Linear Graph/Equation (Quiz4/5 solution)

Posted by Mr Johari

Quiz 4 (Solution)

Quiz 5 Solution

VIVA SEETO Q1,8,12

CAT 1 Q1



CAT2 Q8


CAT3 Q12

VIVA GWENDOLYN Q

CAT1Q3

GEometry 5 (Review Self Practise)

posted by Mr Johari

FINAL ASSESSMENT

posted by Mr Johari

Please refer to Mathematics Department Googlesite for information on your Final Assessment.

SECONDARY ONE END OF YEAR EXAMINATION

1. Format

• 2 Papers
• Paper 1 – 60 minutes
• Paper 2 – 1 hour 15 minutes
• Calculator is allow for both papers
• Students are required to bring along all necessary stationery including mathematical instrument sets
• No borrowing of stationery is allow during the examination

2. Topics tested

• Chapter 1 – Factors and Multiples
• Chapter 2 – Real Numbers
• Chapter 3 – Approximation and Estimation
• Chapter 4 – Introduction to Algebra
• Chapter 5 – Algebraic Manipulation (Include Expansion of Quadratic expression, Use of Algebraic rules in Expansion and Factorisation of Quadratic expression, Factorisation of Quadratic expression using Cross-Multiplication method)
• Chapter 6 – Simple Equation in One Unknown
• Chapter 7 – Angles and Parallel Lines
• Chapter 8 – Triangles and Polygons
• Chapter 9 – Ratio, Rate and Speed
• Chapter 10 – Percentage
• Chapter 11 – Number Pattern
• Chapter 12 – Coordinates and Linear Graphs (Include calculation of Gradient using 2 coordinates point, Equation of a straight line )
• Chapter 16 – Data Handling (Include Mean, Mode and Median)

GEometry 5 (Polygon)

posted by Mr Johari

Task 1: Complete the worksheet on Polygon given in class. Use the slides below as reference. You could also use the info from ACE Learning

Task 2: Attempt the Quiz questions from ACE Learning on Polygon (angles)

Polygon Notes

View more presentations from acavis.

Understanding Properties of Different types of Polygons

Great Polygon Powerpoint

View more presentations from Sandra Harris.

VIVA See Toh Q1, Q12

Viva Voce, Category 1, Question 1 Click here > http://www.youtube.com/watch?v=ch_quFMFKww

Viva Voce, Category 3, Question 12 Click here> http://www.youtube.com/watch?v=VsTSuEi6sxg

Hardy's Viva Voice 2010

Category One, Question Five: Click here!
Category Two, Question Six: Click here!
Category Three, Question Thirteen: Click here!

Note: Sorry, I made a mistake for Category Three, Question Thirteen. I typed the intro wrong.

VIVA JIA LE Q5, 10, 15

CAT1Q5, CAT2Q10, CAT3Q15

VIVA BENJAMIN FHENG Q2, 6. 15

CAT1Q2, CAT2Q6, CAT3Q15

VIVA JUNWEI Q

ViVA STACEY Q5, 10, 15

CAT1Q5, CAT2Q10, CAT3Q15

ViVA JOHANAN Q2, 7, 11

CAT1Q2, CAT2Q7, CAT3Q11

ViVA GOH JUN HONG Q4,7,11

CAT1Q4, CAT2Q7, CAT3Q11

ViVA MICHELLE Q3,10,13

CAT1Q3, CAT2Q10, CAT3Q13

ViVA CHRISTOPHER Q1,7,11

CAT1Q1

CAT1Q7

CAT3Q11

ViVA YU CHONG Q1,8,11

CAT1Q1

CAT2Q8

CAT3Q11

ViVA RAYNER Q2,7,11

CAT1Q2, CAT2Q7, CAT3Q11

VIVA Niklaus Teo Q2, 6 and 11

VIVA Lee Si Yuan Category 3: Question 14

VIVA Lee Si Yuan Category 2: Question 8

VIVA Lee Si Yuan Category 1: Question 1

ViVA NAVEENA Q3,7,15

CAT1Q3, CAT2Q5, CAT3Q15

ViVA TIM Q3,8,11

CAT3Q1

ViVA CHERIN Q2,8,11

CAT1Q2

CAT2Q8

CAT3Q11

ViVA JONAN Q5,8,11

CAT1Q5,8 & 11

ViVA PRESTON Q5,8,13

CAT1Q5

CAT2Q8

CAT3Q13

VIVA VOCE 2010 (EDITED please read)

posted by Mr Johari

Viva Voce
Linear Equation / Expression
INSTRUCTION:

You are required to complete a viva voce assessment. This is a reinforcement of familiar activity based on topics covered in class. This will also helped you with your revision process. You should not take more than 1 hour to complete the entire exercise.

