Linear Equation (Graph) reference

posted by Mr Johari

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

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 2 (Gradient) solution

posted by Mr Johari

answers to Linear Graph 2 (Gradient)

Level Test

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

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

posted by Mr Johari
source: http://www.math.com/school/subject2/lessons/S2U4L3DP.html

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.

Maths eLearning Week Kenneth Teh

Sorry Mr Johari for the really later submission. I am truly sorry about it.

Question 1:

I agree with this statement, because a square has 4 sides and 2 pairs of parallel lines, so it is a rhombus. However, a rhombus does not have any perpendicular lines, so it is not a square.

Question 3:

It is a trapezium. The sum of the opposite angles of a trapezium are equal, i agree with that, as the sum of the opposite angles of a trapezium are equal.

Question 5:

Yes it is a parallelogram because the lengths of the opposite sides of BFDE are equal, and thesum of the angles of each side is 180 degrees.

Questions 1, 2 and 4 by Catherine Lim Kai Ting

Q1... 'A square is a rhombus but a rhombus is not a square'.

Technically, that sentence is correct as square has four sides and all four sides have the same length and it is the same for a rhombus except that a rhombus need not be made up of four right-angles (perpendicular lines).

Q2... Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.
- This statement is correct as the meaning of quadrilaterals is a figure with four sides and a square and a parallelogram both have four sides.

B ) Opposite sides of a square and a parallelogram are parallel.
- This statement is also correct as squares are made up of two parallel lines and a parallelogram is also made up of two parallel lines.

C ) A trapezoid has one pair of parallel sides.
- Trapezoid is a type of quadrilateral with a set of parallel line. The other two lines are vertical and diagonal and cannot be considered a second set of parallel line.

D ) All the above

Hence, the answer is D, all of the above.

Q4... 'All parallelograms are squares?' Do you agree with this statement?

No, I do not agree with the statement. Parallelograms is a shape that is made up of two parallel lines which may or may not be of the same length. A square is also made up of two parallel lines but they are of the same length.

:P Sorry for submitting this work late. I hope the answers are right and you are satisfied with them :)

Matthew ... questions 1, 2 and 4

Question 1

Basically all the squares as they have all the properties of a rhombus

2 paris of parallel lines

all the lines are straight Properties of a rhombus

the lines are all of equal length

2 paris of parallel lines

all the lines are straight Properties of a square

the lines are all of equal length

All the angles inside are 90 degrees

so we can consider a square a rhombus since it has all the properties of it but we cannot say that a rhombus is a square as it lacks 1 property of a square.

Question 2

D ( answer )

A is true because a quadrilateral is a figure that has 4 sides.

B is true as you can see in the below diagrams

C is true as shown in the below diagram

Question 4

No I do not agree with the statement as though all squares are parallelograms but not all it cannot be the inverse as the parallelogram lacks 2 of the properties of a square

2 paris of parallel lines

all the lines are straight Properties of a square

the lines are all of equal length

All the angles inside are 90 degrees

2 paris of parallel lines

all the lines are straight Properties of a parallelogram

Abigail Agustines :D

Q1. A rhombus has 4 equal sides, 2 sets of parallel lines, opposite equal acute angles, opposite equal obtuse angles. A square has 4 equal sides, 2 sets of parallel lines and 4 right angles, which are considered as both acute and obtuse angles as they are all 90 degrees. However, not all acute angles are 90 degrees and not all obtuse angles are 90 degrees, as a result, all square are rhombuses but not all rhombuses are square.

Q4. No, all parallelogram is not a square because all of the sides of a square have the same length. At the same time, some parallelograms are rectangles which means not all parallelograms are squares.

Q5. BFED is a parallelogram because it has four sides which are parallel to the line on its opposite side and the angles add up to 180⁰

E-learning 2010

Hi 105-ers,

Welcome back !

I would like to thank the following students for competing your e-learning posting by the given deadline. Appreciate the effort and research behind the thinking process. Some even attempted more than the required number of questions.

Samuel Ong, Alpha, Daniel, Aisyah, Mirza, Wu Shen, Amrit, Vivek,

Kun Yao, Zhixiang, Jonathan, Elijah, Zhi Yong

Keep up the great work.

