Missing Names

There are no real names for the blog names listed below. If your blog name is on the list, please email your real name, blog name and Student ID IMMEDIATELY to fariel.mohan (at) utt.edu.tt

These are very important to your grades. Please pass the message along to your classmates

asriel10star

Bailey

Bansee

fella

GR

lifesaver

Marc

Quantum100

ravi

samuelmansingh

shady

sin

star

ThatGuy

the best one

the dawg

Weezy

Again, if your name appears on the list, please email your real name, blog name and Student ID IMMEDIATELY to fariel.mohan (at) utt.edu.tt

Area of a Venue

An event management company is planning to host an event and need to know how many tickets to print, based on the size of the venue. The venue is 300 metres long, and is measured in even intervals to find the distances across it, and the following measurements were recorded in order:

58 m, 75 m, 94 m, 102 m, 85 m, 92 m, 98 m, 74 m, 60 m, 70 m and 74 m.

How large is surface area of the venue?

Solve the following question

Townsville is 50 km from Villagetown. From Villagetown, Townsville is thirty degrees to the right of Boroughcity.

1. How far is Boroughcity from Townsville?

2. How far is Boroughcity from Villagetown?

Straight Line Grapshs

Where does the line cut the x and y axis?

1. y = 5x - 8

2. 4y = 16x + 64

3. 6x = 12 - y

4. y² = 144 + 16x²

5. y + 3x = 18

Stats Project marks

So far no group has submitted this project
You cannot failed this course. Failing twice you are out of UTT

I need the Excel file of the questionnaires to validate the studentIDs
and the questionnaires themselves.

Please note the hroup gets a mark but cannot get your group mark
until I quiz you on the project.




The marks shown in comment below is for Math111D, I posted in wrong blog

THe quiz for stats project MUST be after all official exams, so it is on Monday 3rd May 2009
Does anyone have exams then
Time 9:00 am - 11:30 am first come first examine

MATH 111D Project (20%) marks

Marks on http://math110dclass.blogspot.com/

(at http://ourmathsclass.blogspot.com/2009/04/project-20.html )

Statistics Project

You have until the first official day of exams to submitted.
THe project can be emailed to fariel.mohan@utt.edu.tt

Project submission consists of

1. Report with 3 different graphs
2. All filled questionaires must be submitted to very validity of student ids, if not project is 0.
3. Ms Excel file showing data entry of questionaire, if not project is 0.
4. Since no presentation, monday after last exam, from 9:00 - 12:00 , I need to question each member to determine contribution to project. No other day is allowed. If not there, your mark is 0.

Remember final exam has no area or volume except for area of sector and no stats

ONLY ALBEBRA and TRIGS

Solve the follow Trigs Questions

1. A Laser points to the top of a cliff at an angle of 47 degrees, and another points to the foot of the cliff. The laser gives the distance to the top of the cliff as 40 metres.

i. How tall is the cliff?
ii. How far away from the base of the cliff is the laser?


2. A line needs to be pulled from the top of a pole to transport material from one site to the top of a building, but the line cannot be elevated more than 40 degrees because of specifications. The building stands 45 metres tall, and the pole is 1 metre tall, and currently 50 metres away from the base of the building.

i. Can they mount the line to the top of the pole? If they can, why? If they can't, why not and where should the pole be moved to allow them to mount the line?

ii. If they can mount the line, what is the distance between the top of the pole and the top of the building?

Revision

Plot the curve 8x^3 -2x^2 -5x -1 = 0
Show the x intercepts

Question for revision

1. solve the simultaneous equation

3x -2y = 1

9x^2 + y = 7

1. Draw the curve on graph paper and find the roots (where y = 0)

5x^3 - 3x^2 -32x - 12 = 0

1. in a ap the 20th term is 92 and the sum of the first 20 terms is 890. Find

i) the first term

ii) the common difference

iii) the sum of the first 10 terms

1. in a gp the 2nd term is 3 and the 5th term is 5.184. Find

i) the first term

ii) the sum of the first 15 terms

GP Question

A sequence is 0.5, 1, 2, 4...

What is the 13th term? What is the ratio (r) used?

Sector Question

1. A circle of diameter 30 cm has a sector of 65 degrees removed. What is the perimeter and surface area of the rest of the circle?


2. A circle of diameter 15 cm has part of a right-angled triangle overlapping it. One angle of the triangle, measuring 37 degrees, is at the dead centre of the triangle, and one side of length 25m, extends outward to the right angle.

What is the area of the triangle that is outside of the circle?

Angle of Elevation/Depression

Find the angle of elevation in the following:

1. You are standing 15 metres away from a 30 metre high pole, and look at the top of the pole. What angle are you looking with?

2. Your friend is at the top of a building, 200 feet high, and he throws a line to you that is 250 feet long. You pull the line and stretch it from your friend to you. What angle are you looking up to your friend with?

3. A Bridge spans a 300 m wide river. There are two support cables, attached to the top of a 50 m column at either end of the river and then to the centre of the bridge. What angle does the support cable leave the bridge with?

4. A stunt rider needs to build a ramp that has an angled surface length of 50m, and will meet the top of a vehicle that is 8m high. What angle does the same angled surface need to be elevated with?