Task
The instruction, questions and assessment rubric can be downloaded from your class Maths googlesite under VIVA 2010.
Your task is to select any 3 questions, one from each category (1, 2 and 3) and record your explanation.
Your explanation must be concise, relevant and clear.
You may use any suitable multimedia platforms for this. Ensure that the file is not too large for uploading or posting.

Grading
Grading will be based on
Part 1: Problem Solving Skills and Strategies
Part 2: Concept and Mathematical Communication

Submission and Deadline
Please post your videos in your Class Maths Blog or upload to youtube and post the link in the comments.

Name your videos/posts using the header VIVA name category question eg. VIVAJohariCategory1Question1 by 10 October 2010

All the best - its the mathematical precision that we are looking for ...

for your reference

Geometry 4 (summary)

posted by Mr Johari

source: http://www.craville.110mb.com/maths

Summary 1

Point, Ray, Line, Segment, Angles etc

Geometry Vocabulary

View more presentations from Jeniah Jones.

Summary 2

Angles, Parallel Lines, Polygons

Geometry

View more presentations from Kristen T.

Application of Geometry (in the real world)

Geometry in the Real World

View more presentations from Connor Johns.

geometry 3

posted by Mr Johari

Task 1
Find the definition of the following
(a) line bisector
(b) angle bisector


Task 2
Watch the following videos and learn how a line is bisected
Video 1


Video 2


Task 3
Complete the worksheet on CONSTRUCTION.

(a) TASK 1: To construct: an angle of 60°.

(b) TASK 2: To construct: the angle bisector of a given angle.

(c) TASK 3: To construct: A line through R perpendicular to PQ.

(d) TASK 4: To construct: A line through R parallel to PQ.

(e) TASK 5: To construct: A line 3 cm from PQ and parallel to PQ.

Geometry 2

posted by Mr Johari

source: e-learning Mathematics activity
Task 2

Now go to 102 Maths blog and comment on the posting by the students on the following question:
Please follow the appropriate protocol in giving comment:
.1 no malicious comment
.2 must be responsible for your own comment - identify yourself
.3 focus on the process and answer not the person

.4 focus on the concept and the explanation given - check clarity and understanding

work to comment on
a. Lionel
b. Goh Jia Sheng

c. Idris

d. Karan

e. Benz Kew

f. Tay Kun Yao

g. Elijah Wong

reference: Properties of Quadrilateral

Recapitulation of Questions posted for your reference
Choose either 1: Question 2 or Question 3 or Question 4

Question 2:
Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.
B ) Opposite sides of a square and a parallelogram are parallel.
C ) A trapezoid has one pair of parallel sides.
D ) All the above

Question 3:

A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides equal in length, the other pair not equal in length, and a pair of opposite angles that are supplementary1. Identify this figure, and justify your answer with reasons.

' sum of two angles equals 180degrees'

Question 4:
‘All parallelograms are squares?’ Do you agree with this statement?
Justify your answer with example/s.

Geometry 1

posted by Mr Johari

Objectives:

the definition of points, segment, ray and plane

A. Task (odd numbered index only)

working independently and using the wall-wisher ACTIVITY 1 identify the a) attributes & characteristics and b) the symbol/notation used for

1. point

2. lines

3. segment

4. ray

5. plane

Objectives:

the fundamental angle properties.

B. Task (even numbered index only)

working independently and using the wall-wisher ACTIVITY 2 identify the following angle properties (please include a diagram to illustrate your responses)

1. complementary angle

2. supplementary angle

3. angles at a point

4. vertically opposite angles

5. corresponding angles

6. internal angles

REVIEW: The following video shows the differences between a right, acute, obtuse and straight angle.

Angles and Parallel Lines 1

posted by Mr Johari

source: GCSEBitesize

Task:

An angle can be defined as two rays or two line segments having a common end point. The endpoint becomes known as the vertex. An angle occurs when two rays meet or unite at the same endpoint.


