F.4 Math Ex.
Please to sove the following questions.
1. The weight of Mary is x kg. John is 10kg heavier than Mary while
Yvonne id 5kg lighter than Mary.
a) Express the weights of John and Yvonne in terms of x.
b) Mary, John and Yvonne are going to enter a lift in which there are 4
people of weights 36 kg, 42 kg, 53 kg and 70 kg respectively. Suppose
the maximum load of the lift is 350 kg, find the maximum weight
of Mary such that the lift will not be overloaded.
2. There are 100 coins in a bag. n of them are &5 conins and the rest are
$2 coins. It is known that the total amount of these coins is greater than
a) Find the least value of n.
b) If the number of $5 coins is doubled and the number of $2 coins is
halved, determine whether the total amount of these coins will exceed
$400 or not. Explain your answer.
3.For each of the following quadratic functions, find
i) the direction of opening
ii) the coordinates of the vertex,
iii) the axis of symmetry
of its graph.
a) y = 2(x-3)^2 + 4
b) y = -(x+5)^2
4.A fast food shop provides three different sets of lunch A, B and C.
Customers who order a lunch set can have a cup of coffee or tea for free.
Roger chooses a lunch set and a drink at random
a) Use a tree diagram to list out all the possible outcomes
b) Find the probability that Roger orders lunch set B and a cup of tea
5. A wallet contains three $20 banknotes, four $50 banknotes and five $100
banknotes. A banknote is drawn from the wallet at random. Find the expected
value of the banknote drawn.
- 土扁Lv 79 年前最愛解答
Weight of John = (x + 10) kg
Weight of Yvonne = (x - 5) kg
36 + 42 + 53 + 70 + x + (x + 10) + (x - 5) ≤ 350
3x + 206 ≤ 350
3x ≤ 144
x ≤ 48
Maximum weight of Mary = 48 kg
5n + 2(100 - n) > 300
3n + 200 > 300
3n > 100
n > 100/3 » 33.33
Since n is an integer, the least value of n = 34
Total amount of coins
= $[5*(2*n) + 2*(1/2)*(100 - n)]
= $(10n + 100 - n)
= $(9n + 100)
Since n > 100/3, then
9n + 100 > 9(100/3) + 100
9n + 100 > 400
Hence, the total amount of thesecoins will exceed $400.
The curve opens up.
The coordinates of the vertex = (3,4)
The axis of symmetry : x - 3 = 0
The curve opens down.
The coordinates of the vertex = (-5, 0)
The axis of symmetry : x + 5 = 0
The tree firstly has 3 branches : A, B and C.
A : A+coffee, A+tea
B : B+coffee, B+tea
C : C+coffee, C+tea
Number of possible outcome = 6
P(B+tea) = 1/6
= $20*(3/12) + $50*(4/12) + $100*(5/12)
= $(63 and 1/3)資料來源： 土扁