F.1英文數學 ( 20點 )!!!!!!!!!!!!!

2012-08-04 12:08 am

1. Use estimation to determine whether the following estimations are reasonable or not .

( 1 ) 287.6 + 734.9 - 422.8 ～ 1000
( 2 ) 8.54 × 5.16 ÷ 2.89 ～ 15
( 3 ) ( 225 + 668 ) ÷ 24.8 ～ 60
( 4 ) 19.7 × 51.3 - 236 ～ 750

2. In a hotel of 40 floors , the floor with most visitors has 80 visitors while the floor with least visitors has 60 visitors only. How would you estimate the total number of visitors in the hotel?Explain your answer.

3. Which of the following is the best strategy to estimate the height of a building ?
A . Benchmark strategy
B . Decomposition-recomposition strategy
C . Estimating in groups
D . Using formulas

4. Suppose the cost $y of making x booklets is given by the function y = ax + 4 00 . The following table shows some values of x and the corresponding values of y :

x = 1000 , 2000 , 3000 , 4000
y = ax + 400 = 2400 , 4400 , 6400 , 8400
Find the cost for making 5500 booklets.

5. Consider the equation x - 2x + 3x - 4x + 5x - 6x + 7x - 8x + ... + 97x - 98x + 99x - 100x = 200. Solve the equation and briefly explain how you can solve it.

6. The perimeter of a rectangle is 44 cm. If the length is 2 cm longer than the width, find the area of the rectangle.
A . 10 cm^2
B . 12 cm^2
C . 44 cm^2
D . 120 cm^2

7. How many terms are there when we expand the expression
(x - 1)(x^99 + x^98 + x^97 + x^96 + ... + x^2 + x + 1)
Briefly explain your answer.

8. Steven bought 400 apples at a total of $1000. Later he found that 10 of the apples have decayed. Then sold the remaining apples at $3 each. Find the profit or loss percentage of Steven if all the remaining apples were sold.

回答 (1)

PeterChow

2012-08-04 3:24 am

✔ 最佳答案

1.
( 1 ) 287.6+734.9-422.8 ≈ 290+730-420 = 300+700-400-10+30-20 = 600
So, 1000 is not reasonable
( 2 ) 8.54×5.16÷2.89 ≈ 9x5÷3 = 15
So, 15 is reasonable.
( 3 ) (225+668)÷24.8 ≈ (225+675)÷25 = 900÷25 = 100÷25x9 = 36
So, 60 is not reasonable.
( 4 ) 19.7×51.3-236 ≈ 20x50-240 = 1000-200-40 = 760
So, 750 is reasonable.
2.
Average number of visitors on the two floors = (80+60)÷2 = 70
Use this as a benchmark, the total number of visitors = 70x40 = 2800
3.
A . Benchmark strategy
Using the height of one floor as a benchmark, multiply this number by the total number of floors of the building.
4.
Find the value of a from the above datum.
1000a+400=2400
a=2
So, the cost of making 5500 booklets = 5500x2+400 = 11400
5.
(x - 2x) + (3x - 4x) + (5x - 6x) + (7x - 8x) + ... + (97x - 98x) + (99x - 100x)
= -50x
=200
x = -4
6.
6. The perimeter of a rectangle is 44 cm. If the length is 2 cm longer than the width, find the area of the rectangle.
Let l be the length and w be the width.
2l+2w = 44
l=w+2
By solving this set of equations, l=12 and w=10.
So, the area of rectangle = 12x10= D .120 cm^2
7.(x - 1)(x^99 + x^98 + x^97 + x^96 + ... + x^2 + x + 1)
=(x^100+x^99+...+x^2+x)-(x^99+x^98+...+x^2+x+1)
=x^100+1
So, there are 2 terms after expansion.
8.
After selling the remaining apples, he got 3x(400-10)=$1170
So the profit percentage = (1170-1000)÷1000x100 = 17%

參考: me

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