Take your time to read instructions before taking this test.

There are 30 questions which you are to answer in 10 minutes that gives you roughly 30 seconds per question.

If you can get at least 60%, you can be rest assured that you’ll ace MTH 201 exam

In a normal exam you will be asked between 40 – 60 questions but I only arranged 40 questions

Note

Do not be in a hurry to answer the questions

Do not waste time on a question you don’t know

Move as fast as possible and starting with questions that don’t have calculation first to save time

Always crosscheck

Don’t be in a hurry to submit, you are not in a competition

Don’t be scared. Getting an A is easy

Don’t be over confident, you can end up a D, E or F. Calm your blood, no be only you sabi book

Please do well to use our comment box incase there’s a message you want to pass to us

70 – 100 A

60 – 69 B

50 – 59 C

45 – 49 D

40 – 44 E

0 – 39 F

I wish you success

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MTH 201

1 / 30

1. A function is said to be continuous if:

A. It can be drawn without lifting the pencil off the paper

B. Its derivative exists at every point

C. It has a second derivative everywhere

D. It has breaks or holes in its graph

2 / 30

2. Newton’s method may fail if:

A. The function f(x) is continuous

B. f ′ (x)=0 at some iteration

C. 𝑓 ( 𝑥 ) is undefined in the interval

D. The initial guess is too close to the root

3 / 30

3. An integral is best interpreted as:

A. The measurement of angles between two lines

B. The difference between two functions

C. The accumulation of quantities or areas under a curve

D. The relationship between velocity and mass

4 / 30

4. The Trapezoidal Rule approximates the area under a curve by:

A. Drawing straight lines through function values

B. Splitting the interval into trapezoids

C. Fitting cubic functions across each segment

D. Connecting endpoints with parabolas

5 / 30

5. The advantage of Newton’s method over the Bisection method is:

A. Independence from derivatives

B. Lower computation cost

C. Faster convergence

D. Guaranteed success for any function

6 / 30

6. Partial differentiation deals with functions:

A. Defined implicitly

B. That depend on multiple variables

C. Having a single variable

D. Containing only constant terms

7 / 30

7. An inflection point of a curve occurs when:

A. The concavity of the curve changes

B. The curve is discontinuous

C. The first derivative equals zero

D. The curve reaches a maximum value

8 / 30

8. A definite integral represents:

A. The area under a curve between two bounds

B. The slope of the tangent line

C. The derivative at a point

D. The value of a function at one endpoint

9 / 30

9. The Bisection method requires that the function:

A. Be integrable

B. Be differentiable at all points

C. Be linear in form

D. Have opposite signs at the endpoints of the interval

10 / 30

10. A transcendental function is one that

A. Represents only polynomial equations

B. Is always continuous and differentiable

C. Can be solved algebraically

D. Involves trigonometric, exponential, or logarithmic expressions

11 / 30

11. The main limitation of the Trapezoidal Rule is:

A. It is always less accurate than Simpson's 1/3 rule

B. It assumes linear behavior over small intervals

C. It is time-consuming for smooth functions

D. It can only approximate discontinuous functions

12 / 30

12. A first-order differential equation is characterized by:

A. No derivatives at all

B. A partial derivative

C. A derivative of the second order

D. Only one derivative of the unknown function

13 / 30

13. For $\ln(x)$ , the derivative $f^{'} (x)$ is:

A. ln ⁡ ( 𝑥^2 )

B. ln(x)/x

C. x^2

D. 1/x

14 / 30

14. Newton-Cotes quadrature methods are used to approximate:

A. Zeros of transcendental functions

B. Infinite sums

C. Definite integrals of functions

D. Solutions of differential equations

15 / 30

15. Differentiability implies:

A. A function is not defined at that point

B. A function has a defined slope at a specific point

C. A function is always continuous everywhere

D. There are discontinuities in the function

16 / 30

16. Numerical integration is used to:

A. Approximate definite integrals that cannot be solved analytically

B. Solve algebraic equations

C. Eliminate transcendental functions from models

D. Find derivative values at certain points

17 / 30

17.

A. Gives an exact number representing the area under the curve between 𝑎 a and 𝑏 b

B. Cannot be solved without differentiating first

C. Represents the indefinite integral of the function

D. Always equals zero

18 / 30

18. The derivative of a constant function is:

A. Undefined

B. The function itself

C. Zero

D. A non-zero constant

19 / 30

19. The Simpson's 3/8 Rule differs from the 1/3 Rule by:

A. Avoiding higher-order derivatives

B. Using intervals divisible by 3

C. Requiring only one interval

D. Approximating functions with degree 1

20 / 30

20. A function has a maximum when:

A. 𝑓 ′ ( 𝑥 ) 0

B. f ′ (x)=0 and 𝑓 ′ ′ ( 𝑥 ) < 0 f ′′ (x)<0

C. 𝑓 ′ ( 𝑥 ) > 0 and f ′′ (x)>0

D. f(x)=0 and f ′′ (x)=0

21 / 30

21. In the Trapezoidal Rule, the formula includes:

A. The difference between the limits of integration

B. All derivatives of the function

C. The average of the first and last function values

D. Function values at all midpoints

22 / 30

22. The main disadvantage of the Bisection method is:

A. It needs a large initial interval

B. It is slower compared to other methods

C. Its inability to converge

D. It requires the function to be discontinuous

23 / 30

23. Quadrature methods for numerical integration require:

A. Discrete data values for functions

B. Finding the roots of integrands

C. Transforming all values into logarithmic form

D. Solving differential equations explicitly

24 / 30

24. Newton’s method is generally used when:

A. The root of f(x)=0 is not easily accessible

B. Function 𝑓 ( 𝑥 ) has no derivative

C. Solving differential equations only

D. Calculating integrals over infinite intervals

25 / 30

25. Differential calculus focuses on:

A. Solving quadratic equations analytically

B. The rate of change of quantities and slope of curves

C. Simplifying arithmetic operations

D. The study of integrals and their properties

26 / 30

26. The integral of a function is commonly used to determine:

A. Points of inflection

B. Instantaneous velocity of a particle

C. The slope of a tangent line

D. The area under a curve

27 / 30

27. The second derivative of a function determines:

A. The tangent line's slope

B. The rate of change of the slope of the function

C. Points where the function is undefined

D. The intercept of a function

28 / 30

28. Simpson’s rules are based on:

A. Linear interpolations

B. Integrating non-continuous data

C. Summing areas under exponential functions

D. Polynomial approximations of data points

29 / 30

29. The primary objective of calculus is to:

A. Simplify algebraic expressions

B. Solve matrix-based problems

C. Analyze changes and accumulation in mathematical models

D. Study arithmetic operations exclusively

30 / 30

30. Newton’s Method starts with

A. Using random values for calculation

B. Approximating a root using the tangent line of 𝑓 ( 𝑥 )

C. Eliminating derivatives from a function

D. Solving equations for definite integrals

Your score is

The average score is 28%

MTH 201 CBT PRACTICE

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