# 5條基礎數學問題 20點

1.A principal(P) is deposited at an interest rate of i % per annum. if the interest is paid at the end of the first year and accumulated for the following years. find a

formula for the amount of money (A2)compounded after eight years.

2.A liquid at 33°C was put in a refrigerator with a thermometer to indicate the temperature of the bottle.the temperature of reduced to 31°C and 29°C after 1 and 2

minutes. if the temperature of the soft drink drops in constant speed,what is the

temperature in 12 minutes after it has been put in the refrigerator?

3.Mary wants to join the investment plan with her husband . mary deposit \$2000 into an investment account monthly. she gets a constant interest rate of 0.38% per month.what is the final value of his investment account after 2 years?

4.At a fixed temperature, gas pressure P is inversely proportional to container volume V. suppose that for a volume of 12 liters ,the pressure is 4.5 psi. find

the pressure P as a function of volume V for this temperature. what is the

pressure for a volume of 15 liters?

5.The relationship between the velocity of the body, v and the time, t , is described by part linear variation .the velocity of the body moving in a straight line with

uniform acceleration is 20m/s after 5 seconds and is 26m/s 3 seconds later. find the equation for the relationship between velocity of the body and time

Rating

Ques. 1.

A2 = P x (1 + i/100)^8

A2 = the sum of principal and total interest

(i.e. The amount of money you get back after 8 years)

Note: ^ means raised to the power

x means multiplication sign

Total interest, T = P x (1 + i/100)^8 – P

Ques. 2.

Tf = Ti - (r x t)

where Tf = final temperature, Ti = initial temperature,

r = rate of dropping in temperature per minute, t = time elapsed in minutes

Tf = 33°C - (2°C/min. x 12 min.)

Tf = 33°C - 24°C

Tf = 9°C

The temperature after 12 minutes is 9°C

Ques. 3.

A = Principal + Interest

P = Principal = \$2000

I = interest rate per month = 0.38% per month

t = length of time in months = 2 years = 2 x 12 months = 24 months

A = \$2000 x (1 + 0.38/100)^24

A = \$2000 x (1.0038)^24

A = \$2190.60

Final value of her investment account after 2 years = \$2190.60

Ques. 4.

For Pressure, P, is inversely proportional to container volume V,

Pressure x Volume is a constant

P x V = k

Where P = pressure, V = volume, k = constant

k = P x V = 4.5 psi x 12 L = 54 psi.L

P x V = 54

P = 54 psi.L/15 L

P = 3.6 psi

The pressure for a volume of 15 liters is 3.6 psi

Ques. 5.

v = at + b

velocity v is dependent variable

time t is independent variable

a is the acceleration which is a constant. It is given by the slope on the graph.

b is the y-intercept of x-y linear equation

In this case, b is the velocity when time t = 0 second

You have two set of data (x1, y1) and (x2, y2)

(20, 5), (26, 5 +3 )

That is (20, 5), (26, 8)

Slope is given by (y2 – y1)/(x2, x1)

(26 m/s – 20 m/s)/(8 s – 5s) = (6 m/s)/(3s) = 2 m/s/s

The slope is also the acceleration = 2m/s/s

v = at + b

v = 2t + b

We have to find b

When t = 5 s, v = 20 m/s

20 m/s = (2 m/s/s) x (5 s) + b

20 m/s = 10 m/s + b

b = 20 m/s - 10 m/s

b = 10 m/s

v = 2t + 10

where v = velocity (m/s) of the body and t = time (s)

Comment:

Question 4 involves Boyle's Law