Find the angle of depression of the following:

1. A camera is mounted on a 10ft pole on the outside of a building, and is aimed at a spot that is, in a straight line from the lens of the camera, 15 metres away. What is the angle of depression for this camera to aim at the spot?

2. A door on the bottom of an aeroplane is 180cm long. When the plane lands, it is just 75cm clear of the ground. What is the maximum angle that the door can open?

3. You are looking up at a helicopter which is 45 m away. You look up at the pilot with an angle of 63 degrees, what is the angle of depression that would allow the pilot to look back at you?

4. A sniper is on the edge of a 53 foot high cliff and spots an enemy. Conveniently, there are grid lines on the ground which tell you that the enemy is exactly 72 feet away from the base of the cliff. What angle of depression would the sniper have to aim with to hit the enemy with his water balloon?

Final exam

Topics not possible

1. Vectors
2. Area and volume

Topics coming are

Algebra

1. factorization
2. expanion
3. factorizing factorising quadratics
4. AP/GP
5. Graphs straight line y = mx + c
6. Graphs quadratics
7. graphs cubic plotting and find point for cutting the x-axis

Trigs

1. simple right angle trigs with and without calculator
2. angle of elevation
3. 3D angles of elevation
4. sine /cosine rules
5. Area of triangle
6. Sector

GP questions

1. Find the eight term (ar^7) of the GP 8, 4, 2, ...
2. If $100 is invested each year at 5% compound interest annually, what would be the total amount of the investment after 10 years.
3. A GP has a first term of 12 (a = 12) and the fifth term of 18 (ar^4 = 18), find the 13th term (ar^12)
4. A GP has a second term of 18 (ar=18) and a fourth term of 8 (ar^3=8), find the first term (a) and the common ratio (r)

GP

The second term of a geometric progression is 3 and the fourth term is 12.
Find the first term, a
and the sum of the first 10terms,

Question say GP i.e. a, ar, ar^2, ar^3

• 2nd term ar = 3
• 4th term ar^3 = 12
• now divide ar^3 by ar and you get r^2 = 12/3 = 4
• r^2 = 4 then r=2
• Now ar = 3 so a(2) = 3 then a = 3/2

Sum of first 10 terms = a(1 - r^n)/(1 - r)

a = 3/2, r = 2 and n = 10 so substitute and solve

Trigonometry Q

You are standing 15 m away from a post, and looking a bulb at the top of it, with an angle of 45 degrees. A friend is standing 60 degrees to your right, and looks at the same bulb at an angle of 65 degrees.

1. How high is the bulb?
2. What is the straight-line distance between your friend and the bulb at the top of the post?
3. How far (in meters) are the two of you standing from each other?


Cosine Rule:
a² = b² + c² - 2 b c cos(A)
b² = c² + a² - 2 c a cos(B)
c² = a² + b² - 2 a b cos(C)

Expand and Factorize Qs

Expand:

3(4x + 2y)

(8x - 2y) (4x + 6y)

(10i + 7j) (2j - x)

(17 + 2x) (2x + 3y)

(8w + 4x) (10x - 2W)




Factorize:

x^2 + 6x + 8

30 + x^2 + 13x

y^2 + 6y - 16

8 - x^2 - 6x

z^2 + 1z -56

AP questions

If first term is -11 and common differebce is 20

1. what is the 2nd term
2. what is the 3rd term
3. what is the fourth term
4. what is the 10th term
5. if last term is 179, how many terms are there?

2. If a = -11 and last term is 79 and the sum of all the terms are 340, what is the sum of terms?

Sum of terms = n/2 (first + last), so right away n number of terms can be found.

then common difference d can be found since last term = first + (n - 1) d

AP

The first term of an AP is -11 and its last term is 179. The sum of the whole series is 1680. Calculate 1) the number of terms
2) the sum of all the terms from the 5th to the 11th terms (both inclusive)

Anwser
Find the number of terms n from S = n/2(a + l)

1. From the first line first term a = -11
2. and last term l = 179
3. Sum = n/2 (a + l)
4. 1680 = n/2 (-11 + 179)
5. 1680 = n/2 (168)
6. 1680 = 84 n
7. n = 1680/84
8. n= 20

the sum of all the terms from the 5th to the 11th terms (both inclusive)

Sum of first 11 terms - sum of first 4 terms remember a =-11

Need to get the common difference d

last term 179 is really the 20th term so

20th term = a + (20 - 1) d = 179

-11 + 19d = 179

19d = 190

d = 10

Now you know a = -11 and d = 10

• sum up to 10 terms means n = 10
• sum up to 4 terms means n = 4

Statistics Questions

Find the mean, median and mode of the following groups:

1. 45, 50, 47, 47, 51, 53, 56, 58, 48, 49, 45, 50, 47, 46

2. 6, 8, 4, 8, 6, 9, 1, 2, 8, 4, 6, 7, 3, 7, 4, 3, 7, 7, 5


3. A class' test results are as follows:
75, 84, 99, 54, 88, 60, 45, 81, 49, 80, 55, 43, 21, 84, 85
What is the mean, median and standard deviation?

