sample question

(1) 

In order to find the height of a tree, some children walk 50 m from the base of the tree and measure the angle of elevation as 10^o. Find the height of the tree.

Reverse percentages

           Reverse percentages

1.  Arham thinks his goldfish got chickenpox.  He lost 70% of his collection of goldfish. If he has 60

   survivors, how many did he have originally?

2. When heated an iron bar expands by 0.2%. If the increase in length is 1 cm, What is the original 

   length of the bar?

3. A one year old car is worth $11250. If its value had depreciated by 25% in that first year, calculate its price when new.

4. A sterio system is sold for $1998 and an 11% profit made. Find the original cost of the stereo.

5. A dealer gains5%  by selling a washing machine for $950. Find the original cost of the washing machine.

6. A dealer bought a second hand car and spent $650 on repairs. He made a profit of 20% by selling the car for $18 650. For how much did he purchase it?

7. By selling a set of Biology books for $408, the book seller suffers a loss of 4%. What was the cost price of the books?

8. A television has a sale price of $180. This is a saving of 25% on the original price. Find the original price.

9. A company increased its productivity by10% each year for the last two years. If it produced 56 265 units this year, how many units did it produce two years ago?

10. This year a farmer’s crop yielded 50 000 tonnes. If this represents a 25% increase on last year, what was the yield last year?

Angles of elevation and depression

Grade 9           Angles of elevation and depression                                                                 work sheet

(1) In order to find the height of a tree, some children walk 50 m from the base of the tree and measure the angle of elevation as 10^o. Find the height of the tree.

(2) A man standing on top of a mountain 1200 m high observes the angle of depression of a steeple to be 43^o. How far is the steeple from the mountain?

(3) A ladder is placed on horizontal ground with its foot 2 m from a vertical wall. If the ladder makes an angle of 50^o with the ground, find (a) the length of the ladder, 

     (b) the height of the wall. Give answers correct to 1 d.p.

(4) The length of the shadow of a vertical pole is 3.42m long when the rays of the sun are inclining at an angle of 40.5^o to the horizontal. What is the height of the pole?

 Give answer to 2 d.p.

X

(5) A boy X can be seen by two of his friends Y and Z, who are swimming in the sea.

40 m

      If the angle of elevation of X from Y is 23^o and from Z is 32^o, and the height of X

      above Y and Z is 40m. Calculate the horizontal distance:

      (i)  between X and Z.                     (ii) between X and Y              

      (iii) between Y and Z.

(6) A radio mast of 30m high is supported by two cables as shown.

      From the diagram:

        (i) find the distance between the two points A and B.

(1) The height of a tower is 15 m. A man looks at the tower from a distance of 120m. What is the angle of elevation of the top of the tower from man?
(2) Find the angle of depression ao of the structure.
(3) The height of a tree is 25 m. The shadow of the tree has a length of 30 m. Calculate the size of the angle marked po in the diagram
(4) A hot air balloon, M, is 900m vertically above a point N on the ground.      A boy stands at a point O, 1200m  horizontally from N.                  (a) Calculate the distance, OM, of the boy from the balloon.                  (b) Calculate the angle MON.
(5) A and B are two villages. If the horizontal distance between them is 12km and the vertical distance between them is 2 km, calculate:      (i) the shortest distance between the two villages,      (ii) the angle of elevation of B and A.
(6) A man at the top of a vertical cliff observes a boat (B) at sea. From the diagram,                 (i) State the angle of depression of the boat from the man.                 (ii) How far is the boat from the cliff?
(7) Two planes A and B are flying directly above each other. A person (P) can see both of them. The vertical height between B and P is 5 km. if the angles of elevation of the planes        from person are 65o and 75o, calculate:        (i) horizontal distance of P from the two planes.        (ii) the vertical distance between A and B.

(8) Two people A and B are standing either side of a transmission mast.

      A is 130m away from the mast and B is 200m away.

      If the angle of elevation of the top of the mast from A is 60^o.

      Calculate

     (i) the height of the mast

     (ii) the angle of elevation of the top of the mast from B.

 (9) A girl standing on a hill at A, overlooking a lake, can see a small boat at a point B on the lake.

 If the girl is at a height of 50m above B and at a horizontal

 distance of 120m away from B, calculate:

(i) the angle of depression of the boat from the girl,

(ii) the shortest distance between the girl and the boat.

