GENERAL ENGINEERING ECCC NEW EXAM QUESTIONS
AND CORRECT ANSWERS FOR TOP PERFORMANCE
1. Q: What is the derivative of sin(x)? ANSWER cos(x)
2. Q: What is the integral of 1/x dx? ANSWER ln|x| + C
3. Q: What is Euler's formula? ANSWER e^(ix) = cos(x) + i·sin(x)
4. Q: What is the determinant of a 2x2 matrix [[a,b],[c,d]]? ANSWER ad -
bc
5. Q: What is the Pythagorean theorem? ANSWER a² + b² = c², where c is
the hypotenuse
6. Q: What is the chain rule in calculus? ANSWER d/dx[f(g(x))] =
f'(g(x))·g'(x)
7. Q: What is the quadratic formula? ANSWER x = [-b ± √(b²-4ac)] / 2a
8. Q: What is a Laplace transform used for? ANSWER Converting
differential equations from time domain to frequency domain
9. Q: What is the divergence theorem? ANSWER ∫∫∫(∇·F)dV = ∫∫(F·n)dS,
relating volume and surface integrals
10. Q: What is Taylor series expansion? ANSWER f(x) = f(a) + f'(a)(x-a) +
f''(a)(x-a)²/2! + ...
11. Q: What is the gradient of a scalar field? ANSWER A vector field
representing the direction and rate of maximum increase
12. Q: What is a Fourier series? ANSWER Representation of periodic
functions as sum of sines and cosines
13. Q: What is the dot product of two vectors? ANSWER A·B = |A||B|cos(θ)
= AxBx + AyBy + AzBz
14. Q: What is the cross product used for? ANSWER Finding a vector
perpendicular to two given vectors
,15. Q: What is a homogeneous differential equation? ANSWER An
equation where all terms contain the dependent variable or its derivatives
16. Q: What is partial differentiation? ANSWER Differentiation with
respect to one variable while keeping others constant
17. Q: What is the method of separation of variables? ANSWER A
technique for solving differential equations by separating variables on different
sides
18. Q: What is a matrix eigenvalue? ANSWER A scalar λ where Av = λv for
some non-zero vector v
19. Q: What is Green's theorem? ANSWER Relates a line integral around a
closed curve to a double integral over the region
20. Q: What is the Runge-Kutta method? ANSWER A numerical method for
solving ordinary differential equations
21. Q: What is a complex number? ANSWER A number of the form a + bi,
where i = √(-1)
22. Q: What is the binomial theorem? ANSWER (a+b)^n = Σ(n choose
k)a^(n-k)b^k
23. Q: What is L'Hôpital's rule? ANSWER Method for evaluating limits of
indeterminate forms using derivatives
24. Q: What is a double integral used for? ANSWER Computing volume
under a surface or area of a region
25. Q: What is the curl of a vector field? ANSWER Measures the rotation or
circulation of the field
26. Q: What is a differential equation order? ANSWER The highest
derivative present in the equation
27. Q: What is Newton-Raphson method? ANSWER An iterative numerical
method for finding roots of equations
28. Q: What is a unit vector? ANSWER A vector with magnitude equal to 1
29. Q: What is the inverse of a matrix? ANSWER Matrix A^(-1) such that
A·A^(-1) = I (identity matrix)
30. Q: What is integration by parts? ANSWER ∫u dv = uv - ∫v du
, 31. Q: What is a probability density function? ANSWER Function
describing the probability distribution of a continuous random variable
32. Q: What is standard deviation? ANSWER Measure of spread of data
from the mean, σ = √(variance)
33. Q: What is a harmonic function? ANSWER A function satisfying
Laplace's equation ∇²f = 0
34. Q: What is the mean value theorem? ANSWER f'(c) = [f(b)-f(a)]/(b-a)
for some c in [a,b]
35. Q: What is Simpson's rule? ANSWER Numerical integration method
using parabolic approximations
36. Q: What is a vector space? ANSWER A set with defined addition and
scalar multiplication operations
37. Q: What is linear independence? ANSWER Vectors where no vector can
be written as a linear combination of others