1. How may degrees are there in one full turn?

2. Imagine you are facing North. You turn clockwise through 90 degrees. Which direction are you facing now?

3. Imagine the capital letter M. What letter does it look like when it's rotated 180 degrees?

4. An angle less than 90 degrees is known as ...

5. An angle between 90 degrees and 180 degrees is known as ...

6. If two of the angles inside a triangle are 90 degrees and 50 degrees, what is the third angle? What angle property/properties did you use in you reasoning?

7. Are the lines in the capital letter L parallel or perpendicular?

8. Will two parallel lines ever cross? Why?

Post your answers under comment:

linear Inequality (Intro)

posted by Mr Johari

source: Connections

Introduction to Linear Inequalities

• Suppose you have a gift card for $100 to an electronics store and want to spend it on CDs and DVDs. You want a special-edition DVD that costs $24.99, and the CDs you want are all on sale for $11.99 each. Assuming that you use only the gift card and you are going to buy the DVD, what is the maximum number of CDs you can buy?
• You know you can buy at least one CD. What about two CDs? It can be time consuming to keep checking.
• Suggest ways to solve this problem.

• Post your solution to Nur_Johari_SALLEH.s109inequality12010@blogger.com

Algebra: Revision (Algebraic Fraction)

posted by Mr Johari

ALGEBRAIC FRACTION

Revision:

Solving Equa

Video 1: Solving Multi-Step Equations with Fractions


Video 2: Solving Equations with Fractions


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Linear Graph (worksheet 12B)

posted by Mr Johari

LINEAR GRAPH

Solution to WORKSHEET 12B − GRADIENTS & LINEAR EQUATIONS


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linear Graph resource

posted by Mr Johari

LINEAR GRAPH

reference of Linear Equation. (click here)

• Focuses on
• What is linear equation?
• Plotting and Table of Values
• Slope / Gradient of a Line
• Slope and y-intercept (how to form a Linear Equation)

linear Graph worksheet (Equation) solution

Linear Graph (Equation of Line)

posted by Mr Johari

Worksheet focuses on the following concept:

• gradient of line
• intersection with both axes (i.e. x-intercept and y-intercept)
• sketch of line

Linear Graph worksheet (Gradient) solution

Linear Graph (Gradient of a Line)

posted by Mr Johari

reference on Linear Equation, Gradient, intercepts.

Slideshare on Linear Equation

Supplementary Worksheet on Linear Graph

This worksheet focuses on the concept of gradient

Please refer to hard copy of the worksheet given to you earlier.

Level Test

Level Test Term 3

posted by Mr Johari

Level Test

As mentioned at the beginning of the term, the Mathematics level test will be conducted in week 10.

Detail will be as follows:

Duration: 40 minutes

Topics tested:

• Introduction to Algebra [chapter 4]
• Algebraic Manipulation [chapter 5]
• Simple Equations in one unknown [chapter 6]
• Coordinates and Linear Graph (sketching of graph, concept of equation of line and gradient) - [chapter 12]

linear Graph part 2

Linear Graph (Chapter 12)

posted by Mr Johari

source: http://www.math.com/school

This is a supplementary note that focuses on linear equation:

Part 2: Graphing Linear Equation (Exercise)

Complete the 2 exercises, state your answers as comments. Where possible justify your answers with simple working.

Question 1: focuses on the linear graph of the form y = mx + c
Question 2: focuses on the characteristics of the linear graph.

[Coordinate, gradient/slope, intercept, equation]

Linear Graph part 1

Linear Graph (Chapter 12)

posted by Mr Johari

source: http://www.math.com/school

This is a supplementary note that focuses on plotting of a linear equation:

Part 1: Graphing Linear Equation

Method 1: Given linear equation, plot the graph.

Technique: Using plotting points and coordinates. (i.e. identify any points for x and find corresponding values of y for plotting)

Method 2: Given linear equation, plot the graph.

Technique: Using gradient and y-intercept

Form the general linear equation ie. y=mx+c, where m is the gradient and c is the y-intercept.

Exercise: (for self practice - answer provided)

Given a linear line, find the equation of the line.