# Note : Teachers are required to provide suitable diagrams for the questions

Sequences

TERM:-                                                                                                                                   Grade:-

Week:-                                                                                                                                     Periods:-

LESSON TITLE: Sequence

Period:-1 – 2

                 Lesson Objectives:-

                                                Students will be able to continue the given number sequence

Key Vocabulary:-Sequence, Terms, Pattern, Next term.

Key questions:- 

(i)     What do you mean by sequence?

(ii)   What you mean by pattern?

(iii) How can we find the next terms of a given sequence?

Teacher Activity	Student’s activity
Introduce sequence Give suitable example such as Even numbers sequence, multiples of three numbers sequence, multiples of five numbers sequence. Show the students how to find the next terms of the given sequence.                 Give more example questions for practice.	Listen to the teacher, understand  the meaning of the word sequence and Understand Pattern of numbers sequence given        Finds the next term of the given sequence

Period:-3

                 Lesson Objectives:-

                                                Students will be able to find the Arithmetic Progression and continue the sequence calculate the n^th term of the sequence

Key Vocabulary:- Arithmetic Progression, Common difference, n^th term.

Key questions:- 

(i)     How can you find that a given sequence is an Arithmetic Progression?

(ii)   Give the significance of the word common difference?

(iii)  How can you find the n^th term of tan A.P?

Teacher Activity	Student’s activity
Introduce Arithmetic Progression Show how to find the common difference and find the next term of the sequence and Give suitable example to find the  nth term of A.P and extend this idea to find a particular term of a given sequence.               Give more example questions for practice	Listen to the teacher, understand  the sequence A.P             Find the next three terms, a particular term and the nth term of an A.P

Period:-4 – 5 

                 Lesson Objectives:-

                                                Students will be able to find the next terms of a sequence by applying the First successive difference& Second successive difference method

Key Vocabulary:-First Successive difference, Second successive difference

Key questions:- 

(i)     What is the first successive difference of the given sequence?

(ii)   What is the second successive difference of the given sequence?

Teacher Activity	Student’s activity
Introduce First successive and second successive difference type sequence and Show how to find the successive difference of the sequence and find the next terms          Give suitable example to find the next terms	Listen to the teacher, understand  the significance of the First successive and second successive difference        Find the next three terms  of  the sequence by using the First successive and second successive difference type sequence.

Period:- 6 – 7

                 Lesson Objectives:-

                                                Students will be able to find the sequence idea involved in the diagram pattern and solve problems involving diagrams

Key Vocabulary:- Squares, rectangles, Triangles, Dots

Key questions:- 

(i)     How many triangles are there in the first figure?

(ii)   How many dots would come in the 10 the diagram?

Teacher Activity	Student’s activity
Give Suitable questions to find the pattern in which the given diagrams are arranged Explain how to find the pattern and using it how to find the required solutions           Give more example questions related to real life situations for practice.	Listen to teacher, understand  the significance of the given diagram.       Find the number of dots ,number of squares ext. Draw conclusions.

Materials:-IGCSE Mathematics, Ric Pimentel  and terry Wall Page numbers From 25 to 29

                 Extended Mathematics for IGCSE, David Rayner, Page numbers from 6 to 7

                 Core Mathematics for IGCSE, David Rayner, Page numbers from 42 to 44

Teaching Aids:-  Work sheet, black board.

Evaluation:-   Oral Questions, class Work, Completing class work

Reflection:-

………………………………………..

                                                                         ……………………………………….

                                                                                                                             (Supervisor)

PROPERTIES OF QUADRILATRALS;

LESSON PLAN                          

MATHEMATICS                                                                                 

Term                                                                                                                Grade

Week                                                                                                                          Periods

From :

LESSON TITLE:  PROPERTIES OF QUADRILATRALS;

                               ANGLESUM PROPERTY OF TRIANGLE AND QUADRILATERALS

PRE-REQUISITE KNOWLEDGE:, angle at a point, angle in a straight line and  angles in parallel lines                                              

TEACHING AND LEARNING PROCESS                                               

PERIOD   1 Learning Objectives: Students will be able to                                         Appreciate the properties of quadrilaterals and use them to solve problems
Key Vocabulary:  parallel; diagonal; bisect; quadrilateral; parallelogram; square; rhombus; kite; trapezium
Key Questions: 1.      What are the properties of various quadrilaterals? 2.      How will you use them to solve problems?
TEACHER ACTIVITY	STUDENT ACTIVITY
Explains & Describes properties of quadrilaterals	Understands the properties of quadrilaterals
Explains the questions and helps the students in finding out the solution.	Tries to solve the question and asks if they have any doubt.
Gives more questions for practice and explains the questions so that the student can easily find out the solution using all the concepts	Understands and tries to find out the solution from the method taught by the teacher
Gives some more questions as home-work and some in the weekend assignment	Complete their work and ask the teacher if they have any doubt

