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8/8/2019 Maths B Notes - Term 4
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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
8/8/2019 Maths B Notes - Term 4
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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. .
8/8/2019 Maths B Notes - Term 4
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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
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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.
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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.