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