What is the standard deviation in the following sets:
4. 12, 15, 12, 13, 18, 19, 14

5. 100, 102, 108, 118, 107, 129, 111, 104

Stats project

Important sections

1. data collection 3%
2. data entry in excel 3%
3. 3 different graphs using excel 3 %
4. demonstration of mode, mean, median 3%
5. report and data collection forms and excel file and minute meetings 3%

std dev questions

1. find the standard deviation of 1, 5, 4, 2, 6, 2, 1,1 5,3
2. find the standard deviation of 20, 17, 17, 14, 12, 11, 7, 8, 9, 16, 19, 22

A sample of data can have a lot of different numbers and it will require grouping to make any sense e.g 3-5 hrs, 6-8 hrs, 9-11 hrs, 12-14 hrs, 15-17 hrs, 18-20 hrs can represent the difefrnt ranges to group the numbers

Find the standard deviation for

0-4 2

5-9 7

10-14 12

15 - 19 17

20-24 22

25 - 29 27

Standard deviation

A conclusion is drawn from a sample of data. e.g. a conclusion can be drawn from the time usage of 50 internet users. these 50 users are a sample of all internet users.
if a conclsion has to be drawn from the population thatwill be impractical. So a sample of the population is selected an used. This means that the deviation from the mean is important.
Steps for calculating standard deviation

1. find the mean
2. subtract the mean from each member
3. square the difference
4. find the sum of these squares
5. divide this sum by n-1
6. find the square root of this result

Statistics

Statistics is all about numbers, is this true
why does one keep a set of numbers
do you know anything or place with a set of numbers
Why does the play whe outlet keep a set of previous play for the day?

Think of the grocery bill when you are buying items for a graduation or party?
A lot of common items are bought.
Information of interest will be which item cost the most money?
Which item do you have the most of?
How many different items do you have?
What item cost the least?
What item do you have the least of?


23 12 16 13 12 23 23 12 27 16 13 23 43 13 12 23 23 12 23 12 23 43 16 23 26 23 26

What information can you create or obtain from the numbers?

The different numbers are
27 numbers
23 12 16 13 27 43 (just 6 different numbers)
23 occurred the most (10 times)
27 occured the least ( 1 time)
23 occurred 10 times
12 occurred 6 times
16 occurred 3 times
13 occurred 3 times
etc

23 which occured the most is called the mode

median
1st arrange is a descending or ascending order
2nd remove one from both sides and the last one is the median. if two are left the average of the two numbers are found
the mean is the average of all the numbers

12 12 12 12 12 12 13 13 13 16 16 16 23 23 23 23 23 23 23 23 23 23 26 26 27 43 43

Trapezoidal Rule Questions

A lake has the following lenghts, in order: 100m, 150m, 200m, 175m, 250m, 150m, 100m, 50m. The lengths were measured at intervals of 50m, what is the surface area of the lake?

A cieling need to be covered. Measurements are taken every 10 inches, and the lengths are recorded as 100in, 150in, 200in, 150in, 200in, 200in, 150in, 200in and 50in. What is the area of the ceiling?

A floor needs to be covered in vinyl carpet. The floor however is irregularly shaped and measures, from one end to the other, in order, 10m, 30m, 50m, 60m, 20m, 20m, 30m, 10m and 5m. How large is the floor if teh measurements are taken every 2m?

A cover is built for a reservoir located in a natural landform. Surveyors measure the landform's width every 10 metres and record the following distances: 125m, 130m, 190m, 230m, 200m, 180m, 150m.

The first and last distnaces across a plot of land are 60 feet and 100 feet respectively. The other distances are 80ft, 100ft, 120ft, 100ft, 90ft and 110ft. How big is the plot of land?

What is the area of a figure that measures 1, 2, 4, 5, 3, 2, 1 and 8 inches across, respectively, if the measurements are taken every 0.5 inches?

A satellite photograph covers an island. The key on the island shows that the distances across the island are, from left to right, 100km, 120km, 300km, 200km, 180km, 100km, 150km and 175km. If the measurements are 50km apart, how much surface area is there on the island?

A hole was broken on the side of a metal fence and it needs to be covered over with sheeting. If the hole measures, from top to bottom, at intervals of 15 cm, 1m, 50cm, 1.5m, 150cm, and 75cm, what area needs to be filled?

A painter paints an outline on the road, to be covered in white paint for an advertising spot. The outline is measured every 10 cm and is 50, 40, 30, 50, 45, 40 and 80cm wide, and 10 and 30 cm wide at the ends. How much area needs to be painted?

One end of a field is 100m wide, and the other end is 110m wide. How much area is there on the field for sports if every 15m the field is measured and the distances (excluding the other two already mentioned) are 105m, 110m, 108m, 103m, 97m, 98m, 105m and 103m?

