VCE Methods Question Thread!

[snowisawesome]

The polynomial f(x) = 2x^3 + ax^2 - bx + 3 has a factor of x+3. When f(x) is divided by x-2, the remainder is 15.
Find a and b

f(-3) = 0
2(-3)^3 + a(-3)^2 - b(-3) + 3 = 0
-54 + 9a + 3b + 3 = 0
9a + 3b = 51 (equation 1)

f(2) = 15
2(2)^3 + a(2)^2 - b(2) + 3 = 15
16 + 4a - 2b + 3 = 15
4a - 2b = -4 (equation 2)

using simultenous equations, I found that a = 30 and b = 62, but the answers said that a = 3 and b = 8

Is there is a mistake in my working?

[RuiAce]

The polynomial f(x) = 2x^3 + ax^2 - bx + 3 has a factor of x+3. When f(x) is divided by x-2, the remainder is 15.
Find a and b

f(-3) = 0
2(-3)^3 + a(-3)^2 - b(-3) + 3 = 0
-54 + 9a + 3b + 3 = 0
9a + 3b = 51 (equation 1)

f(2) = 15
2(2)^3 + a(2)^2 - b(2) + 3 = 15
16 + 4a - 2b + 3 = 15
4a - 2b = -4 (equation 2)

using simultenous equations, I found that a = 30 and b = 62, but the answers said that a = 3 and b = 8

Is there is a mistake in my working?

According to Wolfram, you used the remainder and factor theorems correctly but stuffed up the simultaneous equations.

[Lear]

Using substitution -

2b=4a+4 (2)
b=2a+2

Sub into (1)
9a + 3(2a+2)=51
9a+6a+6=51
15a=45
a=3

b=2a+2
b=8

Hope it helps

[snowisawesome]

Thanks guys

Silly question, but is (-x)^4 = x^4
and is 2(-x)^3 = -2x^3

[chooby]

Thanks guys

Silly question, but is (-x)^4 = x^4
and is 2(-x)^3 = -2x^3

Yep! Both correct. WIth negative bases, if the exponent is even, the product would be positive and if the exponent is odd, the product is negative.

[snowisawesome]

Thanks chooby

Does anyone know if methods sacs from my school before 2016 are still similar to the current study design and are ok to use for revising for sacs?

[kalopsia]

Thanks chooby

Does anyone know if methods sacs from my school before 2016 are still similar to the current study design and are ok to use for revising for sacs?

The methods course is still pretty similar to the old study design, just with a few new things added in (eg. sampling) and a few things taken out (eg. transition matrices). So, you can definitely use old sacs for revision.

[snowisawesome]

The methods course is still pretty similar to the old study design, just with a few new things added in (eg. sampling) and a few things taken out (eg. transition matrices). So, you can definitely use old sacs for revision.

Thanks
Do you by any chance know the difference between a test sac and an application sac?

[kalopsia]

Thanks
Do you by any chance know the difference between a test sac and an application sac?

There isn't much difference. A test sac is probably what you're used to (eg. topic test). Your Unit 3 SAC will be an application task. An application sac can be described as a longer sac, over 1-2 weeks, 4-6 hours long, and will cover several areas of study. In our school our application task was a 4 hour sac hold over three days, consisting of 2 one hour parts and one two hour part.

[snowisawesome]

There isn't much difference. A test sac is probably what you're used to (eg. topic test). Your Unit 3 SAC will be an application task. An application sac can be described as a longer sac, over 1-2 weeks, 4-6 hours long, and will cover several areas of study. In our school our application task was a 4 hour sac hold over three days, consisting of 2 one hour parts and one two hour part.

Thanks

Do you know when solving a log equation whether you include the negative value of x in the answer or only the positive value of x?

[Sine]

Thanks

Do you know when solving a log equation whether you include the negative value of x in the answer or only the positive value of x?

sub in your prospective solutions into the initial equation and check which one's work

[snowisawesome]

sub in your prospective solutions into the initial equation and check which one's work

If it's on exam 1, how hard will the numbers be generally?

[Sine]

If it's on exam 1, how hard will the numbers be generally?

from experience pretty simple. They should be whole numbers or very nice fractions (e.g. 1/2, 1/3 etc). Generally solving log equations is a exam 1 question anyway.

[skrt skrt]

Hi people, just need help with this reflection question.  Its question 10 in chapter 3B for the Cambridge Methods book.
state a transformation which maps the graph of y = f(x) to the graph of y = f1(x):

e) f(x)= 1/4x^2   ,  f1(x)=1/x^2


Answer is dilation of a factor of 2 from the y-axis

 

[Lear]

If i’m not mistaken I believe it’s a dilation of factor 4 from the x axis.