Graphs of Standard Functions
(Recap)
Functions are relations
- one to one linear graph
- many to one
- one to many (y^2=x)
- many to many (x^2/a^2 + y^2/b^2 =1) eclipse graph
Functions must be
- logical
- reliable
- reasonable
- predictable
How to test for function (graphically)
- vertical line test
cut once: is a function
cut more than once: not a function
--------------------------------------------------------
Linear
- y=kx
- k is the gradient passes through origin
- k>0, sloping up /
- k<0, sloping down \
|k| modulus/ absolute value
- taking the numerical value of k
Quadratic
as |k| increases, the graph becomes narrower
Reciprocal
inverse proportion : y=k/x => xy=k
2 ---(reciprocal)-----> 1/2
when x increase, y decreases
what are values that
x cannot be? -> x≠0
y cannot be? -> y≠0
k cannot be?-> k≠0
At values where x and/or y do not exist, there will be asymptote.
asymptote - a line that continually approaches a given curve but does not meet it at any finite distance.
Wednesday 27 March 2013
Wednesday 13 March 2013
Wednesday 6 March 2013
Notes from 7MARCH2013 math class ._.
Reflection type of error (EMAIL TO MRS SIN)
(a) concept
(b) carelessness
(c) lack of practice
-blank out
-shortage of time
50 words: what are you going to do?
FIY:
(A-MATH)
Mean: 52.03% ≠16
Median: 53.33% ≠16-17
(a) concept
(b) carelessness
(c) lack of practice
-blank out
-shortage of time
50 words: what are you going to do?
FIY:
(A-MATH)
Mean: 52.03% ≠16
Median: 53.33% ≠16-17
6th March Lesson Summary - Discriminant (Wed) -Darren
Lesson Summary for 6th March Wednesday - Discriminant
Remember that in the formula:
y = a(x-h)^2 + k
H = to the x-intercept
&
K = to the y-intercept.
And remember the flow chart that if your 'a' must be equal to 1 before u continue the 'completing the square' hence, you must factorise the 'a' first, to put the coefficient outside of the bracket so you could have the remaining of a=1 and carry on the 'completing the square' to solve the equation.
\
Also remember these few important key points in this chapter.
Sorry for the bad quality photos XD Keep practicing the applications of these formulas and ull do well. Just understanding is not enough! Hope this is helpful. All the best for the results for the rest of your tests! :D
y = a(x-h)^2 + k
H = to the x-intercept
&
K = to the y-intercept.
And remember the flow chart that if your 'a' must be equal to 1 before u continue the 'completing the square' hence, you must factorise the 'a' first, to put the coefficient outside of the bracket so you could have the remaining of a=1 and carry on the 'completing the square' to solve the equation.
Also remember these few important key points in this chapter.
Sorry for the bad quality photos XD Keep practicing the applications of these formulas and ull do well. Just understanding is not enough! Hope this is helpful. All the best for the results for the rest of your tests! :D
Monday 4 March 2013
5/3 Lesson Summary
Labels:
lesson summary
HOMEWORK DUE
• Wednesday (6/3): A02d
• Friday (8/3): A02e
– Prepare $12.50 for Math TYS. This will be bought for collectively as a class.
– If you wish to know your A/E-math results for this Level Test, please email Mrs Sin (yeo_chuen_chuen) about it, stating your name, class and index number :)
* Complete pg 154 - 155 of Math notes. You should have finished the graph sketching in class.
Write down the Completed Sq of each graph/function.
Quadratic Equations and Graphs
1. Identifying when to use SUM & PRODUCT of ROOTS (α, β)
- when part of the function has more than two unknowns (refer to pg 153: x^2 +x(2-k)+k = 0), use sum & product of roots.
- find sum (-b/a) > find product (c/a) > form eqn from sum > form eqn from product > solve via simultaneous and quadratics
* refer here.
2. Quadratic Roots Identities – α, β
(α + β) ² = α² + 2αβ + β²
(α – β)² = α² – 2αβ + β²
α² – β² = (α + β)(α – β)
α² + β² = (α + β) ² – 2αβ
QUADRATIC EQUATION CAN ALSO BE WRITTEN AS:
x² – (SUM OF ROOTS: b/a) + (PRODUCT OF ROOTS: c/a) = 0
3. Properties of Quadratic Graphs
1. Intersect x-axis at 0, 1, 2 points
2. Symmetrical in the line y=k, where k is the y-coordinate of vertex (turning point)
3. Always has a y-intercept at c.
4.
Sandy (06) to take over tomorrow's lesson summary & math homework updates!
DIS IS IFF
30Point8FM.
• Wednesday (6/3): A02d
• Friday (8/3): A02e
– Prepare $12.50 for Math TYS. This will be bought for collectively as a class.
– If you wish to know your A/E-math results for this Level Test, please email Mrs Sin (yeo_chuen_chuen) about it, stating your name, class and index number :)
* Complete pg 154 - 155 of Math notes. You should have finished the graph sketching in class.
Write down the Completed Sq of each graph/function.
Quadratic Equations and Graphs
1. Identifying when to use SUM & PRODUCT of ROOTS (α, β)
- when part of the function has more than two unknowns (refer to pg 153: x^2 +x(2-k)+k = 0), use sum & product of roots.
- find sum (-b/a) > find product (c/a) > form eqn from sum > form eqn from product > solve via simultaneous and quadratics
* refer here.
2. Quadratic Roots Identities – α, β
(α + β) ² = α² + 2αβ + β²
(α – β)² = α² – 2αβ + β²
α² – β² = (α + β)(α – β)
α² + β² = (α + β) ² – 2αβ
QUADRATIC EQUATION CAN ALSO BE WRITTEN AS:
x² – (SUM OF ROOTS: b/a) + (PRODUCT OF ROOTS: c/a) = 0
3. Properties of Quadratic Graphs
1. Intersect x-axis at 0, 1, 2 points
2. Symmetrical in the line y=k, where k is the y-coordinate of vertex (turning point)
3. Always has a y-intercept at c.
4.
Sandy (06) to take over tomorrow's lesson summary & math homework updates!
DIS IS IFF
30Point8FM.
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