Wednesday, 27 April 2016

Assignment 7.3 Solving Equations - Word Problems

Click HERE to access the answers presented by Abigail, Jeffrey and Zhenghang.

In particular, for Q4 (Speed), look out what Abigail does before she tackles the question.

In the following video clip, Mr Dean Ang described how he would identify and extract the information systematically and place them in a simple diagram that helps us to visualise and answer the question. 

For Q4, go straight to TIME: 8:10

Tuesday, 26 April 2016

SDL (02) Revision: Rate & Speed (Q1) The Traveller's Route

Instructions
Refer to the Handout and attempt the task on writing papers.
Remember to label the parts and show your working clearly.

Eunice is driving from Singapore to Malacca, Malaysia.




Eunice is driving from Singapore to Malacca, Malaysia. She leaves Singapore Woodlands checkpoint at 08 30 and travels the first 60 km of the journey at an average speed of 25 m/s and the next 120 km at an average speed of 80 km/h. She stops at Muar for a 30-minute break before continuing the last part of her journey at an average speed of 90 km/h in 35 minutes.

(a) Convert 25 m/s to km/h. [1]
(b) What time does she reach Muar? Give time in the 24h notation. [3]
(c) Find the average speed for its entire journey, giving your answer in km/h. [3]


SDL (02) Revision: Rate & Speed (02) The Singapore Flyer

Instructions
Refer to the Handout and attempt the task on writing papers.
Remember to label the parts and show your working clearly.

At a height of 165m, Singapore Flyer is one of the world’s largest Giant Observation Wheel and also one of Asia’s biggest tourist attractions.



The diameter of the Singapore Flyer measures at 150 metres, and it travels at an average speed of 0.24 metres per seconds. 

(a) Express its average speed in km/h

(b) How long (in minutes) does it take for the flyer to complete one revolution?

(c) The company is promoting the "dining capsule" concept, inviting people to dine in the capsule. If the meal lasts for one hour, how many revolutions would the diner have gone through for his meal?

Additional information

Circumference of Circle = 2 π r   where r is the radius and use π = 3.142


Sources:
Video clip: Youtube https://www.youtube.com/watch?v=bt-9iRriklI
Information: http://www.singaporeflyer.com/about-us/fun-facts-about-the-flyer/

Monday, 25 April 2016

SDL (02) Revision: Ratio (Q2) Precious Gold

Instructions
Refer to the Handout and attempt the task on writing papers.
Remember to label the parts and show your working clearly.


By mass, Yellow Gold 18K is made up of 75% of Gold (Au), 15% of Silver (Ag) and the remainder is made up of Copper (Cu), by mass.

(a) Find, by mass, Au : Ag : Cu, giving your answer in the simplest form. [1]

(b) A goldsmith is tasked to make a piece of jewellery with Yellow Gold 18K. With 2.25g of Silver, how much of gold and copper would be needed to form the alloy? [2]

(c) If this piece of jewellery is to be melted into liquid alloy
(i) Find is the volume of the alloy. [3]
(ii) Compare the volume with that of a 15g of pure 24 carat gold, which has a greater volume – Yellow Gold 18K or 24 carat gold? [2]

Given that the density of Gold is 19.3 g/cm3, Silver is 10.49 g/cm3 and Copper is 8.92 g/cm3.

Source: http://www.gold.org/jewellery/about-gold-jewellery


Watch the following clip for background info that would help you understand the context of the question better:

Mass, volume and density are related by an equation: density = mass ÷ volume




SDL (02) Revision: Ratio (Q3) Fresh Lemonade for all

Instructions
Refer to the Handout and attempt the task on writing papers.
Remember to label the parts and show your working clearly.



Ms Lee, the Sports & Wellness teacher, is going to conduct a fresh juice making class in the “Eat Healthy, Live Healthy” week. She is going to teach participants how to make fresh lemonade, with reference to a recipe available at https://www.sunkist.com/recipes/fresh-lemonade/

Find out, from the website, the amount of ingredients that Ms Lee needs to prepare for each participant, enough to make the beverage for 4 servings.

(a) Express the ratio of lemon juice, water and sugar in its simplest form. [2]

(b) If only 10 cups of lemon juice are available, what is the maximum number of participants that Ms Lee can have for the workshop if she needs to ensure every participant has the same amount of ingredients for the workshop? [1]

(c) Based on the constraint she has in (b), how much water and sugar does she need for her workshop? [2]
 You may check your answer at the website.

(d) If Ms Lee wants to prepare enough lemonade for all participants (not including herself), find out from the website how much of each type of ingredients she needs. [1]


Source: https://www.sunkist.com/recipes/fresh-lemonade/

Sunday, 24 April 2016

[Something Interesting] Generating infinite number of RATIONAL numbers

You will be introduced to 2 ways to generate infinite number of rational numbers!
Learn about the Stern-Brocot numbers!



[Something Interesting] PRIMES: Are there infinite number of prime numbers?

