Monday 26 September 2022 05:32 PM Indiana student only one in the world to win perfect score on Calculus exam trends now

1. Curve C is described by the equation 0.25x2 + y2 = 9. Determine the y coordinates of the points on curve C whose tangent lines have slope equal to 1.

A) -3 sqrt(5) / 5 , 3 sqrt(5) / 5

B) - sqrt(35) / 2 , sqrt(35) / 2

C) -3 , 3

D) - sqrt(2) / 2 , sqrt(2) / 2

E) -3 sqrt(2) , 3 sqrt(2)

2. Find the solution to the differential equation dy/dx = cos(x) / y2 , where y(π/2) = 0.

A) y = (3 sin(x) - 3)

B) y = sin(x) - 1

C) y = (3 sin(x) - 3)1/3

D) y = (3 sin(x) - 3)3 E) y = (3 sin(x) - 3)-1/3

3. The set of all points (ln(t - 2) , 3t), where t is a real number greater than 2, is the graph of:

A) y = ln(x/3 - 2)

B) y = 3x

C) x = ln(y - 2)

D) y = 3(ex + 2)

E) y = ln(x)

4. Let P(x) = 2 x3 + K x + 1. Find K if the remainder of the division of P(x) by x - 2 is equal to 10.

A) -7/2

B) 2/7

C) 7/2

D) -2/7

E) K cannot be determined

5. f and g are functions such that f'(x) = g(x) and g'(x) = f(x). The second derivative of (f . g)(x) is equal to:

A) f"(x) g"(x)

B) g'(x) g(x) + f(x) f'(x)

C) 4 g(x) f(x)

D) 2 g(x) f(x)

E) g(x) f(x)

Answers: 1. A, 2. C, 3. D, 4. A, 5. C

Source: Free Math Tutorials - Advanced Placement Calculus AB Test Practice Questions with Answers