Friday, 30 September 2016

Revision (1) Basic Geometry

For discussion
  1. Fairfield Methodist School EOY Exam 2013 Paper 1 Q13
  2. Fairfield Methodist School EOY Exam 2013 Paper 1 Q14
  3. ACS (Barker) Mid-Year Exam Part 1 Q10
  4. ACS (Barker) Mid-Year Exam Part 2 Q5
  5. SST 2013 EOY Exam Paper 2 Q7
  6. SST 2014 EOY Exam Paper 1 Q7
  7. SST 2015 EOY Exam Paper 1 Q9 


Click HERE to see responses

Revision (2) Data Handling

Discussion for

  • Fairfield Methodist P1 Q20: Tally, Frequency Table, Bar Chart
  • SST 2013 EOY P1 Q8: Dot Diagram; Mean, Median, Mode
  • SST 2014 EOY P1 Q6: Stem and Leaf Diagram; Mean, Median, Mode
  • SST 2015 EOY P1 Q11: Pie chart; Mean, Median, Mode

*Summative Assessment [15 min]

Thursday, 29 September 2016

Revision: Mensuration

For discussion:

  • Fairfield Methodist 2013 P1 Q17
  • Fairfield Methodist 2013 P2 Q5
  • Fairfield Methodist 2013 P2 Q9
  • SST 2014 Paper 1 Q8
  • SST 2014 Paper 2 Q12
  • SST 2015 Paper 1 Q8
  • SST 2015 Paper 2 Q9 - discussion on accuracy of computed answers

Wednesday, 28 September 2016

Revision: Direct & Inverse Proportion

For discussion:
  • SST 2013 P2 Q1: Direct Proportion
  • SST 2013 P2 Q4: Inverse Proportion
  • SST 2014 P2 Q11(a): Direct Proportion
  • SST 2014 P2 Q11(b): Inverse Proportion
  • SST 2014 P2 Q8: Ratio; Direct Proportion

Revision: Algebra (1)

Revison: Algebra (2)

For discussion: 

  • Fairfield Methodist 2013 P1 Q5: Solving Equation
  • Fairfield Methodist 2013 P1 Q9: Substitution*
  • Fairfield Methodist 2013 P1 Q11: Simplifying Expressions
  • Fairfield Methodist 2013 P2 Q3: Factorisation*
  • Fairfield Methodist 2013 P2 Q4: Algebraic Fraction*
  • SST 2013 P1 Q5: Simplifying Expressions; Substitution*
  • SST 2013 P1 Q6: Simplifying Expressions
  • SST 2013 P1 Q10: Comparison of terms
  • SST 2014 P2 Q1: Solving Equation (Fraction)
  • SST 2014 P2 Q2: Application of Special Product*
  • SST 2014 P2 Q3: Factorisation - Identifying common factors
  • SST 2014 P2 Q6: Factorisation - Cross method
  • SST 2014 P2 Q7: Factorisation - Special Product

Thursday, 22 September 2016

Direct Proportion: 3-minute Quiz



Click HERE to see the responses

Understanding: Direct Proportion

[This is a recap of what was carried out in class on 21 Sep]

Through the scenario....

The ice cream vendor sells cones of ice cream at the price of $1.50 per cone. 

The total amount collected = price of 1 cone X number of cones sold
The total amount collected = $1.50 X number of cones sold
Hence, $1.50 is the rate. 

Instead of writing out in words, we let
  • Total amount collected be represented by y
  • Total number of cones sold represented by x
With this, we form the relationship
  • y = 1.5 x (where 1.5 is the rate)
In other words, 
  • when the number of cones sold increases, the amount collected will increase.
  • when the number of cones sold decreases, the amount collected will decrease.
y and x are variables because as one of them changes, the other changes.

1.5 remains constant as it is a fixed value that the vendor priced each cone of ice cream at.

Instead of writing 1.5, we let k to represent this constant value.

Hence, we can generalise the above as: 
  • y = k x (where k is the constant)

Applying what we learnt in the topic, Functions and Linear Graphs,
y = k  will be a linear graph, where k is the gradient and the line passes through the origin! 
Hence, we can represent it as: 








Understanding: Inverse Proportion

[This is a recap of what was carried out in class on 21 Sep]

Through the scenario...

It takes 1 person 100 days to paint a house.

With 2 persons, we will need 100÷2 days.
With 3 persons, we will need 100÷3 days.

Let the number of persons be x and the number of days be y

By tabulating the above scenario, we will get:


Now, to plot the points, we'll get:
[Notice that while the values decrease, the points do not fall on a straight line?]
[In other words, the decrease does not follow equal 'steps' like what we see in the linear graph]


By joining the dots, we get a reciprocal graph with the equation:



A standard reciprocal graph will look like this (appears in both 1st and 3rd quadrant):


Depending on the context - the part of the graph in the 3rd quadrant may not the relevant (e.g. in this case, the number of days and number of people could not be negative).

If we study the relationship carefully, this is an inverse relationship:

Since 100 is a constant value, we represent 100 by k . Hence, the above can be rewritten as:




Inverse Proportion (Examples) Half-Lives of Elements

One approach to describing reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value. This period of time is called the half-life of the reaction, written as t1/2

Source: http://chemwiki.ucdavis.edu/Physical_Chemistry/Nuclear_Chemistry/Half-Lives_and_Radioactive_Decay_Kinetics





Term:
an asymptote (/ˈæsɪmptt/) of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. 

Other interesting read: Nuclear Disaster in Japan