AP Calculus QIV Practice Test 1

AP Calculus Quarter IV Test I Sections 5.1-5.3 Name:_________________________________________________________________________ I. Suppose that f and g are continuous functions and that: ∫ −4 0 f x dx =− 3 2 , ∫ 0 5 f x dx =−6 and ∫ −4 0 g x dx = 5 6 use the properties of integrals to find: 1. ∫ 5 −4 1 2 f ( x ) dx 2. ∫ 0 −4 −2 f x dx − ∫ −4 0 −3 g x dx 3. ∫ 5 0 − 7 3 f x dx 4. ∫ 0 −4 [−2 f x − 1 3 g x ] dx II. Given the function f x =15 2 x − x 2 1. Find the average value of the function over the interval [-4,7]. At what point in the interval does the function assume its average value? III. A wholesaler receives a shipment of 500 boxes of certain product every 2 weeks. The boxes are sold to retailers and x days after the shipment arrives the inventory of cases still remaining is I ( d )=300 − 23 14 d 2 . Find the average daily inventory and the average daily holding cost if the cost of holding one box is 2 cents a day. If a new order needs to be placed the day the average inventoy is reached, when should that order be placed? IV. Adiesel generator runs continuously, consuming at a gradualluy ncreasing rate until it must be temporarily shut down to have the filters replaced. Day Mon Tue Wed Thu Fri Sat Sun Liters/hour 0.019 0.020 0.021 0.023 0.025 0.028 0.031 1. Estimate the amount of oil consumed by the genrrator during the week. 2. Estimate the average consumption V. Find the area enclosed between the graphs of y =− x +1 and y =− x 2 − x +2

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Transcript of AP Calculus QIV Practice Test 1

AP Calculus Quarter IV Test I

Sections 5.1-5.3

Name:_________________________________________________________________________

I. Suppose that f and g are continuous functions and that: 40

f xdx=32 , 0

5f xdx=6 and

40

g x dx=56 use the properties of integrals to find:

1. 54 1

2f (x)dx

2. 042 f xdx4

03 g x dx

3. 507

3f x dx

4. 04[2 f x1

3g x ] dx

II. Given the function f x =152 xx2

1. Find the average value of the function over the interval [-4,7]. At what point in the interval does the function assume its average value?

III. A wholesaler receives a shipment of 500 boxes of certain product every 2 weeks. The boxes are sold to retailers and x

days after the shipment arrives the inventory of cases still remaining is I (d )=3002314

d 2 . Find the average

daily inventory and the average daily holding cost if the cost of holding one box is 2 cents a day. If a new order needsto be placed the day the average inventoy is reached, when should that order be placed?

IV. Adiesel generator runs continuously, consuming at a gradualluy ncreasing rate until it must be temporarily shut down to have the filters replaced.

Day Mon Tue Wed Thu Fri Sat SunLiters/hour 0.019 0.020 0.021 0.023 0.025 0.028 0.031

1. Estimate the amount of oil consumed by the genrrator during the week.

2. Estimate the average consumption

V. Find the area enclosed between the graphs of y=x+1 and y=x2 x+2