The video attempts to explain there are infinite number of prime numbers out there?
Let's watch the 'proof' (by contradiction) - which you would be able to appreciate that more when you do higher Mathematics :)

At 4:55, you will learn how prime numbers are defined even before algebra was introduced to the mathematical world. Something that is easy to understand :)




Tuesday, 19 April 2016

[19 April 2016] What we did this morning and preparation for next lesson

Today, we did the following in class:

1. Worksheet on solving simple equations with one unknown
In total, we saw 6 formulae.
In each formula, the relationship of the variables are presented as an equation.

Click HERE to access the discussed solution (by Elise; as well as the suggested solution)

2. 5-min Quiz on Algebra: Substitution 
Click HERE to access the worked solution presented by Daniel and Nadia.
There is a difference in presentation.



Homework

2 handouts on Factorisation are given to you:
  • Revision for Common Test - Go through p1. Need not do the rest. We will select questions for discussion
  • Self Practice 3: Factorisation of Quadratic Expressions - It is about Factorisation using Cross Method. You may check your answer against the copy uploaded in the GoogleSite
In addition, do bring along 2013 ad 2014 Common Test Papers for discussion on Thursday.





Monday, 18 April 2016

[18 April 2016] Today's lesson focus was... Solving Equations for Word Problems

The focus of the lesson is to learn how apply the knowledge and skills we learnt in Algebra to solve word problems. You should have noted down the proper way to present the working in your study notes.

Homework

Complete the worksheet that was given this morning.

Remember to:
  • Define the unknown with a variable
  • Form an equation
  • Conclude your answer with a statement
Click HERE to access worksheet

For submission, remember to attach the worksheet to your answers.








Linear Equations & Formulae: 8-minute Quiz 1

1. Attempt the following questions on writing paper. 
2. Write your name, register number and class.
3. Copy the Heading "Linear Equations: 8-minute Quiz 1".
4. Copy the Question before writing out your answer.





Half of the class scored 9 out of 9, that means 50% of the class has more or less mastered the skills to manipulate algebraic expressions to solve equations.
Click HERE to access the worked solution (by Lucaas).




Saturday, 16 April 2016

[15 April 2016] Homework and Preparation for next week

(A) Homework 
  • Assignment 7.2
(B) Getting ready for next week
We'll select questions from the previous year's papers for discussion. You should attempt all the questions.
  • 2013 Common Test Papers
  • 2014 Common Test Papers
(C) What's up next week?
  • Revision and Discussion on Factorisation
  • Going through self-directed learning materials on Ratio, Rate, Speed
  • Discussion of previous years' papers
  • Time-Revision - 2015 Common Test Papers

Solving Equations involving algebraic fractions

Watch the examples (patiently) to recall the steps (and strategies) to solve equations involving algebraic fractions.



Challenging Question 2: Solving Equations



Among the 11 submissions, Alex, Peng Kiang, Nadia and Emmanuel Chew managed to form the equations and find the answer. However, they missed out an important step: To define the algebra expression for the numerator and denominator before forming the equation.


Below is the working by Alex:



Below is the complete presentation by Jeffrey:






Challenging Question 3: Solving Equations


This question is an example of how a problem can be solved using different methods. This includes by "Guess and Check" (in a systematic way). However, if you read the question carefully, it requires us to use algebra - form an equation using the information available and solve for the unknown.

4 correct entries received...

1. Sian Yin's working shows that the question can be solved using "Guess and Check" method. However, it did not fulfil the requirement of the question


2. Jonathan attempted to present the expression (representing the number) in a "number" form. However, we are unable to 'reason' this 'form' out mathematically. He managed to form the expressions to form each side of the equation; however, did not form the equation that is the requirement of the question.


3. Peng Kiang's answer is correct and his working flows. However, he did not describe how he arrived at the 2 expressions. As a result of skipping the steps, one might find it difficult to follow-through and make meaning out from the first step.



4. Jeffrey's working shows the various steps clearly: Defining the numbers (using the variable y), forming the equation and solving it systematically.


Solving Equations: Assignment 7.1 Tier B (Q7, Q8)

Assignment 7.1 Tier B Q7

Below are two ways to explain why there are 2 possible x values in this case:


The above can be illustrated in the graph as shown below:




Assignment 7.1 Tier B Q8



Friday, 15 April 2016

[15 April 2016] Strategy to solve Equations (with Algebraic Fractions)

Today's lesson focused on solving equations involving algebraic fractions.

We discussed the strategies and how to apply them in a systematic manner to solve such equations. With other examples, we also discussed that there are more than one way to approach the questions.


We also selected questions in Lesson 4 (Study Notes: p8, p9).
You can check against the suggested working in the previous post: Click HERE to access.

With this, you should be able to work on Assignment 7.2


Tuesday, 12 April 2016

[12 April 2016] Challenging Question 1 - Linear Equations

17 submissions were received this morning and almost all of you managed to get the answers correct. However, many of you did not express the information clearly in algebra (which is expected). In addition, many of you included the unit (cm) in the equation. This caused confusion (whether the letter represents a variable or unit).