                                                                                                                                                                                   

PERIOD   1 Learning Objectives: Students will be able to                                         Solve problems involving angles at a point, angles on a straight line
Key Vocabulary:  point, straight line, sum
Key Questions: 1.      What is the sum angles at a point? 2.      What is the sum of angles on a straight line?
TEACHER ACTIVITY	STUDENT ACTIVITY
Explains & Describes the sum angles at a point and sum of angles on a straight line	Understands the properties to solve problems.
Explains the questions and helps the students in finding out the solution.	Tries to solve the question and asks if they have any doubt.
Gives more questions for practice and explains the questions so that the student can easily find out the solution using all the concepts	Understands and tries to find out the solution from the method taught by the teacher
Gives some more questions as home-work and some in the weekend assignment	Complete their work and ask the teacher if they have any doubt

                                   

PERIOD   1 Learning Objectives: Students will be able to                                         Solve problems involving angles in parallel lines
Key Vocabulary:  alternate, allied, corresponding
Key Questions: 1.      How many angles can be created on parallel lines? 2.      How will you use parallel line properties to solve problems?
TEACHER ACTIVITY	STUDENT ACTIVITY
Explains & Describes alternate, allied, corresponding angles	Understands the properties to solve problems.
Explains the questions and helps the students in finding out the solution.	Tries to solve the question and asks if they have any doubt.
Gives more questions for practice and explains the questions so that the student can easily find out the solution using all the concepts	Understands and tries to find out the solution from the method taught by the teacher
Gives some more questions as home-work and some in the weekend assignment	Complete their work and ask the teacher if they have any doubt

                                                                                                           

PERIOD  5 Learning Objectives: Students should be able to know ·         Sum of interior angles of a triangle is 180˚ ·         Sum of interior angles of a Quadrilateral  is 360˚
Key Vocabulary:   sum of interior angles,
Key Questions: How many triangles can be formed from a quadrilateral simultaneously? What is the sum of exterior angles of a triangle/quadrilateral?
TEACHER ACTIVITY	STUDENT ACTIVITY
Asks the students about triangle and quadrilateral.	Tries to recall a triangle and quadrilateral
Asks about angle sum property of triangle and quadrilateral.	Recall  the angle sum property of triangle and a quadrilateral.
Shows that any quadrilateral can be drawn as combination of two triangles.	Recognize that one diagonal separates a quadrilateral into two triangles.

………………………………………….

                  (Subject Teacher)

percentage and money exchange - Japan

1. Japan's population is estimated at around 127 million.

  (a) Write  Japan's population in standard form

  There are about 136,000 Western expatriates.

  (b) What percentage of the Western expatriates are in Japan?

   About 19.5 percent of the population was over 65 years of age.

  (c) Find the number of people who are below 65.

The Japanese population is rapidly aging as a result of a post–World War II baby boom followed by a decrease in birth rates. A growing number of younger Japanese prefer not to marry or have families. Hence Japan's population is expected to drop to 100 million by 2050 and to 64 million by 2100.

(d) Calculate the expected percentage decrease in population in the year 2050 and 2100.

Japan's legislative organ is the National Diet, a bicameral parliament. The Diet consists of a House of Representatives with 480 seats, and a House of Councilors of 242 seats.

(e) Express the number of House of councilors seats as a percentage of the total number of seats.
........

2. The Asakusa Samba Carnival is held annually, on a Saturday towards the end of August, in Asakusa, Tokyo.  The cost of tickets for Adults     -  350 JPY and Children -  150 JPY

The carnival starts at 7.15 am everyday and closes at 11.30 pm.

2000 Adults and 6000 Children attended on the first day

a) Calculate the amount of money they got by selling the tickets

               (i) To adults                                                                                                                                   

              (ii) To children  

              (iii) The total amount           

  b) Calculate the percentage of the amount of money collected from children.

 c) Convert the above total amount to dollars, if $1 = 80.86 JPY.

 d) Convert the timing to 24 hr clock time.                          

 e) Calculate the duration of the carnival in a day                

 f) Mrs. Carolene has got some dollars with her. How many dollars she has to pay to enter the           carnival along with her two kids. If  $1 = 80.86 JPY