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- Graph parallelogram WXYZ with coordinates W(-9,9) X(-6,9) Y(-4,4) Z(-11,4).Translate by moving right 5 and up 2.
- What are the coordinates of the transformed image?
- Line segment WX and line segment YZ are parallel. In the transformed image, is line segment W’Z’ parallel to line segment Y’Z’? Explain your answer.
- What is the original image called before being transformed?
- What notation do we use to label the new image?
Consider the following example in real world situations that describe a correspondence between phenomena:
-the income tax a person pays depends on the person's total income.
-the number of years of experience on a job has a direct bearing on the salary received.
-the amount by which your savings will grow in a year depends on the interest offered by the bank.
-the area of a circle depends on the radius of the circle.
-the distance travelled in a car at a certain rate depends on the time travelled.
A, express each situation in functional words. For example, the income tax is a function of the total income.
-for each situation, indicate the dependent and independent variable.
-write the two variables as an ordered pair, and write the function using the notation y(x).
D, explain the meaning of a function in your own words, illustrate with your own specific example.
-the income tax a person pays depends on the person's total income.
-the number of years of experience on a job has a direct bearing on the salary received.
-the amount by which your savings will grow in a year depends on the interest offered by the bank.
-the area of a circle depends on the radius of the circle.
-the distance travelled in a car at a certain rate depends on the time travelled.
A, express each situation in functional words. For example, the income tax is a function of the total income.
-for each situation, indicate the dependent and independent variable.
-write the two variables as an ordered pair, and write the function using the notation y(x).
D, explain the meaning of a function in your own words, illustrate with your own specific example.
QUESTION THREE (10 marks)
Villandry's inventory includes three items for which the following details are available.
Supplier's Net realisable
list price value
Shs. Shs.
Product A 3,600 5,100
Product B 2,900 2,800
Product C 4,200 4,100
The company receives a 2½% trade discount from its suppliers and it also takes advantage of a 2% discount for prompt payment.
Required:
(a) Calculate the total value of products A, B and C which should be shown in inventory in the statement of financial position.
(b) Explain the difference that changing from a weighted average to FIFO method of inventory valuation is likely to have on an entity's profit or loss.
Villandry's inventory includes three items for which the following details are available.
Supplier's Net realisable
list price value
Shs. Shs.
Product A 3,600 5,100
Product B 2,900 2,800
Product C 4,200 4,100
The company receives a 2½% trade discount from its suppliers and it also takes advantage of a 2% discount for prompt payment.
Required:
(a) Calculate the total value of products A, B and C which should be shown in inventory in the statement of financial position.
(b) Explain the difference that changing from a weighted average to FIFO method of inventory valuation is likely to have on an entity's profit or loss.
QUESTION TWO
Discounted cash flow methods of investment appraisal are considered a superior technique as evaluation tools. Why would an enlightened shrewd investor still find these techniques wanting while committing to an investment decision? (6 marks)
Discounted cash flow methods of investment appraisal are considered a superior technique as evaluation tools. Why would an enlightened shrewd investor still find these techniques wanting while committing to an investment decision? (6 marks)
1. An arithmetic progression has first term 4 and common difference 1 2. State the 100th term.
2. A geometric series has first term 6 and common ratio 3. Find the sum of the first 10
terms.
3. A = 1 −7 , B = 3 7 , C = 1 0
−1 2
−1 0
−1 1
Find:
a) BC,
b) 5A − 2C,
c) A + C,
4. Find the inverse of A = −2 1 5 −3
5. Use matrices to solve the following simultaneous equations:
2x + 3y = 10 x − 2y = −9
6. Find the gradient function of y = 3x3 − 9x + 2. Find the value of the gradient function at x = 1, x = 0 and x = −1.
7. A particle moves along a coordinate axis. Its position at time t is given by s(t) = t3 − 9t2 + 24t + 4. Find:
(a) What is the velocity of the ball ?
(b) What is the acceleration of the ball?
(c) Find the speed.
(d) what is the velocity at t = 3.
(e) What is the acceleration at t = 3.
8. Find the area under y = 1t between t = 1 and t = 5
2. A geometric series has first term 6 and common ratio 3. Find the sum of the first 10
terms.
3. A = 1 −7 , B = 3 7 , C = 1 0
−1 2
−1 0
−1 1
Find:
a) BC,
b) 5A − 2C,
c) A + C,
4. Find the inverse of A = −2 1 5 −3
5. Use matrices to solve the following simultaneous equations:
2x + 3y = 10 x − 2y = −9
6. Find the gradient function of y = 3x3 − 9x + 2. Find the value of the gradient function at x = 1, x = 0 and x = −1.
7. A particle moves along a coordinate axis. Its position at time t is given by s(t) = t3 − 9t2 + 24t + 4. Find:
(a) What is the velocity of the ball ?
(b) What is the acceleration of the ball?
(c) Find the speed.
(d) what is the velocity at t = 3.
(e) What is the acceleration at t = 3.
8. Find the area under y = 1t between t = 1 and t = 5
Ntsako walks to school each day at a constant pace of 75 m per minute.
The school is 1.8 km from his house.
1.2.1.1. Use a sketch or diagram to represent the problem. (2)
1.2.1.2. Solve the problem (3)
1.3. Use the concept of ratio to answer the following questions.
1.3.1. In week 1, Mpho deep cleans a paving at 4 m2 per hour. How long will it take her to deep clean
an area of 12 m long and 6 m wide? (3)
1.3.2. In week 2, Maria joins and each of them cleans 4 m2 per hour. How long will it take the two of
them to deep clean an area of 12 m long and 6m wide? (4)
1.3.3. In week 3, Lerato joins and each of them cleans 4 m2 per hour. How long will it take the three of
them to deep clean an area of 12 m long and 6 m wide? (4)
1.4. Calculate the following:
1.4.1. Which is the best price for washing powder? Motivate your answer.
R45 for 2.5 kg
R55.50 for 3 kg
R72 for 4 kg (3)
The school is 1.8 km from his house.