Expand and Factorize

(27x + 56y) (3 - t)

(52x - 12w) (23x + 3w)

(ax + bx) (x + bx)

(3x - 5) (10x + 4)

(12y - 3x) (20x - 20y)

(4a + 2a) (2x - 4)

(30x - 2y) (30x + 2y)

w (23a + 33x)

(10x - 3) (25y + 11x)

(x - y) (25a)

p (54 + p)

(11x + 11y) (px - 33y)

24x (5x - 5y)

(3r + ab) (3ab + r)

(2xy - x) (z - 20)




Factorize:

7xy^2 + 21xy + 14x

x^2 + 13x + 42

z^2 + 6z - 16

-w^2 + 15w - 50

a^2 + 25a + 150

3x^2 - 5x + 2

6y^2 + 14y + 12

y^2 - 9y - 36

AP Question Set

If the interval is 15, and each row increases by 6, given that the 6th row has 700 seats, how many seats are there in the first row?

If there are 100 rows and there are 600 seats in the final row, how many are there in the first row if there are 8 more in each row?

If a sequence has 34 terms, the first row has 12, and the final row has 65, what is the common difference?

What is the common difference in a series that begins at 10 and ends at -50, if there are 14 terms?

If a sequence goes 41, 49, 57, 65, et cetera, taking 57 to be the first term, what is the value of the 4th and 14th terms?

In a sequence of 18 items, if the final item is 44 and the difference is 8, what is the first item?

The first item in a sequence of 38 items is 6 and the final item is 86, what is the common difference?

How many numbers are divisible by 5 between 42 and 193?

The 23rd term in a sequence that increases by 8 is 134. What is the 1st term?

A park has thirty-three trees in the 5th row of trees. If the trees increase by 4 every row, how many are there in the first row?


If the third term in a sequence is 6.5, and the fifth is 13.5 and the seventh is 20.5, what is the first term?

In 46 numbers, the last term is 12, and the difference is 3.4. What is the first term?

The 15th number in a sequence is 54, and the first is 30. What is the common difference?

How many numbers leave a remainder of 2 when divided by 7 in the range 4 to 104?

After counting by threes, the 54th number is 431. What was the 22nd number?

A sequence begins at 92, goes to 103, then to 114, and then 125 and continues along this line. If a sequence begins at 114 and ends at 499, how many terms are in the sequence?

The common difference in a sequence is -13. If the final term is -65 and the sequence is 12 items long, what is the 1st, 5th and 6th terms?

Beginning at 5, a sequence ends at 65. How many terms are there in the sequence if the common difference is 12?

20 is the 5th number in an evenly progressing sequence and 80 is the 10th. What is the first?

In 65 numbers, the final number is 64.1. If the sequence progresses by 2.1, what is the 10th term?

Express the following as a single logarithm:
1. log [3] 7 + log [3] 5

2. log [2] 16 + 3log [2] 4 - log [2] 8
3log [5] 9 + log [5] 2
4. log [5] 5 + log [5] 10 - log [5] 3 = 0
3.
4.

Log set 3

1. Solve log[7](x^2) = log[7](2x – 1).
2. Solve 2log[3](x) = log[3](4) + log[3](x – 1)
3. Solve log2(x) + log2(x – 2) = 3

1. A closed box has a fixed surface area A and a square base with side x .
   (a) Find a formula for the volume V of the box, as a function of x .
   (b) Find the rate of change of V with respect to x.
2. The revenue from selling q items is given by the formula R(q) = 500q - q^2
   and the total cost is given by C(q) = 150 + 10q . Write down a function that gives the total
   profit earned. Find the rate of change of total profit with respect to q.
3. For positive constants A and B, the force between two atoms in a molecule is given by
   f(r) = A/r^2 + B/r^3 where r > 0 is the distance between the atoms.
   What is the expression for the instantenous rate of change of force between the atoms with respect to distance?

Log set 2

1. Find the value of the unknown variable in each of these:
   (i) 2^x = 128 , (ii) 3^y = 1/9 , (iii) 5^x = 625 , (iv) 4^s = 164 , (v) 16^t = 4 ,
   (vi) 8^ = 1/4 .
2. Solve each of the following equations for the value of x (i) log 3x = 6

ii) log[3]x + 3log[3](3x) = 3 iii) log (5x - 1) = 2 + log (x - 2) iv) 2logx = log(7x - 12)

3. Write each of the following as a single logarithmic expression:
(i) log[10](x + 5) + 2 log[10] x (ii) log[4](x^3 - y^3) - log[4] (x - y)

iii) 1/2 (3 log[5] (4x) + log [5] (x + 3) - log[5] 9)

Expand and Factorize

Expand:

(x + 13) (2x + 5)

(7y + 6) (1y + 50)

(y - 5) (y + 5)

(65t + 1) (3t + 15)

(-7y - 7) (-11y - 21)

(3z - z) (6z + z)

(8 + 2w) (-5 - 2r)

(-r + 12) (-5r - 12)

(x + b) (a - b)

(22i - 10) (4i - 3)



Factorize:

x^2 +5x +6

y^2 - y - 6

m^2 - 5m - 24

x^2 + 13x + 42

z^2 + 18z + 80

r^2 + 36 + 15r

e^2 + 10e + 28

54 + 15c + c^2

t^2 + 2t - 15

x^2 + x - 2

AP question set 2

Explain all steps and strategy not answers

1. If d = 3 and n= 30 and S30 = 1875, find a and S5.
2. Write the first 7 terms if a = 4 and d = 2.
3. Write the first 7 terms if a = 6 and d = -1/2.
4. If the 2nd term = -2 and the 5th = 43, write the first 7 terms.
5. If the 3rd term = 5/2 and the 5th = -3/2, write the first 7 terms.
6. A beach now has an area of 9500m2 but is eroding such that it loses 100m2 more of its area each year than during the previous year. If it lost 400m2 during the last year, what will be its area 8 years from now?

