Maths... help!!!

1::: If A(x-1)2 + B(x-1)+C = 2x2 – 7x + 8, find the values of A, B and C.

2::: In a test, a boy obtains 2 marks for each question he answers correctly and loses 1 mark for each question he answers incorrectly. He answers 18 questions and obtains 15 marks. How many questions does he answer correctly?

3::: A wire of length 100 cm is bent into the form of a rectangle. It is found that the area of the rectangle is 504cm2. Find the length and width of the rectangle.


Q1.
A(x-1)^2+B(x-1)+C=2x^2-7x+8
Ax^2-2Ax+A+Bx-B+C=2x^2-7x+8
By comparing like term
A=2
B-2A=-7
B=-7+4
B=-3
A-B+C=8
2-(-3)+C=8
C=3

Q2.
let the number of correct questions be x, the number of incorrect questions be y
2x-y=15------------(1)
x+y=18-------------(2)
(1)+(2),3x=33
x=11
In (2),
11+y=18
y=7

Q3.
let the length be x, the width be y
2(x+y)=100
x+y=50
x=50-y-----(1)
xy=504----(2)
Sub(1) into (2)
y(50-y)=504
0=x^2-50x+504
0=(x-36)(x-14)
therefore, x=36 or 14
y=14 or 36

Q4.
let the present age of John be x,the present age of Tom be y
x-12=y---------(1)
x+12=2y------(2)
(1)-(2),
-24=-y
y=24
x-12=24
x=36

2006-11-15 21:46:25 補充：
^x即是x次方

1. A(x2-2x+1)+Bx-B+C=2x2-7x+8
Ax2+(-2A+B)x+A-B+C=2x2-2x+8
A=2, -2A+B=-7, A-B+C=8
-2(2)+B=-7, 2-B+C=8
B=-3 , 2-(-3)+C=8
C=3

2. Let x be the correct number of question; 18-x be the wrong number of question
2x-(18-x)=15
2x-18+x=15
3x=33
x=11

3. Let x be the length and y be width of the rectangle
x*y=504...............(1)
2x+2y=100...........(2)
From (2), x+y=50, y=50-x.........(3)
Sub (3) into (1)
x*(50-x)=504
50x-x2=504
x2-50x+504=0
x=36 or x=14
For x=36
y=50-36
y=14
For x=14
y=50-14
y=36
Therefore, Length and width are 14cm and 36cm

1.
A = 2
B = -3
C = 3

2.
11

3.
length = 36
width = 14

2.11

3.length:36

width:14

第一條唔識, sorry!