1.2.1.1. Use a sketch or diagram to represent the problem. (2)
1.2.1.2. Solve the problem (3)
1.3. Use the concept of ratio to answer the following questions.
1.3.1. In week 1, Mpho deep cleans a paving at 4 m2 per hour. How long will it take her to deep clean
an area of 12 m long and 6 m wide? (3)
1.3.2. In week 2, Maria joins and each of them cleans 4 m2 per hour. How long will it take the two of
them to deep clean an area of 12 m long and 6m wide? (4)
1.3.3. In week 3, Lerato joins and each of them cleans 4 m2 per hour. How long will it take the three of
them to deep clean an area of 12 m long and 6 m wide? (4)
1.4. Calculate the following:
1.4.1. Which is the best price for washing powder? Motivate your answer.
R45 for 2.5 kg
R55.50 for 3 kg
R72 for 4 kg (3)
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QUESTION 2
2.1. Technology versus traditional tools for teaching. Which method is better?
Discuss this statement either in support of technology or traditional tools.
(10)
2.2. Do a research on the software that is available in the market today. Choose one that you can use in your
Grade 5 class to teach mathematics. Discuss your choice with the following in mind:
The name of the software.
How it works?
The benefits.
The shortcomings (if any). (10)
1.2.1. Ntsako walks to school each day at a constant pace of 75 m per minute.
The school is 1.8 km from his house.
1.2.1.1. Use a sketch or diagram to represent the problem. (2)
1.2.1.2. Solve the problem (3)
1.3. Use the concept of ratio to answer the following questions.
QUESTION 2
2.1. Technology versus traditional tools for teaching. Which method is better?
Discuss this statement either in support of technology or traditional tools.
(10)
2.2. Do a research on the software that is available in the market today. Choose one that you can use in your
Grade 5 class to teach mathematics. Discuss your choice with the following in mind:
The name of the software.
How it works?
The benefits.
The shortcomings (if any). (10)
1.2.1. Ntsako walks to school each day at a constant pace of 75 m per minute.
The school is 1.8 km from his house.
1.2.1.1. Use a sketch or diagram to represent the problem. (2)
1.2.1.2. Solve the problem (3)
1.3. Use the concept of ratio to answer the following questions.
2.3. GeoGebra is one of the software available today in the market. Briefly describe it. (2)
2.4. Why is GeoGebra so popular? (2)
2.5. GeoGebra can be applied in the area of numbers.
Name three ways in which it can be applied. (6)
2.6. There is a number of uses of tablets in the classroom.
Discuss any five that you can use in your class. (5)
2.7. Mention three advantages and three disadvantages of using a tablet
as an instructional media.
2.4. Why is GeoGebra so popular? (2)
2.5. GeoGebra can be applied in the area of numbers.
Name three ways in which it can be applied. (6)
2.6. There is a number of uses of tablets in the classroom.
Discuss any five that you can use in your class. (5)
2.7. Mention three advantages and three disadvantages of using a tablet
as an instructional media.
QUESTION 2
2.1. Technology versus traditional tools for teaching. Which method is better?
Discuss this statement either in support of technology or traditional tools.
(10)
2.2. Do a research on the software that is available in the market today. Choose one that you can use in your
Grade 5 class to teach mathematics. Discuss your choice with the following in mind:
The name of the software.
How it works?
The benefits.
The shortcomings (if any). (10)
1.2.1. Ntsako walks to school each day at a constant pace of 75 m per minute.
The school is 1.8 km from his house.
1.2.1.1. Use a sketch or diagram to represent the problem. (2)
1.2.1.2. Solve the problem (3)
1.3. Use the concept of ratio to answer the following questions.
1.3.1. In week 1, Mpho deep cleans a paving at 4 m2 per hour. How long will it take her to deep clean
an area of 12 m long and 6 m wide? (3)
2.1. Technology versus traditional tools for teaching. Which method is better?
Discuss this statement either in support of technology or traditional tools.
(10)
2.2. Do a research on the software that is available in the market today. Choose one that you can use in your
Grade 5 class to teach mathematics. Discuss your choice with the following in mind:
The name of the software.
How it works?
The benefits.
The shortcomings (if any). (10)
1.2.1. Ntsako walks to school each day at a constant pace of 75 m per minute.
The school is 1.8 km from his house.
1.2.1.1. Use a sketch or diagram to represent the problem. (2)
1.2.1.2. Solve the problem (3)
1.3. Use the concept of ratio to answer the following questions.
1.3.1. In week 1, Mpho deep cleans a paving at 4 m2 per hour. How long will it take her to deep clean
an area of 12 m long and 6 m wide? (3)
The advertising alternatives for a company include television, radio, and newspaper advertisements. The costs and estimates for audience coverage are given in the table below:
TV newspaper radio
Cost per advertisement $2000 $600 $300
Audience/advertisemet $100,000 $40,000$18,000
The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?
(a) Formulate the problem above in mathematical model.
(b) Formulate the problem in standard form.
(c) Solve this business problem using the Simplex method.
TV newspaper radio
Cost per advertisement $2000 $600 $300
Audience/advertisemet $100,000 $40,000$18,000
The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?
(a) Formulate the problem above in mathematical model.
(b) Formulate the problem in standard form.
(c) Solve this business problem using the Simplex method.