AP questions

1. Find the common difference between successive terms of the arithmetic sequence for ehich the first rem is 5 and the 32nd trem is -119.
2. How many numbers between 10 and 1000 are divisible by 6?
3. Find the 4th and 14th terms for 2,5,8,.......
4. A package delivery company uses a metal ramp to slide packages from the sorting area to the loading. If a package is pushed to start it down the damp at 25 cm/s and the package accelerates as it slides such that it gains 35cm/s during each second, after how many seconds is the velocity 305cm/s?
5. Find the sum of the first 1000 positive integers.
6. Find the sum of the first ten terms of the arithmetic progression in which thr first term is 4 and the common difference is -5.
7. If a = 2, d = 2/3 and Sn = 72, find n. Find S4.
8. THe voltage across a resistor increases such that during each second the increase is 0.002mV less than during the previous second. Given thath the increase during the first second is 0.350 mV, what is the total voltage increade during the first 10 s?
9. If the 6th term of an AP is 56 and the 10th term is 72. Find the 1st term, the common difference and the sum of the first 10 terms.
10. If the 17th term of an AP is -91 and the 2nd term is -73. Find the 1st term, the common difference and the sum of the first 40 terms.

AP /GP

What is a series or progression?

Why is this usefull in life?

Does anything you do remind you of AP?
Does anything around you remind you of AP?

What are the important things in a series or progression?

Things that are changing must have a starting position.
Your age had a starting point. Your height had a starting point.
Everything you know bankaccount, friendship, a movie, etc

Now if it is changing, then it means by what amount it is changing?
If these amount is the same then we have an AP.

If you need the 7th position or term then

• out of the 7 terms, the 1st must be the start
• then the rest will be the consistant changes. In this case it will be (7-1) which is 6
• So the 7th term 1st + (7 -1) change i.e. a + (n-1)d is the nth term

Give some examples of terms e.g. 27th term, 32nd term, etc

Arithmetic progression questions

A Stadium is built with 200 seats in the first row. After that, each row has 50 more seats than the previous row. How many seats are in the 25th row?

The 15th value in a set that increases by 6 is 250, what is the first value?

What is the sum of the values of a set that contains 23 numbers, begins at 5 and increases by 4?

A housing estate is built with five homes on the first row, and there are 3 more homes on each row. How many homes are there on the 15th row?

If there are 50 boxes on the bottom of a stack which is 15 rows tall, and as the stack grows in height, there are 2 less boxes in each row, how many rows of boxes are there in the first row?


Please post other questions for the class if you do have any to solve.

Volume and Area Questions II

NOTE: Use the Trapezoidal rule for all irregular shaped questions. Assume measurements are taken in order (first to last) unless otherwise stated.

1. An artificial green needs to be covered in turf, and the gardener in an effort to calculate exactly how much is needed, measures the lengths across the green at 1 metre intervals. The gardener measures lengths of 1, 3, 9, 4, 5, 6 and 8 metres respectively. What area needs to be covered?

2. A parade float is in the shape of an island. The designer decides to cover the island in green cloth to make it look more realistic, and measures the width of the float every 50 centimetres, and records the first length as 1.5 metres, and the others as 2.5, 3, 4, 3, 2.5, 3 and 1 metre respectively. How much cloth will be placed on the float?

3. A section of a roller coaster's tracks needs to have a cover installed to put up a sign. The track on this section has no curves, but does go up and down. The engineers measure each of the nine supports, which are spaced 3 metres apart, and record the following lenghts in order: 4, 5, 6, 3, 2, 3, 4, 5, 5 (in metres). What area will the sign cover?

4. An artist designed abstract pool needs to be covered in case of rain, and other bad weather. The pool is measured in intervals of 30 centimetres and has lengths of 0m, 2m, 1m, 2m, 3m, 4m, 3m and 1 m, where m is metres. What is the surface area of the cover?

5. A satellite photo of a parcel of land shows that the distances from one side of the resort, which is 500 metres long, to the other, is 0 metres, 100 metres, 320 metres, 200 metres, 150 metres, 200 metres, 400 metres, 350 metres, 250 metres, 200 metres and 10 metres. How large is the parcel of land, given that the distances are measured at even intervals?

6. A hole in the side of a blimp needs to be patched. How much material is needed if the gap, measured at 1 foot intervals, is 3 feet, 2 feet, 4 feet, 4 feet, 5 feet, 3 feet, 2 feet and 1 foot?

7. Trinidad Asphalt is loading asphalt to fill a pot hole that is 1 foot, 6 feet, 3 feet, 4 feet, and 2 feet wide at points in the pothole, which are 1 foot apart from each other. What surface area does the pothole have?

