sir, could you please do out the full Q. 12 on 2.6 because I dont understand it at all?
The full solution to Q.12 using the quicker method (method 1) is uploaded. Using the alternative method the steps are identical to Curve D solutions:
Roots: x= -2 and x = 6
Function in terms of factors: h(x) = k(x+2)(x-6)
h(2) = k(2+2)(2-6)=4
h(x)= (-1/4)(x^2 -4x -12)
Complete square form: h(x) = (-1/4)(x^2 -4x +4 -4 -12)
h(x) = (-1/4)( (x-2)^2 -16)
h(x) = -1/4(x-2)^2 +4
ie: a=-1/4, p=4, q=2
I mean a = 1/4 (in last line)
sir, what's the answer to that question? The back of the book says p=16 for curve C
Thank you for this.
The book answer is incorrect for curve C. It has multiplied the correct answer by 4 which doesn't affect the solutions but does change the function. The test is to input x = 2 which should give an output of y = 4. This is true in my solution (uploaded) but not in book solution.
sir will we need to know quadratic and linear questions in context?
sir could you help me with 2.10 Q 1 i am really stuck
The solutions to this question are included in the 2.10 questions uploaded from class:
sir could you do 2.1 question 6 please
Solution uploaded in latest blog
is there any topic we dont need to do
i mean any execise in chapter 2 thats not on the test
I would like students to be familiar with everything in Chapter 2 at this stage.
in Q 1 2.10 i dont understand where the K came from
never mind got it
k is the "multiplier". There are an infinite number of cubic equations that have the roots x = -1, x = 1 and x = 3 as in part (i). The specific function is the factors multiplied by the specific multiplier. The value of k is found by the constraint that is contains another specific point other than the roots in part (i) we know that it contains (0, 3) i.e. if we input 0 it will give us an output of 0. This means that k=1 so now we know that this curve is 1 multiplied by the factors.
sir would you be able to do Q.17 page 88 advanced revision exercise please
This is the same as Q5 in the first test as in Blog 6-11-2013 . (linked below)
Part (iv) the image of the curve in the x-axis is the negative of the first answer: i.e. f(x) = -2x^3 + 24 x^2 -90x + 100
Part (v) is found by noticing that the reflected roots in the y-axis would be x= -2, x= -5 and x= -5 giving factors (x + 2)(x +5)(x +5) with the multiplier remaining n=2 since the reflection doesn't rescale of stretch the curve....
You're very welcome
Is there anything on chapter 2 we dont need to know? In the last test we didnt need to know section 2.4 and 2.3. Do we need to know them for this test?
Test is on whole chapter