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**1 April 2013 **

**1 April 2013**

1) domain: x, Range: y

2) Modulus absolute value is the absolute distance from zero.

3) The usage of completing the square depends on the type of question.

4) When the gradient is less, the graph is steeper.

Random Scribe Thing

Intersection of curve and line

TOA CAH SOH

⬆ The tangent in TOA is not equal to the graph tangent.

Tangent in graphs represent the gradient in the graph. And also as it is the gradient (Rise/Run)

Eg.

x^2-xy+y^2=1 -----(1)

2x-y=k ---------------(2)

First Step: Solve both equations simultaneously.

From (2),y=2x-k -----(3)

Substitute (3) into (1)

x^2-x(2x-k)+(2x-k)^2=1

x^2 -2x^2+kx+4x^2-4kx+k^2=1

3x^2-3kx+k^2-1=0

If Z is an unknown constant, write it in Zx, not xZ as the constant is in front of the variable.

Edit: Note: Flip the inequality sign when you multiply by negative - .

Intersection of curve and line

TOA CAH SOH

⬆ The tangent in TOA is not equal to the graph tangent.

Tangent in graphs represent the gradient in the graph. And also as it is the gradient (Rise/Run)

Eg.

x^2-xy+y^2=1 -----(1)

2x-y=k ---------------(2)

First Step: Solve both equations simultaneously.

From (2),y=2x-k -----(3)

Substitute (3) into (1)

x^2-x(2x-k)+(2x-k)^2=1

x^2 -2x^2+kx+4x^2-4kx+k^2=1

3x^2-3kx+k^2-1=0

If Z is an unknown constant, write it in Zx, not xZ as the constant is in front of the variable.

Edit: Note: Flip the inequality sign when you multiply by negative - .

Logarithms

- The power law of logs do not apply if the power affects the whole log.

Eg. ( log 3) ^2

Exponential Equations

- When an equation seems difficult, simplify it using substitution.

Eg, Logarithms , Algebraic

- Use 'discriminant' instead of b^2 - 4ac.

- Question may use terms a, b or c

- Thus b^2 - 4ac will not equate to the discriminant

- Negative inequalities have to be flipped when both sides are multiplied by negative (exception)

- When question ask for 'show that'

- Find discriminant expression

- Find a range that the discriminant always satisfies

- Link back to question (write 'shown')

- Notes for question 12b

- Expression of discriminant

- Find range of discriminant that is always true

- Link back to question and copy the right question

- Find the range of values by determining the condition of the roots

Write your equation for the graph: (y=)

Once the equation is set, you will see your equation by pressing (trace)

You'll see a blinking cursor, set it to where your zoom's upper-left corner is. (Enter) Then set it to where the zoom's lower-right corner is. (Enter) it would zoom to your desired zoom

For use of both the above, find the left and right bounds, where you think the maxi/mini is. Then make a guess on where the maxi/mini point is. The calc will help find it for you afterwards.

:D :D :D :D

Ways to solve quadratic equations

1) Factorisation

2) Completing the square

3) General Formula

4) Calculator

5) Graph

The (b^2 - 4ac) within the general formula determines the nature of the roots of an quadratic equation.

If (b^2 - 4ac) = 0, one of the roots is 0, the other root will be a real number. (x will have one value)

If (b^2 - 4ac) < 0, both roots are real (x will have 2 values)

If (b^2 - 4ac) > 0, both roots are imaginary or complex number (x will have no values)

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