O-Level Additional Math

[Concerndad]

(6r-7t)(3q-2s)+(2s-3q)(3r-2t)

=(6r-7t)(3q-2s)-(3q-2s)(3r-2t)
=(3q-2s)[(6r-7t)-(3r-2t)]
=(3q-2s)(6r-7t-3r+2t)
=(3q-2s)(3r-5t)

Rgds,
Concerndad

[suiyuan]

Secondary Two Maths


Hi

Solve this equation
(x-2)^2 = 3(2x-3)(2-x)

(x-2)^2 means (x-2) to the power of 2.

Please help.

Thank you.

[PiggyLalala]

suiyuan:

Secondary Two Maths


Hi

Solve this equation
(x-2)^2 = 3(2x-3)(2-x)

(x-2)^2 means (x-2) to the power of 2.

Please help.

Thank you.

(x-2)^2 = 3(2x-3)(2-x)
(x-2)^2 = -3(2x-3)(x-2)
(x-2)^2 + 3(2x-3)(x-2) = 0 ( note: (2-x) = -(x-2)
(x-2)[(x-2) + 3(2x-3)] = 0
(x-2)[ x- 2 + 6x -9] = 0
(x-2)( 7x - 11) = 0
x- 2 = 0 or 7x - 11 = 0
x = 2 or 11/7

[FrekiWang]

suiyuan:

Secondary Two Maths


Hi

Solve this equation
(x-2)^2 = 3(2x-3)(2-x)

(x-2)^2 means (x-2) to the power of 2.

Please help.

Thank you.

(x-2)^2-3(2x-3)(2-x)=0
(x-2)^2+3(2x-3)(x-2)=0 (note that -(2-x)=+(x-2))
(x-2)[(x-2)+3(2x-3)]=0
(x-2)(7x-11)=0
x=2 or x=11/7

[JadeDry]

hometutors.sg:

JadeDry:

I currently use \"New Syllabus Mathematics\" (8th Grade) books, and would appreciate if you could recommend additional good quality publications.


Thanks in advance.

A good tutor / mentor would be able to select what is good for the student.

Thank you for your time.

I have just finished:

Secondary one Mathematics Tutor: 1A and 1B.

Shinglee New Syllabus Mathematics 6th edition 1

and Singlee Mathematics Workbook 1.

I am homeschooled and have been studying singapore math from 1st grade, since my parents are my teachers I would like to see what you people think I should get for 8th Grade.

Thank you in advance for your assistance.

[suiyuan]

Sec Two Maths


1) Given that x^2 = 5x – 1, find the value of 2x^4 + 2/x^4

2) a)Factorise 2x^10 – 13x^5 -15 completely.
b)Factorise 10x^10y – 65x^5y-75y

Note a) ^2 means to the power of 2 b) 2/x^4 means 2 divided by x^4

Please help.

Thank you

[CoffeeCat]

suiyuan:

Sec Two Maths


1) Given that x^2 = 5x – 1, find the value of 2x^4 + 2/x^4

2) a)Factorise 2x^10 – 13x^5 -15 completely.
b)Factorise 10x^10y – 65x^5y-75y

Note a) ^2 means to the power of 2 b) 2/x^4 means 2 divided by x^4

Please help.

Thank you

Do you happen to be from some IP school or sth?
Your teacher probably koped qns 1 from SMO.

Qns 1)
Lousy Method : solve for x, substitute and torture yourself in the process.
Proper Method : divide the quadratic equation by x throughout to get
x + 1/x = 5
You will get x^2 + 1/x^2 = 23 by squaring the above.
Repeat the process one more time.
Final ans should be 1054 if I have no calculation error.

Qns 2a)
Notice 10 is twice that of 5. hence imagine you substitute y=x^5. You will reduce the problem to factorising a quadratic expression.

Qns 2b)
Ambiguous.......Please use brackets.
10x^10y means 10x^(10y) or 10(x^10)y

Since it's part b, i will assume the latter.
First extract common factors from all terms, which is just 5y. After that what you have should be part a.

[JadeDry]

Hello again, I have a problem that I am unsure about:


Simplify the following expression:

3/4((x squared)(y)) X 5/9((x)(z cubed)) / ((20/9)(x quadrupled)(y squared)(z))

These are my workings:
3/4((x squared)(y)) X 5/9((x)(z cubed))=

15/36((x cubed)(y)(z cubed))


15/36((x cubed)(y)(z cubed)) / ((20/9)(x quadrupled)(y squared)(z))=

3(Z squared) / 16(xy)

Are my calculations correct?

On a side note, is Z cubed/ Z= Z squared or Z cubed?

Thanks in advance.

[suiyuan]

Sec Two Maths


Find the smallest possible value of the expression 3x^2 + 27y^2+5z^2-18xy-30z+125.

Note a) ^2 means to the power of 2

Please help.

Thank you

[FrekiWang]

suiyuan:

Sec Two Maths


Find the smallest possible value of the expression 3x^2 + 27y^2+5z^2-18xy-30z+125.

Note a) ^2 means to the power of 2

Please help.

Thank you

Note that
3x^2-18xy+27y^2=3(x^2-6xy+9y^2)=3(x-3y)^2
5z^2-30z=5(z^2-6z)=5(z^2-6z+9-9)=5(z^2-6z+9)-45=5(z-3)^2-45

So the original express is
(3x^2-18xy+27y^2)+(5z^2-30z)+125
=3(x-3y)^2+5(z-3)^2-45+125
=3(x-3y)^2+5(z-3)^2+80

Since the square of any number is non-negative (0 is the smallest possible), the minimum value of the whole expression is 80.

PS: A bit too much for a sec 2 student, probably from one of the top schools?