Mathematics F.1 急快10

1) Write down the general term

Tn = n/(n + 1)

2) The charges of organizing a birthday party at a restaurant include a rental of $50 and the charges for snacks which are $5 per person. Let x be the number of participants and $y be the total charges.

(a) Is y a function of x? Explain.
y is a function of x, This is a linear equation y = 50 + 5x
When you draw a vertical line, it only cuts the line once. i.e. There is only one value of y for one value of x. That is a function.

(b)Express y in terms of x.
y = 5x + 50

(c)Find y when x=10.
y = 5x + 50
  y = 5(10) + 50 = 100
y = 100

(d)Find x when y=125.
y = 5x + 50
125 = 5x + 50
5x = 125 – 50 =75
x = 75/5
x = 15

3) Edward ran from Hong Kong to Guangzhou at an average speed of 4 km/h and then ran back at 3 km/h. If he spent a total of 91 hours for the trip, what is the distance between Hong Kong Guangzhou?(only need answer)

Answer. The distance is 156 km

4) One number is 18 greater than another number. If the smaller number is subtracted from three times the greater number, the result is 78. Find the sum of the two numbers

Let small number be x and large number be (x + 18)
3(x + 18) – x = 78
3x + 54 – x = 78
2x = 78 - 54
2x = 24
x = 12
x is the small number, the big number is 12 + 18 = 30
The sum of two numbers = 12 + 30 = 42

2<二次方
5) If a triangle has height (10-2x) cm, base 9cm and area (7-x) cm, find the value of x.

area of a triangle = base X height / 2
7-x = 9(10 -2x)/2
2(7 – x) = 9(10 – 2x)
14 – 2x = 90 – 18x
18x – 2x = 90 – 14
16x = 76
x = 76/16
x = 4.75