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# F.3 maths(20分) 超urgent

1. It is given that x ≤(less than or equal to) -2 and 3x+y=1.

(i) Express x in terms of y.

(ii) Represent the range of values of y by an inequality.

(iii) Represent the solutions of the inequality obtained in (ii) graphically.

2. The value of a flat dropped by 15% during the first half of 2005. If the percentage change in the value of the flat over the whole year is 2%, what is the percentage change during the second half of the year?

3.A bag contains 2 black balls and 3 balls of colours red, orange and green. Two balls are drawn from the bag at random.

a) Tabulate all the possible outcomes.

b) Find the probability that

(i) one orange ball and one green ball are drawn,

(ii) at least one ball drawn is black.

4.The sum of the digits of the ones and the tens of a two-digit number is 8 and this two digit number is less than 40. Then let x be the digit of the ones in the two-digit number. Represent the range of values of x by an inequality.

5. A circular target has a radius of 35cm. The three outer rings are of equal widths while the bull's eye is a circle of radius 5 cm. Jack throws a dart randomly at the target and hits it. What is the probability that

(a) he does not hit the bull's eye?

(b) he hits the white region of the target?

Thanks a lot~~~

### 1 Answer

- 1 decade agoFavorite Answer
1.

(i) 3x+y=1

3x = 1-y

x = (1-y)/3

(ii)

x <= -2

(1-y)/3 <=-2

1-y <=-6

1<=y-6

7<=y

2. Let V be the value of the flat at start of 2005,

price of the flat at middle of 2005 is P * (1-15%)

price of the flat at tne end of 2005 is P * (1+2%)

percentage change at the 2nd half of 2005

= P(1+2%)/P(1-15%)-1

=102%/85%-1

=20%

3. (a)

BB

BR

BO

BG

RB

RO

RG

OB

OR

OG

GB

GR

GO

b(i) possibility are OG & GO, so probability is 2*1/5*1/4=1/10

(ii) possibility that none of ball are black is either

one red + one orange, or

one red + one green, or

one orange + one green

and from b(i), probability of each of them is 1/10,

so probability of at least one ball is black = 1- 3/10 = 7/10

4. Let x be the digit of the ones in the two-digit and y be the digit of the tens of the two-digit number.

x+y = 8 (or y = 8-x)

y*10 + x <=40

(8-x)*10 + x <=40

80-10x + x <= 40

40 <= 9x

x >= 40/9 (i.e. 4.44...)

since x must be an integer, so we can also write it as x>=5

also since y is the tenth digit of the two-digit number, it must at least 1,

so x <= 7, i.e.

5<=x<=7

5.

(a)

Target size = pi * 35 * 35

bull eye size = pi * 5 * 5

probability he hit the bull eye = (pi *5 * 5) / (pi * 35 * 35) = 1/49

(b)

I assume "white region" is the outmost circle

white region size = pi * 35 * 35 - pi * 25 * 25 = 600 *pi

probability he hit the white region = 600 * pi / (pi *35 * 35) = 24/49