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  1. AP Calculus
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Integration and Accumulation of Change

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

If the function f(x)f(x)f(x) is continuous and positive on the interval [1,9][1,9][1,9], how does multiplying f(x)f(x)f(x) by a constant 333 before integrating it from 111 to 999 affect the value of ∫19f(x),dx\int_1^9 f(x),dx∫19​f(x),dx?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

If the graph of the first derivative f(x)f(x)f(x) of an integrally-defined function h(x)h(x)h(x) changes from negative to positive at x=kx = kx=k, what can be concluded about h(x)h(x)h(x) at x=kx = kx=k?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

When asked what an extrema for a function is, what value should one give?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

If the graph of the first derivative f(x)f(x)f(x) of an integrally-defined function h(x)h(x)h(x) changes from positive to negative at x=lx = lx=l, what can be concluded about h(x)h(x)h(x) at x=lx = lx=l?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

Given that ∫37g(t),dt=12\int_3^7 g(t) ,dt = 12∫37​g(t),dt=12, what does ∫73−g(t),dt\int_7^3 -g(t) ,dt∫73​−g(t),dt equal?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

If the graph of the first derivative f(x)f(x)f(x) of an integrally-defined function h(x)h(x)h(x) is increasing on the interval (g,h)(g, h)(g,h), what can be said about the behavior of h(x)h(x)h(x) on that interval?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

What is an integrally-defined function?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

If F(x)F(x)F(x) is an accumulation function given by F(x)=∫axf(t)dtF(x) = \int_{a}^{x} f(t) dtF(x)=∫ax​f(t)dt, what is the limit of F(x)F(x)F(x) as xxx approaches aaa?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

Where does a relative minimum of a function occur?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

If an accumulation function A(x)A(x)A(x) represents the area under curve y=f(t)y=f(t)y=f(t) from a fixed point to xxx, what does A′(x)A'(x)A′(x) represent?