Question 2, 4 and 5

Q2. My answer is D, as for (a), both the square and the parallelogram have 4 sides, (b)as both the square and the parallelogram have 2 pairs of parallel lines. Lastly, for (c), A trapezoid is the same as a trapezium, thus it also has one pair of parallel side, with the other pair of lines not parallel to each other.

Q4. I disagree with the statement as a parallelogram need not have right angles at all four corners of it, and also does not need to have the opposite sides to have equal lengths.

Q5. It is a parallelogram as BFDE has 4 sides, 2 pairs of parallel lines. As ED is equivalent to AE, and AE is parallel to BF, thus ED is parallel to BF. This confirms that ED and BF are parallel to each other, and also confirming that BE is parallel to FD.

Question 4 and 5 (Add-on) - Elijah Wong

Question 4:
I do not agree with the statement. Squares have 4 equal sides and 2 pair of parallel sides that meet at right angle while a parallelogram do not have 4 equal sides. However, a parallelogram have 2 two pair of parallel sides that do not meet at right angles.

Question 5:
BFED is a parallelogram as it has 4 sides, 2 pair of parallel lines and it has a pairs of angles that add up to 180.

Questions 1, 2 and 3 - Elijah Wong

Question 1:
I agree with the statement. A square is a rhombus as the square has the same/ equal length and are parallel to each other. A rhombus is not a square as it does not have 4 right- angled triangles.

Question 2:
My answer is D. A square and a rhombus has four corners and the interior angles add up to 360° thus, both of themare considered quadrilaterals. Both square and rectangle have 2 pairs if parallel lines. A trapezoid is a four-sided figure with one pair of parallel sides.

Question 3:
The figure is a trapezium as it is the only quadrangle that has two sides opposing with the same length and the the other two with different length. Also. the vertical pairs of angles are a total of 180 degrees. Thus, it is a trapezium.

Questions 1, 2 and 4 - Jonathan Then

Question 1 - Yes.

A square is a rhombus as it is a quadrilateral with four equal sides.

But there are rhombuses which are not squares because their angles are not right angles.

Question 2 - D

A square is a regular quadrilateral. It has 4 equal sides.

A parallelogram is a quadrilateral. It has two pair of parallel lines.

A square has 4 equal sides so the opposite side are parallel.

A parallelogram has two parallel lines.

Trapezoid is a four sided figure with one pair of parallel line.

Trapezoid

Question 4 - No, I don't.

All squares are parallelograms, but not all parallelograms are squares.

If all parallelograms are squares, the parallelogram must have equal sides.

Question 1,2,3,4,5 by zhixiang

Q1. A square is a rhombus because the sides of the square and the rhombus are the same length and its is parallel to each other. A rhombus isn't a square because it doesn't have to have 4 right angles.

Q2.All of the above. A quadrilateral is a shape with 4 sides,which is true for both squares and parallelograms. The length and position the sides of the two shapes have makes it parallel to its opposite. A trapezoid has one pair of parallel side

Q3. The figure is a trapezium because it is the only quadrangle that has two sides opposing with the same length and the the other two with different length and vertical pairs of angles are a total of 180 degrees.

Q4.No, all parallelogram is not squares as all sides of a square have the same length. And some parallelograms are rectangles so not all parallelograms are squares.

Q5.BFED is a parallelogram because it has four sides which are parallel to their opposite side and their supplementary angles add up to 180⁰

Question 1, 3, and 4 by Mirza

Question 1, 3, and 4 by Mirza

Q1

The statement is right. A square is a rhombus as it has 4 equal sides, all the sides are parallel to the opposite side. But a rhombus is not a square as the sides are not perpendicular.

Q3

The figure is a trapezium. A trapezium has a set of parallel lines which means the two opposite angles will add up to 180 degrees. The other pair of lines that is not equal in length is the top and the bottom of the trapezium.

Q4

No, a parallelogram does not have equal sides. A parallelogram also do not have angles of 90 degrees unlike a square.(perpendicular lines)

Question 1, 3 and 4 by Tay Kun Yao

Question 1:
Rhombuses don't have right angles at the vertices but squares do.
Thus, rhombuses are not squares.

