WorksheetsBasic Calculus
Total questions: 24
Worksheet time: 12mins
In equation + 2xy + y = 9, what is the value of dy/dx at the point (1,-2)?
A. 0
B. 1
C. -1
D. undefined
Which of the following is an example of an implicit differentiation problem?
a. Finding the slope of a tangent line to a curve
b. Solving a linear equation for a given variable
c. Finding the area under a curve
d. Solving a quadratic equation for it's roots
What is the volume of the sphere?
a. V= 1/3πr³
b. V= 4/3πr³
c. V=1/3πr²
d. V=4/3πr²
What is the derivative of the volume of the spherical balloon with respect to time?
a. dV/dt= 4/3πdr/dt
b. dV/dt= 100πdr/dt
c. dV/dt=25/3πdr/dt
d. dV/dt=4π(5)dr/dt
Which of the following is an example implicit differentiation?
a. x²+3x
b. y= sin x
c. y= lnx
d. 2x+5
What is the derivative of x² with respect to x?
a. 2x
b. x
c. 1
d. 0
Which of the following is the correct derivative of y³ with respect to x?
a. 3y²
b. 3y²y¹
c. 2y²
d. 0
How fast is the radius of the balloon increasing when the radius is 5cm?
a. 1.113
b. 1.131
c. 1.114
d. 1.141
What is the anti-derivative of sinx?
a. tan x + c
b. sin x +c
c. cos x +c
d. ln x +c
Which of the following is the correct anti-derivative of 1/x with respect to x?
a. ex+c
b. x+c
c. 1/x + c
d. ln x + c
What is the height of the man?
a. 5.5
b. 120cm
c. 1.8 m
d. 180 cm
What is the anti-derivative of 4x³ with respect to x?
a. x⁴+c
b. 12x²
c. 2x⁴
d. 16x²+c
What is the rate at which the length of his shadow was changing?
a. 58.36cm/s
b. 58.37cm/s
c. 58.38cm/s
d. 58.39cm/s
What is the rate at which the tip of his shadow was changing?
a. 58.378cm/s
b. 120cm/s
c. 178.378cm/s
d. 178.38cm/s
In evaluating a definite integral, what is the first thing to do?
a. Write down the given
b. Get the derivative of the given function
c. Integrate the function being evaluated
d. Apply the fundamental theorem of calculus
A separable differential equation is an equation which can be written in the form
a. f(y)dy=g(x)dx
b. f(x)dx=g(y)dy
c. f(x)dy= g(y) dx
d. f(y)dx= g(x)dy
Which property allows us to change the limit of integration when evaluating a definite integral?
a. Substitution Rule
b. Fundamental theorem of calculus
c. Linearity
d. Change of variables
What is the integral of ln(2x)?
a. ln(2x) + c
b. ln(x) + c
c. 2ln(x) + c
d. 1/2x + c
Evaluate the integral of sec x tan x
a. sec x + c
b. ln | sec x tan x | + c
c. -sec + c
d. ln | sec x tan 6| + c
What is the area of the region bounded by the x-axis, the curve y= sin x the vertical lines x = 0 and x = π?
a. 0 square units
b. 1 square units
c. 2 square units
d. 4 square units
Which of the following is the correct integral of csc x cot x?
a. csc x + c
b -cscx + c
c. ln | lcsc x + cot x | + c
d. ln | lcsc x - cot x | + c
What is the integration/ anti-derivation?
a. Integration is the process of finding the derivative of the function
b. Integration is the process of finding the anti-derivative of the function
c. Integration is the process of finding the inverse of the function
d. Integration is the process of finding the reverse of the function
The Substitution Rule is primarily used in which branch of Mathematics?
a. Algebra
b. Geometry
c. Calculus
d. Probability
What is the purpose of substitution rule in calculus?
a. To find the derivative of a function
b. To evaluate definite integrals
c. To solve linear equations
d. To simplify complex numbers
