MASTERING THE CALC BC EXAM 2025:
YOUR ULTIMATE GUIDE TO A+
SUCCESS
f(x)=cos^2(3x-5)
f'(x)=
-6sin(3x-5)cos(3x-5)
∫1/t√t dt=
-2t^(-1/2) + c
If f(x)= (5-x)/(x^3+2)
f'(x)=
(2x^3-15x^2-2)/(x^3+2)^2
The position of a particle moving in the xy-plane is given by the vector {4t^3,y(2t)}, where y
is a twice-differeniable function of t.
At time t=1/2, what is the acceleration vector of the particle?
{12,4y"(1)}
To what number does the series
E (-e/pi)^k converge?
π/(π+e)
Look at graph on #6
Which of the following is true?
lim as x->a of f(x) ≠ f(a)
If ∫4 -10 g(x)=-3
and ∫4 6 g(x)=5
then ∫-10 6 g(x)=
8
The length of the curve y=sin(3x) from x=0 to x=π/6 is given by
∫0 π/6 √1+9cos^2(3x)
The slope of the line tangent to the graph of y=xe^x
at x=ln2 is
2ln2 + 2
Let y=f(x) be the solution to the differential equation dy/dx= x-y with initial condition
f(2)=8. What is the approximation for f(3) obtained by using Euyler's method with two
steps of equal length, starting at x=2?
15/4
, If x^2+xy-3y=3, then at the point (2,1)
dy/dx=
5
~(3x+1)/(x^2-4x+3)=
5ln[x-3] - 2ln[x-1] + c
Which of the following is a slope field for
dy/dx= x^2+y^2?
look for graph where slope increases as y increases
If f(x)=3x^2+2x
f'(x)=
lim as h->0 (3(x+h)^2+2(x+h))-(3x^2+2x) / h
Look at graphs for #15.
Which statement is false?
lim as x->1 (f(x)g(x+1)) does not exist
Which of the following is the interval of convergence for the series
E (x+2)^n/2^n
-4<x<0
∫0 5 √((5-x)/5)
10/3
Which of the following are equal to -1?
I. lim x->0- [x]/x
II. lim x->3 (x^2-7x+12)/(3-x)
III. lim x->infinite (1-x)/(1+x)
I and III only
Let f be the function given by f(x)=2cosx+1.
What is the approximation for f(1.5) found by using the
line tangent to the graph of f at x=π/2?
π-2
A particle moves in the xy-plane so that its position for t>= is given by the parametric
equations x=ln(t+1) and y=kt^2, where k is a positive constant. The line tangent to the
particle's path at the point where t=3 has slope 8.
What is the value of k?
1/3
YOUR ULTIMATE GUIDE TO A+
SUCCESS
f(x)=cos^2(3x-5)
f'(x)=
-6sin(3x-5)cos(3x-5)
∫1/t√t dt=
-2t^(-1/2) + c
If f(x)= (5-x)/(x^3+2)
f'(x)=
(2x^3-15x^2-2)/(x^3+2)^2
The position of a particle moving in the xy-plane is given by the vector {4t^3,y(2t)}, where y
is a twice-differeniable function of t.
At time t=1/2, what is the acceleration vector of the particle?
{12,4y"(1)}
To what number does the series
E (-e/pi)^k converge?
π/(π+e)
Look at graph on #6
Which of the following is true?
lim as x->a of f(x) ≠ f(a)
If ∫4 -10 g(x)=-3
and ∫4 6 g(x)=5
then ∫-10 6 g(x)=
8
The length of the curve y=sin(3x) from x=0 to x=π/6 is given by
∫0 π/6 √1+9cos^2(3x)
The slope of the line tangent to the graph of y=xe^x
at x=ln2 is
2ln2 + 2
Let y=f(x) be the solution to the differential equation dy/dx= x-y with initial condition
f(2)=8. What is the approximation for f(3) obtained by using Euyler's method with two
steps of equal length, starting at x=2?
15/4
, If x^2+xy-3y=3, then at the point (2,1)
dy/dx=
5
~(3x+1)/(x^2-4x+3)=
5ln[x-3] - 2ln[x-1] + c
Which of the following is a slope field for
dy/dx= x^2+y^2?
look for graph where slope increases as y increases
If f(x)=3x^2+2x
f'(x)=
lim as h->0 (3(x+h)^2+2(x+h))-(3x^2+2x) / h
Look at graphs for #15.
Which statement is false?
lim as x->1 (f(x)g(x+1)) does not exist
Which of the following is the interval of convergence for the series
E (x+2)^n/2^n
-4<x<0
∫0 5 √((5-x)/5)
10/3
Which of the following are equal to -1?
I. lim x->0- [x]/x
II. lim x->3 (x^2-7x+12)/(3-x)
III. lim x->infinite (1-x)/(1+x)
I and III only
Let f be the function given by f(x)=2cosx+1.
What is the approximation for f(1.5) found by using the
line tangent to the graph of f at x=π/2?
π-2
A particle moves in the xy-plane so that its position for t>= is given by the parametric
equations x=ln(t+1) and y=kt^2, where k is a positive constant. The line tangent to the
particle's path at the point where t=3 has slope 8.
What is the value of k?
1/3