Question 3:
A trapezium.
The opposite angles add up to 180⁰ , there's only one pair of opposite sides that are parallel and the length of one opposite sides are different while the other is the same. Thus, it should be a trapezium.

Question 4:
Not true.
Parallelograms are also rectangles and rhombuses and rectangles and rhombuses aren't squares. Thus, the statement 'All parallelograms are squares' is false.

Vivek's Answers to Activity 3

Question 3:
The object is a Trapezium as a trapezium has a set of parallel lines so the horizontal and vertical pairs of angles are a total of 180 degrees as they make U shape figures.

Question 4
Not all parallelograms are squares as all sides of a square have the same length This does not apply to parallelograms as they can have different sets of lengths. Yet you cannot say that non of the parallelograms are squares as they can have the same length for all their lines.

Question 5

ED=BF so through this we can shift ED towards AE. We will be able to see that They are actually parallel lines. This is because the length in between the lines is always the same so they will never touch each other.

We know that the distance between the 2 lines are the same because ED is half the length of AD and BF is half the length of BC because as parallel lines they are supposed to be the same length across. So half of both of them are the same.

Maths E-learning

Q1. A Rhombus and Square needs to have four equal sides but a Square also has to have four right angled conners. That of which some Rhombi do not fulfill. Therefore not all Rhombi are squares.

Q3. The figure is a trapezium because it is the only quadrangle that has two sides opposing with the same length and the the other two with different length.

Q4. Not all Parallelograms are Squares because not all Parallelograms have four right angles. One example is in Picture 2

Question 1, 2 and 4 by Wu Shen

Q1) A square is a rhombus because the sides of the square and the rhombus are the same length and its is parallel to each other. However, a rhombus is not a square because the angles are not 90 degrees.

Q2) The figure is an isosceles trapezium. The right and left side of the isosceles trapezium is equal length and the top and bottom of the isosceles trapezium is parallel to each other. If one of the angles at the bottom is added with one at the top, it will be 180 degrees

Q4) No, all parallelogram is not squares. Parallelograms are squares only if all four sides are of the same length and all interior angles are 90^o.

Question 1, 3 and 4 by Aisyah Binte Mazlan

Q1) A square is a rhombus because all four sides of a square are equal in length. A square and a rhombus are both parallelograms with all the sides equal. However, a rhombus is not always a square, because the internal angles of a rhombus might not always be 90 degrees each.

Q3) The figure is a Trapezium. A Trapezium has two opposite lines that are parallel to one another, and two that are not. In the figure described, the two sides that are equal in length are the sides that are not parallel to each other, while the parallel lines are not the same length.

Q4) A square is a parallelogram because both pairs of opposite sides are parallel with each other. A square and a parallelogram both have parallel opposite sides. However, a parallelogram is not always a square, because the internal angles of a parallelogram might not always be 90 degrees each.

Q 1,2 and 4 done by Daniel and Alpha

Q1)A square is a rhombus because it has sides of equal length and they are all parallel to the opposite side.A rhombus is not a square because although it has sides of equal length and sides parallel to the opposite,there are no right angles.(90 degrees)

Q2)All of the above.A quadrilateral is a shape with 4 sides,which is true for both squares and parallelograms.Squares and parallelogram have sides that are parallel to the opposite as any quadrilateral without both pairs of sides being parallel is a trapezium.The only quadrilateral with just one pair of parallel lines is the trapezium.Any quadrilateral without any parallel lines is not a quadrilateral.

Q5)Parallelograms have the top and bottom pair shorter than the left and right pair.Sides of opposite sides also are parallel in a parallelogram.If the shape is slanted and meets the following requirements,the shape is a parallelogram.

Question 5,Samuel Ong

BFED is a parallelogram because it has four sides and the supplementary angles add up to 180 degrees.

Question 4,Samuel Ong

I definitely do not agree with the statement:All

View image on Bing

 are squares.

The definition of a parallelogram is when a figure has four sides.

A rectangle,rhombus,trapezium all have four sides,which makes them a parallelogram.

View image on Bing

View image on Bing

Question 3,Samuel Ong

The figure is a TRAPEZIUM. 

View image on Bing

As u can see, the side lines are equal in length while the top and the bottom ones are not.

Question 2,Samuel Ong

Answer: A and B only. C is not because the trapezoid can vary if its lines are parallel .

