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CBT TEST

MTH 201 CBT PRACTICE

Phil

January 17, 2025

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 has a second derivative everywhere

B. Its derivative exists at every point

C. It has breaks or holes in its graph

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

2 / 30

2. The second derivative of a function determines:

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

B. Points where the function is undefined

C. The intercept of a function

D. The tangent line's slope

3 / 30

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

A. Splitting the interval into trapezoids

B. Fitting cubic functions across each segment

C. Drawing straight lines through function values

D. Connecting endpoints with parabolas

4 / 30

4. A function is continuous at a point if:

A. It is differentiable at every point of the domain

B. It is differentiable at every point of the domain

C. The left-hand limit, right-hand limit, and function value are equal

D. Its integral converges

5 / 30

5. 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

6 / 30

6. Numerical integration is used to:

A. Find derivative values at certain points

B. Eliminate transcendental functions from models

C. Approximate definite integrals that cannot be solved analytically

D. Solve algebraic equations

7 / 30

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

A. Using intervals divisible by 3

B. Requiring only one interval

C. Avoiding higher-order derivatives

D. Approximating functions with degree 1

8 / 30

8. The main limitation of the Trapezoidal Rule is:

A. It is time-consuming for smooth functions

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

C. It can only approximate discontinuous functions

D. It assumes linear behavior over small intervals

9 / 30

9. Newton’s method may fail if:

A. 𝑓 ( 𝑥 ) is undefined in the interval

B. The initial guess is too close to the root

C. f ′ (x)=0 at some iteration

D. The function f(x) is continuous

10 / 30

10. The Bisection method requires that the function:

A. Be linear in form

B. Be integrable

C. Have opposite signs at the endpoints of the interval

D. Be differentiable at all points

11 / 30

11. The main disadvantage of the Bisection method is:

A. It needs a large initial interval

B. It requires the function to be discontinuous

C. It is slower compared to other methods

D. Its inability to converge

12 / 30

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

A. Lower computation cost

B. Independence from derivatives

C. Faster convergence

D. Guaranteed success for any function

13 / 30

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

A. ln(x)/x

B. x^2

C. ln ⁡ ( 𝑥^2 )

D. 1/x

14 / 30

14. Partial differentiation deals with functions:

A. Containing only constant terms

B. That depend on multiple variables

C. Defined implicitly

D. Having a single variable

15 / 30

15. The primary objective of calculus is to:

A. Analyze changes and accumulation in mathematical models

B. Solve matrix-based problems

C. Simplify algebraic expressions

D. Study arithmetic operations exclusively

16 / 30

16. Simpson’s rules are based on:

A. Integrating non-continuous data

B. Summing areas under exponential functions

C. Linear interpolations

D. Polynomial approximations of data points

17 / 30

17. Differentiability implies:

A. A function is not defined at that point

B. There are discontinuities in the function

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

D. A function is always continuous everywhere

18 / 30

18. Differential calculus focuses on:

A. Simplifying arithmetic operations

B. The study of integrals and their properties

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

D. Solving quadratic equations analytically

19 / 30

19. Simpson’s 1/3 rule is applicable when:

A. Subintervals are divisible by 3

B. Only two data points exist

C. Subintervals are odd

D. Subintervals are even

20 / 30

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

A. Solutions of differential equations

B. Infinite sums

C. Definite integrals of functions

D. Zeros of transcendental functions

21 / 30

21. The derivative of a constant function is:

A. Zero

B. The function itself

C. Undefined

D. A non-zero constant

22 / 30

22. A function has a maximum when:

A. f(x)=0 and 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

23 / 30

23.

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

B. Represents the indefinite integral of the function

C. Cannot be solved without differentiating first

D. Always equals zero

24 / 30

24. An inflection point of a curve occurs when:

A. The curve is discontinuous

B. The concavity of the curve changes

C. The curve reaches a maximum value

D. The first derivative equals zero

25 / 30

25. 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

26 / 30

26. A definite integral represents:

A. The value of a function at one endpoint

B. The slope of the tangent line

C. The derivative at a point

D. The area under a curve between two bounds

27 / 30

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

A. The area under a curve

B. Instantaneous velocity of a particle

C. The slope of a tangent line

D. Points of inflection

28 / 30

28. Newton’s method is generally used when:

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

B. Calculating integrals over infinite intervals

C. Solving differential equations only

D. Function 𝑓 ( 𝑥 ) has no derivative

29 / 30

29. 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

30 / 30

30. In the Trapezoidal Rule, the formula includes:

A. The difference between the limits of integration

B. The average of the first and last function values

C. Function values at all midpoints

D. All derivatives of the function

Your score is

The average score is 28%

MTH 201 CBT PRACTICE

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