8. A man man decides to paint the town red, but because of the global economic recession, wants to make sure he is as efficient as possible in the purchasing of his paint. If the town is measured at 100 metre intervals and the following distances (in metres) are found respectively: 500, 900, 850, 450, 700, 800, 850, 900, 850, 900, 1000, 1250, 1100, 900, 800, 750. What surface area would he need to paint?

9. A tee-shirt printer needs to purcahse just the right amount of ink to print a splash on a tee shirt. The splash is measured at 1cm intervals and is 1cm high at one end, 2cm at the other, and the lengths in between are 2cm, 3cm, 4cm, 2cm, 3cm, 5cm, 3cm and 2cm.

10. A footprint is seen at a crime scene and investigators want to find out the surface area to link it to another suspicious footprint they have found. They measure the following lengths, at 1 inch intervals, respectively. and find 2.5 inches, 2.8 inches, 2.5 inches, 2.4 inches, 2.2 inches, 2.2 inches, 2.0 inches, 2.4 inches, 2.5 inches, 2.6 inches and 2.7 inches. What is the area of the footprint?

11. An oil barrel measures 4 feet in diameter and is 6 feet high, how much oil can it hold?

12. A grain silo is in the shape of a cylinder and is placed on a square base that fits it perfectly with no overlap of any kind. The base measures 6 metres along one side. If the silo is 20 metres tall, how much grain can it hold?

13. You think a can of Juice is rather small for it to hold the 2000 centimetres cubed that it says on the label. You measure the can and get the following dimensions: Height: 15 centimetres, Diameter: 5 centimetres, Circumference: 15.714 cm. How much juice does the can actually hold?

14. How much water can your dog's bowl hold if it has a radius of 6 inches and a height of the same?

15. A programmer needs to tell the computers how much grease to fill in a cylindrical tube of height 30 centimetres and diameter 6 centimetres. How much will he need to tell the computers to fill the tubes?

16. If a coin measures 2cm in diameter and .1 cm in thickness, and ten of these are placed in a tub of water that is full to the brim, how much cm³ will the coins cause to spill?

17. An absorbant rope is used to trace the edge of an oil spill. Measuring the rope at 1.5 metre intervals, the distances across the spill, in order, is found to be 1m, 3m, 10m, 20m, 15m, 10m, 15m, 20m, 10m, 5m, 10m, and 2m. How much oil has spilled?

18. A cupboard door needs to be lined with insulating material, and the door measures 30cm, 40cm, 45cm, 45cm, 45cm, 40cm, 35cm, 30cm and 20cm across, at points which are 12 cm apart. How much insulation is needed?

19. A patch of grass in a field is dead, determine how much grass died if you are told that the area was measured in gaps of 32 inches and the distances across were found to be 40 inches, 4 feet, 5 feet, 53 inches, 6 feet, 50 inches and 23 inches.

20. A hole needs to be patched. The following measurements are taken at 1.25 cm intervals: 1cm, 2.20cm, 2.10cm, 1.75cm, 1.44cm, 1.20cm, 1.0cm, 1cm, .55cm and 0cm. How much area needs to be patched?

Expansion

Expand the following.

(5x + 3) (x + 7)

(10x + 2) (-1x + 20)

(y - 5) (y + 5)

(3w + 1) (3x + 5)

(11u - 11) (6u - 1)

(xy - x) (3x + xy)

(8 + 30r) (5 + 2r)

(100t + 12) (52t - 12)

(a + b) (a - b)

(22i - 10) (4i - 3)

Simpson's Rule questions

1. The widths of a plane wing were measured as 0.30m intervals. Calculate the surface area of the pool given the respective lengths were 0, .16, .23, .32, .35, .3 and .2. Draw the diagram on paper then write and explain your answer.
2. The ariel view of a lake with 1.5km intervals had lengths respectfully of 0, 4.8, 5.7, 10.5, 15.2, 18.5, 18.8, 17.9, 11.3, 8.8 and 3.1 Draw the diagram on paper then write and explain your answer.
3. The widths of a kidney-shaped swimming pool were measured as 20m intervals. Calculate the surface area of the pool given the respective lengths were 0, 6, 7, 8, 6, 5, 4, 5 and 0. Draw the diagram on paper then write and explain your answer.

Simpson Rule

Another approach for measuring area of irregular shapes is the Simpson 's Rule. This also uses equal intervals. Unlike drawing trapeziums, arcs of parabola are drawn somewhat getting closer to the real area. The formula is

A = h/3 {yo + 4y1 + 2y2 +4y3 + ....+ 2yn-2 + 4yn-1 + yn)

Trapezoidal Rule

1. A plate cam for opening and closing a valve has an irregular shape. The widths of the face of the cam are 2cm intervals. Find the area of the face of the cam if the length respectfully are 3, 4, 3, 3, 2 and 0. Draw a diagram in a paper then explain your answer.
2. From a satellite photograph of a lake, the widths were 26 kmm intervals. The lengths were 0, 45, 50, 60, 61, 66, 74, 87, 76, 66, 86, 77, 0 respectfully. Draw a diagram in a paper then explain your answer.
3. The widths of a kidney-shaped swimming pool were measured as 20m intervals. Calculate the surface area of the pool given the respective lengths were 0, 6, 7, 8, 6, 5, 4, 5 and 0.
4. The widths of a plane wing swimming pool were measured as 0.30m intervals. Calculate the surface area of the pool given the respective lengths were 0, .16, .23, .32, .35, .3 and .2.

