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

$300.

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.

1 個解答

評分
  • 土扁
    Lv 7
    9 年前
    最愛解答

    1.

    a)

    Weight of John = (x + 10) kg

    Weight of Yvonne = (x - 5) kg

    b)

    36 + 42 + 53 + 70 + x + (x + 10) + (x - 5) ≤ 350

    3x + 206 ≤ 350

    3x ≤ 144

    x ≤ 48

    Maximum weight of Mary = 48 kg

    =====

    2.

    a)

    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

    b)

    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.

    =====

    3.

    a)

    i)

    The curve opens up.

    ii)

    The coordinates of the vertex = (3,4)

    iii)

    The axis of symmetry : x - 3 = 0

    b)

    i)

    The curve opens down.

    ii)

    The coordinates of the vertex = (-5, 0)

    iii)

    The axis of symmetry : x + 5 = 0

    =====

    4.

    (a)

    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

    (b)

    Number of possible outcome = 6

    P(B+tea) = 1/6

    =====

    5.

    Expected value

    = $20*(3/12) + $50*(4/12) + $100*(5/12)

    = $(63 and 1/3)

    資料來源: 土扁
還有問題嗎?立即提問即可得到解答。