Remember:

  • Express the information in an equation
  • Write a word/ statement to describe what you are finding (e.g. Perimeter, Area) to add meaning to the string of numbers
  • Check to write the correct unit at the end of the presentation


Working for (a), submitted by Emmanuel Chew




Working for (b), submitted by Clarence








[12 April 2016] Linear Equations

Today's lesson started with the application of 2 important formulae that are related to triangles, where you learnt more about the conditions required when applying the Pythagoras' Theorem.

You would have solved the problem (during lesson) and found the answer to be 30 metres.


Solving Linear Equations: Divide & Conquer

This task is assigned as Homework of today (12 April 2016).

Everybody will need to attempt all the questions.
The following groups will be responsible to contribute the answer (including working) to the class:

  • Group 1: Collection A
  • Group 2: Collection B
  • Group 3: Collection C
  • Group 4: Collection D
  • Group 5: Collection E
  • Group 6: Collection F
Post your answers in the slides by tomorrow (13 April 2016)


Study Notes (Lesson 3) Solving Linear Equations (I)

[7 April 2016] Algebra - Challenging Question 01

Have you tried?


Click HERE to access the suggested answers.
Look out! There are 2 ways to attempt this question.



[10 March 2016] Algebra - Challenging Questions

Below are the proposed worked solutions...

For (a), four sets of correct answers were received.

  • Emmanuel Chew, Jeffrey and Abigail's working were pretty similar, except that Abigail only started 'cancelling' the common terms after she 'converted' the operation, ÷ to x.
  • Look out for Jonathan's working, the line just before arriving at the final answer (i.e. 1). He applied the law of indices to sum up the powers. Well done!


by Jonathan


by Emmanuel Chew


by Jeffrey


by Abigail




For (b), two sets of correct answers were received.

  • Abigail's working is more systematic and the steps are clearly presented.
  • Jeffrey's working came with hidden steps that sometimes one might have difficulty figure out how he arrived at the next line.


by Abigail


by Jeffrey








[12 April 2016] Algebra - Challenging Question 06

Submission by Jeffrey



[Challenging Question 3] Equations - Reasoning out Answers systematically


Monday, 11 April 2016

Making connections across the topics

Equations that changed the World: Do you know anyone of them?

Click HERE to find out more...




Application of "Meaningful" Equation (i.e. Formulae)

Dear S1-01

This morning, we started the topic, Linear Equation, which is built on Algebra. From the diagram (which Elrond will post "above" this post), we saw how the different skills and concepts learnt in algebra will be applied in this topic, and subsequent topics.

In the introduction example, you notice that we substitute values into an equation to find out the unknown values. The 'storyline' can be developed into a word problem, that demonstrates the application of equations in real world.

Key Ideas 
Formulae are meaningful equations.
Equations/ formulae describes relationship between variables (which we will look in greater depth).

We will learn techniques to solve equations (i.e. to find out the unknown variables, usually denoted by x). That is where we carry out the balancing act (i.e. to balance the equation through addition/ subtraction/ multiplication/ division).


Click HERE to access the Health Promotion Board website
Click HERE for the BMI Calculator


Source: Health Promotion Board, Singapore website (http://www.hpb.gov.sg/)

Study Notes (Lesson 2) Solving Linear Equations (I)

Sunday, 10 April 2016

[Exploration] How do "THEY" look like?

On Friday's class discussion, you were introduced to Trigonometric functions, tan x, cos x and sin x . As mentioned, this is beyond the S1 syllabus but it's to give you a heads-up of what it's coming to you in Secondary 2:

This is how the graph, tan x looks like:
Do you notice where the graphs are trying to reach out to (at both ends)?



Similarly, we make a connection between the "factorised" terms and the graphs?

Below are some examples. Do you notice that when you express the quadratic expression into an equation (such that it is equal to zero), the answers will give the "roots" (i.e. where the curve cuts the horizontal axis).

Reference: Assignment 4.7

Set A: Questions 1 & 3













Set B: Questions 2 & 6











Friday, 8 April 2016

[8 April 2016] Getting Ready for Next Week

Dear S1-01

We have completed the unit on Algebra Factorisation today.
On next Monday, we'll start on the new topic, Linear Equations.
This topic builds on what you learnt in Algebra.

To start off this unit,

1. Remember to watch the video lessons (refer to the post below) to understand the concept behind balancing equation - this was assigned two days ago.

2. Refer to the textbook:

  • Read Worked Example 1 (p115)
  • Attempt "Practice Now 1" (p116)
  • Read Worked Example 2 (p116)
  • Attempt "Practice Now 2" (p117)
  • Read Worked Example 3 (p117)
  • Attempt "Practice Now 3" (p118)


Solving Equations through Games!

Remember to Post the screenshot of the score to the Group Padlet. 
You can put up the best score - deadline for submission: Saturday, 9 April 2016





Preparation for the GAME:

  • Writing Papers, Pencil/ Pen
  • Calculator
Do a Screenshot of your final score and post it to the Padlet that belongs to your group.