Irregular shapes

In our last tutorial, approaches were investigated to find the area of an irregular shape. Suggestions

1. Make the best rectangle out of the irregular shape
2. Make many rectangles out of the irregular shape
3. Make many rectangles with equal widths out of the irregular shape
4. Make many trapeziums with equal widths out of the irregular shape

This was named Trapezoidal rule.

A hand was used to show that many trapeziums meant that the 2 outer lengths were the only lengths never repeated

Assignment due Monday March 9th. Trigonometry.

You need to draw the diagrams for each of the following questions and submit them in class on Monday March 9th.


1. A bird is standing on the ground, 5 metres away from a tree, which is seven metres tall. The bird wants to build a nest at the top of the tree, what is the shortest distance the bird must fly to get from its point on the ground to the top of the tree?

2. Your friend climbs up a flight of stairs, travelling 10 metres diagonally, when she gets to the top of the stairs she accidentally kicks over your cell phone which you left charging. To make sure your phone isn’t damaged, you need to calculate how far it fell from the top of the stairs straight down to the floor, and you know the stairs are at an angle of 53 degrees.

3. You are 6 metres away from a target with a canon that rests on the ground. The target is 5m off the ground. What angle would the canon need to be at to hit the target?
4. A friend is sleeping on the street across the road from your building, and you are standing on the balcony of the 5th floor. The road is 20m wide, and each floor is 5m high. What angle would your friend need to look up to see you if you called to him?

5. The same friend from question 4 also happens to make very good paper planes, and writes a note in one and sends it to you. How far does the plane have to travel to get to you if it flies straight from him to you?

6. A projector sits on a stand 1 metre high, and is 8 metres away from the screen. If the top of the image is projected at an angle of 45 degrees from the projector, how high does the screen need to be?

7. You are 15 metres away from your friend, who is standing next to a wall. You know your friend is 1.1 metres tall, and he is the same height as the wall, but on top of that wall is a flag pole. You only know that from the ground where you stand to the top of the flagpole is elevated 30 degrees, how high is the flagpole itself?

8. A boat is tied to a pier using 10 metres of rope between the boat and pier. The point on the pier where the rope is tied to the top of the boat gives an angle of 20 degrees. If the pier itself is 2 metres above the water, how much of the boat is above water?

9. A pulley is used to lift a bucket from one end of a construction site to another, across a 15 metre gap. At each end of the gap there are poles, with a rope to carry the bucket. The first pole is 5 metres high, and the second is 10 metres high. What is the actual distance the bucket travels between the two poles along the rope?

10. The engineers moving the bucket in question 9 want to ensure that it is being done as efficiently as possible, and want to know what angle the bucket is ascending with. What is that angle?

Area and Volume Questions

1. The corner of a square room needs to be covered in carpet. A triangular piece is needed. If one side has to be 5 feet and the other needs to be 7 feet, what area needs to be covered?

2. You are making a flag with two colours. The flag is sewn so the cloth meets a the middle of the flag going diagonally downwards. If you can get exactly the cloth cut exactly as you need it, how much cloth of each colour, in square feet, is needed if the flag’s dimensions are 4 feet by 3 feet.

3. A diamond window is made from four panes of glass, which meet at a “t” in the middle. The T is 1 meter high and 50 centimetres wide. If the bottom left pane of glass breaks, how much glass is needed to replace it?

Quiz on March 9th (10%)

A quiz will be posted on the blogs and the first person that answer my question correct will be required to put a similar question up for another person to answer. If you did not get 5 question scorrect on the blog, you are not allowed to sit the quiz in the classroom on March 9th.

Visualizing the scene

In 3-dimensional scene, one must be able to formulate the scene then draw.
Step 1 Use pens, pencils, rulers, etc
Step 2 Then draw

Formulate, draw then solve the following scenes:

1. A man standing on the beach looks up to the top of the cliff with an angle of elevation of 65 degrees. Ignoring his height and assuming he is standing on level ground with the base of the cliff and he is 15 metres from the base of the cliff, determine the height of the cliff.
2. From the question above, if the man walk 5 metres closer to the cliff and looks up to the top of the cliff, what will his angle of elevation be?
3. A man standing on the beach looks up to the top of the cliff with an angle of elevation of 70 degrees. Ignoring his height and assuming he is standing on level ground with the base of the cliff and he is 20 metres from the base of the cliff, determine the height of the cliff. A lady on the beach look up to the top of the same cliff with an angle of elevation of 40 degrees. Ignoring her height, determine the distance she stands from the base of the cliff.

Trigs

Trigs is based on ratios of line from a right angle triangle.

