S4. Mathematics

1. Weight of 4 people in the lift: 36 kg + 42 kg + 53 kg + 70 kg = 201 kg
Further weight that the lift can hold = 350 kg – 201 kg = 149 kg
Weight of Mary = x kg
Weight of John = x + 10 kg
Weight of Yvonne = x - 5 kg
Weight of Mary, John and Yvonne together = x + x + 10kg + x – 5kg = 3x + 5kg
3x + 5kg = 149 kg
3x = 149 kg – 5 kg = 144 kg
x = 144 kg/3 = 48 kg

maximum weight of Mary = 48 kg (Answer)

2.
Doris attempted 18 questions. (20 - 2 unattempted questions = 18)
Let n be the number of correct answers
The number of incorrect answers = 18 – n
Total mark:~ 5 marks x (n) - 2 marks x (18 – n) = 60
5n – 36 +2n = 60
7n = 60 +36 = 96
n = 96/7 = 13.7 (round it off to 14)
For 14 questions correct, total marks = 5(14) – 2(18-14) = 70 -8 = 62
For 13 questions correct, total marks = 5(13) – 2(18-13) = 65 -10 = 55

The minimum number of questions Doris has answered correctly = 14 (Answer)

3. x - 5√x + 6 = 0
Let y = √x
y^2 -5y + 6 = 0
(y – 3)(y – 2) = 0
y = 3 or y = 2
√x = 3 or √x = 2

x = 9 or x = 4 (Answer)

4. √x - 12/√x = 1
Multiply both sides by √x
x – 12 = √x
x -√x – 12 = 0
Let y = √x
y^2 – y – 12 = 0
(y – 4)(y + 3) = 0
y = 4 or y = -3
√x = 4 or √x = -3
Drop √x = -3

x = 16 (Answer)

5. 1/(x-2)^2 + 1/(x-2) - 6 = 0
Let y = 1/(x – 2)
y^2 + y – 6 = 0
(y +3)(y – 2)
y = -3 or y = 2
1/(x – 2) = -3
1 = -3(x – 2)
1 = -3x + 6
3x = 6 – 1 = 5
x =5/3
1/(x – 2) = 2
1 = 2(x – 2)
1 = 2x – 4
2x = 1+4 = 5
x = 5/2 = 2.5

x = 5/3 or x = 2.5 (Answer)

2012-08-20 09:56:09 補充：
Are you the same person as 發問者：hiu lam?

If "Yes", please proofread all the quadratic function questions, otherwise ignore this message.
What does it mean "find the value o k"?
i) Is (α +β )(α - β) correct?
perhaps it is (α +β )(α + β) or (α - β )(α - β) ?