Questions 1, 2, 3, 4 and 5 by Victor Ang

Question 1
Based on the above conversation discuss, with examples and justification whether the following statement is justified.
'A square is a rhombus but a rhombus is not a square'.
Ans: A square is a rhombus but a rhombus is not a square. A square is a special type of rhombus, it is a quadrilateral which has all four sides the same length and opposite sides are parallel while it is a polygon with all four sides closed up and each of its four internal angles are right angles. So a square is a type of rhombus just like a banana is a type of fruit.

Question 2
All the above
A square and a parallelogram are quadrilaterals. They both have four sides.
Opposite sides of a square and a parallelogram are parallel. They have one pair of parallel side if not they are not considered trapezoid any more.
A trapezoid has one pair of parallel sides. A trapezium has only one pair of side which are parallel and the other two are not.

Question 3
It is a trapezium. The two opposite sides that are not equal are parallel and a pair of opposite angles are supplementary.

Question 4
I do not agree with the statement. Parallelograms are like a fruit and squares are banana. A banana is a fruit but a fruit is not part of that banana, just like a square is a parallelogram but a parallelogram is not a square.

Question 5
The reason is that BF and ED are of equal length and are parallel.

Activity 3 By Johanan Teo

Question 1:

A square is a rhombus but a rhombus is not a square

A square has 4 equal sides so it can be called a rhombus. However, a rhombus does not have four right angles thus it cannot be called a square. 

Question 2 :

Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

The answer I have chose is D. (All of the sentences are correct)

A square and a parallelogram are in the group called quadrilaterals which has four sides and their inside angles add up to 360 degrees. 

Opposite sides of a square and a parallelogram are parallel.

And a trapezoid has one pair of parallel sides. ( In the picture )

Question 4 :

All parallelograms are square. Do you agree with this statement?

No. I do not agree with this statement as a square has to have four right angles but a parallelogram may or may not have four right angles and thus not all parallelograms are square.

Question 1:     
Read through the conversation between a mentor and a student. 
Mentor:     Does anyone recall or know what we call it when 2 lines run side-by-side and never cross?
Student:    Yes. Lines like that are called parallel lines.
Mentor:     Great! We've already learned that quadrilaterals have how many sides? 
Student:    Four.
Mentor:     That's right and we call quadrilaterals with parallel sides parallelograms.
Student:    But, how can all the sides be parallel if a quadrilateral is a polygon and is all closed off? 
Mentor:      Great thinking! I guess what I should have said is that a parallelogram has two pairs of opposite sides that are parallel, like this:

Student:     Oh, so the top is parallel to the bottom and the sides are parallel to each other. I understand now!

Mentor:      Good. Now I want to tell you about a special kind of parallelogram. It's called a rhombus. A rhombus is a parallelogram, but all four sides have the same length.
Student:     So a rhombus is a type of parallelogram just like a banana is a type of fruit.
Mentor:      Right, we should not say that all parallelograms are rhombi, just like we don't say that all fruits are bananas.

   Question for discussion

Based on the above conversation discuss, with examples and justification whether the following statement is       justified.

'A square is a rhombus but a rhombus is not a square'.

I believe that this statement is true. A rhombus is a figure that has opposite sides that are parallel to each other. A square happens to fall in that category. However a square must have all internal angles at 90 degrees before it can be called a square. However, not all rhombuses have 90 degree corners, so not all rhombuses can be a square.

Question 2:

Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

The correct statements are: D

A is correct as both the square and the parallelogram have 4 sides, and a quadrilateral figure has 4 sides. Thus, this statement is correct. 

B is also correct as it is a fact that the opposite sides of a square and parallelogram are parallel. 

C is also correct as it is also a fact that a trapezoid has a pair of parallel sides. 

Since all the statements are correct the correct statement is D. 

Question 3:

A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides equal in length, the other pair not equal in length, and a pair of opposite angles that are supplementary¹. Identify this figure, and justify your answer with reasons.

This figure is a trapezium. A trapezium fits the description. It could have a pair of opposite sides that are equal in length, and it also could have another pair which are not equal in length. The other quadrilateral figures do not fit this description as all of the figure's opposite sides are equal in length, with the exception of the kite. The trapezium also has a pair of opposite angles that are supplementary. Since the trapezium fits this description the best, the figure should be the trapezium. 

Done by: Lee YuChong S1-09 (17)