Draw the following

sin x = 3/5

cos m = 4/7

tan m = 3/ 4

sin m = 3 / 8

cos x = 5 / 8

tan x = 5 / 7

For each find all the angles and all the lengths

Expansion

From factorisation you can get back the original by expansion

Recall what is a term. A term is separated by + or - or =
A term consists of parts.
A book is on ething and consist of parts, toc, chapters, cover, pages, etc
Similarily, a term consists of parts, eg

2 + 3mn + 6twb -12 def + 1/2 mb = 120

This equation consists of 6 terms

• 2 is a number term and is a 1 part
• 3mn is a mn term and consists of 3 parts, a number, a m and a n
• 6twb is a twb term and consists of 4 terms, a number, a t, a w and a b
• 12def is a def term and consists of 4 parts, a number, a d, a e and a f
• 1/2 mb is a mb term and consists of 3 parts, anumber, a m and a b
• 120 is a number and is a 1 part

Identify how many terms are present in the equation, what are the trem, and what are the parts.

1. 12 mn + 3mds
2. 2m^2 + m
3. 6mn - 3mpd + 2 m^2
4. 20 m^2 - m
5. 6mnt - 3mn

For each of the above look for any common part in all the term.

This will go outside the bracket ( ) and inside the bracket put what reamins in each term

The y-intercept

What is the y-intercept?
What really does the y-intercept mean?

From the general equation of a straight line, the y-intercept is c.
Why is this true?

What is the y-intercept's of the following

1. y = 6x + 3
2. y = -12x + 5
3. y = 2x - 6
4. 2y = 5x + 3
5. 3y = - 4x + 1
6. 2y + x = 7
7. 3y + 5x = 11
8. 2y - 4x = 7
9. 4y + 3x + 2 = 0
10. 2y -3x + 5 = 0

Straight line

What is a straight line?
What does a straight line of distance against time mean?
What does a straight line of velocity against time mean?

A general equation for a straight line is
y = mx + c
Does all straight lines have to be written in this form?

From a straight line equation, the gradient is one of the most important thing
to determine. Explain how the gradient is determine form the following lines.

1. y = 6x + 3
2. y = -12x + 5
3. y = 2x - 6
4. 2y = 5x + 3
5. 3y = - 4x + 1
6. 2y + x = 7
7. 3y + 5x = 11
8. 2y - 4x = 7
9. 4y + 3x + 2 = 0
10. 2y -3x + 5 = 0

Graph

What is a graph?
Why are graphs necessary?
Give examples in real life where graphs are critical.
How are graphs used in these examples?

Factorisation Exercise

1) y^2 - 10y + 24 11) 3x^2 + 19x + 6
2) m^2 + 11m + 24 12) 6x^2 - 5x -4
3) x^2 + 7x + 12 13) 2x^2 + 5x -7
4) x^2 + 7x + 10 14) 5x^2 - x - 6
5) x^2 -3x -10 15) 12x^2 + 7x + 1
6) x^2 - 6x + 8 16) 3x^2 + 17x -6
7) 6x^2 + 7x + 2 17) 8x^2 + 6x + 1
8) 8x^2 - 6x + 1 18) 2x^2 + x - 15
9) 2x^2 + 11x + 5 19) 4x^2 + 23x + 15
10) 7x^2 - 6x - 1 20) 2x^2 -7x -4

Recall the approach ax^2 + bx + c ( ) ( )
3x^2 -10x - 8
Step 1 Multiply a by c ac 3 x -8 = -24
Step 2 Write all combinations to get ac __ x __ -1 x 24 1 x -24
-2 x 12 2 x -12
-3 x 8 3 x -8
-4 x 6 4 x -6
Step 3 For each in step2, add the number to get b (-10) 23 -23
10 -10 got it
Step 4 Rewrite question using the two terms for middle term
3x^2 + 2x - 12x - 8
Step 5 Factorize
3x^2 + 2x -12x - 8
x(3x + 2) - 4 (3x + 2)
(3x + 2) (x - 4)

Factorization of expression

An expression consists of terms, knotted terms and + or -.
A term consists of parts
eg 5mt consists of 3 parts, number, m and t and this term is called an mt term
235 consist of 1 part, a number and is called a number term
17bdcf consists of 5 parts, number, b, d, c, f and is called a bdcf term
A knotted term consists of bracket and it has to be untangled, expand to remove bracket

Factorization is taking out all common part in all terms

Factorise the following:

1) 4pm + 5md + 6mdp
2) 4mhd + 8mhdw

Factorisation versus expansion

What is factorisation?
What good is factorisation?
How can factorisation be demonstarted in the real world?

What is expansion?
What good is expansion?
How can expansion be demonstarted in the real world?

What is the use of ( )

What is ( )?
Why is ( ) necessary or what does it signify?
Show by example different uses of ( ).

Equation versus expression

What really is an expression?
Why are expression necessary?
What is an equation?
What is the difference between an equation and an expression?
Give an example in life where an expression is absolutely necessary.
Give an example in life where an equation is absolutely necessary.

An unknown number

Why are things unknown in our life?
Is there any quantity in your life that the quantity is unknown?
Are variables necessary in life?

What is a number

Why is numbers important?
Explain from life how number can be used to increase, decrease, group, share and compare.
What is a fraction?
How will the world be if it had no fractions?
How will the world be if it had no whole numbers?
How will the world be if it had no negative numbers?