A. They are both quadrilaterals because they have four sides. 

View image on Bing

View image on Bing

B. As you can see,the diagram above clearly shows that statement B is true.

Question 1, Samuel Ong

Because a square has 4 right angle and a rhombus doesnt have to have 4 right angles it just has to have 4 congruent sides.

elearning 2010 : Everyday Quadrilaterals

posted by Mr Johari
Learning Objective (Activity 2)

In this learning activity, you will demonstrate your understanding of the properties quadrilateral by identifying objects around us that exhibit these shapes.

Instructions

1. Choose 2 out of the 3 special quadrilaterals - parallelogram, trapezium and kite.
2. Find objects at home that exhibit the shape of these 2 selected quadrilaterals.
3. Take a photo of each object and post them on the Wall Wisher at the class Maths blog

Graphing softwares (please follow up)

Hi 105ans

Happy 45th National Day.

To update you on the happenings in SST Maths scene next 2 weeks.

Week 7

next week we will be having our e-learning lesson from Wednesday to Friday. Do check out the Maths activities on Geometry.

week 8

Ensure that you have NetLogo, TINspire and Geogebra working effectively in your learning device as we will be using them in week 8 for graphing purposes. Should you encounter any problems do inform the SST Apple Centre.

Linear Graph - Cartesian Plane

posted by Mr Johari

The following activity focuses on Cartesian Plane and the coordinate system.

Go through the following link:

Cartesian Plane and complete the worksheet provided by your Maths teacher.

ICT Linear Equation

posted by Mr Johari
This activity is an introduction on function, algebraic equation involving x and y and graphical representation of linear equation.
Approach: Individual or pair work using ICT graphical tools (Grapher or Geogebra)
Resource: ICT Linear Equation worksheet.

Task 1
Complete the given worksheet
section 1, 2, 3 and 4 and answer the corresponding questions given.

In a nutshell:
A. section 1: general for y=a
observation: horizontal straight lines and parallel to each other. No slope and all lines pass through the y-axis according to given equation. eg. line of equation y=2 passes y-axis at 2. The lines do not meet (intercept).

B. section 2: general for x=b
observation: vertical straight lines and parallel to each other. since the lines are all vertical the slope cannot be defined (no value can be given). The lines pass through the x-axis according to the given equation. eg. line of equation x= 4 passes x-axis at 4.

C. section 3: general for y=mx + c, c=0
observation: diagonal straight lines (or lines at an angle) that all converge or meet at the origin (the point where the x-axis meets the y-axis). Henc
e c refers to the point where the lines meet the y-axis (in this case c=0). When m is negative the lines slope downwards (bottom left to top right) and when m is positive the lines slope upwards (top left to bottom right). m is also known as the slope or gradient (refer to geographical concept of slope / gradient of rise and run)

D. section 4: general for y=mx + c
observation: diagonal lines as in section3 but m remains the same (m=2) but the lines meet the y-axis at different values. all lines are parallel (because m=2) but intersect (meet) the y-axis according to the value of c. i.e. if y=2x+4 the slope is positive and the y-intercept (where it meets the y-axis) is at 2.

E. section 5: general for y=mx + c
observation: diagonal lines as in section3 but c remains the same (c=1). The lines have the same intersection point (i.e. meet the y-axis at y=3) but have different slope or gradient.

Conclusion

Task 2
Refer to the link on Graph (by GCSE Bitesize) to learn by graphical representation and plotting.
activity 1: learn about coordinate system

Leading questions for you to answer (post in your comment):
reference: Cartesian Plane and Descartes

1. what is a Cartesian Plane?
2. what is ordinate? abscissa? what is the significance of (x,y)
   
3. give an example of a practical use of coordinate system (provide links to examples)
4. a student was posed with the following problem 'A man Jim has twice the amount of money than his friend Lemin - present the above information as an equation in x and y and show a graphical representation of this equation'. show graphically how much will Lemin has if Jim has $4000.

Task 3

In the following task, you are required to use Geogebra.

You are provided with the graph of y against x.
A linear graph has been plotted with the equation unknown.
Please comment on the following:
(1) the shape of the graph
(2) the possible equation of this linear graph (other than y=2x)