: This could be any of the simple distributions. You

really need to master the set of techniques like taking it

from one, flipping it making it negative if you need to.

Ill put a few examples down of some of the basics, but

Id recommend that if youre not completely satisfied

with your skills in this are you go through a few of them

in the textbook, Chapter 10.

Q6: Working backwards to find the Z score


4/5

Rules that you need to remember:

X~N( 2)

Z =

1.n 302.np 103.nq 10

Also, remember that:

Expected value = np

Variation = npq

Standard Deviation =

Q9 Normal Approximation to Binomial.

This one takes a few steps. See the example below too:

1. Do the three tests, and learn them.2. Work out your mean and standard deviation using

the information provided. Remember the rules to

get them :D

3. From there, convert your x score to a z score,and work out the probability using the table.

This process is easy, you just need to remember all the

steps. Practices can be found in Exercise 10C.

Also, Q10, 11, 12, 15 & 16 Im guessing are all worded

questions of this type. For this, Id recommend having

a look at that extra worksheet we were given. Its quite

good.

Q14 Substitution.

This could be finding the +c or another variable. Either way, heres an example of how you do this. Youre

going to need another point on the graph and just sub in the x and y values.


5/5

ITS TIME TO ROCK OUT WITH YOUR GRAPHICS CALCULATOR OUT

Heres a summary of the things youll need to be able to do:

Integration between Curves:

Finding X-Intercepts:

GRAPH MODE

G-SOLV

ISECT

Arrow up and down to see both points of intersection.

*Use this method to check your algebraic working.

Finding Area belowthe curve:

GRAPH MODE

G-SOLV

ARROW ACROSS OPTIONSDESPAIR.DX (Select your boundaries, and cross reference with your original answer.

*This will not work between curves, as per my stupid example picture

above.

Finding the Probability of Normal Distributions:

This is what needs to be done in Q2 Note that X values dont need to be translated into Z

scores when using the GC.

Maths B Notes - Term 4

Documents

Transcript of Maths B Notes - Term 4