38. Q: What is the rank of a matrix? ANSWER The maximum number of
linearly independent rows or columns
39. Q: What is a conformal mapping? ANSWER A transformation that
preserves angles locally
40. Q: What is the residue theorem? ANSWER Method for evaluating
complex contour integrals
41. Q: What is a Laurent series? ANSWER Power series that includes
negative powers
42. Q: What is the Cauchy-Riemann equations? ANSWER Conditions for a
complex function to be analytic
43. Q: What is Stokes' theorem? ANSWER Relates surface integral of curl to
line integral around boundary
44. Q: What is a Bessel function? ANSWER Solutions to Bessel's differential
equation, common in cylindrical problems
45. Q: What is the convolution theorem? ANSWER Convolution in time
domain equals multiplication in frequency domain
46. Q: What is a Jacobian matrix? ANSWER Matrix of first-order partial
derivatives of a vector function
AND CORRECT ANSWERS FOR TOP PERFORMANCE
1. Q: What is the derivative of sin(x)? ANSWER cos(x)
2. Q: What is the integral of 1/x dx? ANSWER ln|x| + C
3. Q: What is Euler's formula? ANSWER e^(ix) = cos(x) + i·sin(x)
4. Q: What is the determinant of a 2x2 matrix [[a,b],[c,d]]? ANSWER ad -
bc
5. Q: What is the Pythagorean theorem? ANSWER a² + b² = c², where c is
the hypotenuse
6. Q: What is the chain rule in calculus? ANSWER d/dx[f(g(x))] =
f'(g(x))·g'(x)
7. Q: What is the quadratic formula? ANSWER x = [-b ± √(b²-4ac)] / 2a
8. Q: What is a Laplace transform used for? ANSWER Converting
differential equations from time domain to frequency domain
9. Q: What is the divergence theorem? ANSWER ∫∫∫(∇·F)dV = ∫∫(F·n)dS,
relating volume and surface integrals
10. Q: What is Taylor series expansion? ANSWER f(x) = f(a) + f'(a)(x-a) +
f''(a)(x-a)²/2! + ...
11. Q: What is the gradient of a scalar field? ANSWER A vector field
representing the direction and rate of maximum increase
12. Q: What is a Fourier series? ANSWER Representation of periodic
functions as sum of sines and cosines
13. Q: What is the dot product of two vectors? ANSWER A·B = |A||B|cos(θ)
= AxBx + AyBy + AzBz
14. Q: What is the cross product used for? ANSWER Finding a vector
perpendicular to two given vectors
,15. Q: What is a homogeneous differential equation? ANSWER An
equation where all terms contain the dependent variable or its derivatives
16. Q: What is partial differentiation? ANSWER Differentiation with
respect to one variable while keeping others constant
17. Q: What is the method of separation of variables? ANSWER A
technique for solving differential equations by separating variables on different
sides
18. Q: What is a matrix eigenvalue? ANSWER A scalar λ where Av = λv for
some non-zero vector v
19. Q: What is Green's theorem? ANSWER Relates a line integral around a
closed curve to a double integral over the region
20. Q: What is the Runge-Kutta method? ANSWER A numerical method for
solving ordinary differential equations
21. Q: What is a complex number? ANSWER A number of the form a + bi,
where i = √(-1)
22. Q: What is the binomial theorem? ANSWER (a+b)^n = Σ(n choose
k)a^(n-k)b^k
23. Q: What is L'Hôpital's rule? ANSWER Method for evaluating limits of
indeterminate forms using derivatives
24. Q: What is a double integral used for? ANSWER Computing volume
under a surface or area of a region
25. Q: What is the curl of a vector field? ANSWER Measures the rotation or
circulation of the field
26. Q: What is a differential equation order? ANSWER The highest
derivative present in the equation
27. Q: What is Newton-Raphson method? ANSWER An iterative numerical
method for finding roots of equations
28. Q: What is a unit vector? ANSWER A vector with magnitude equal to 1
29. Q: What is the inverse of a matrix? ANSWER Matrix A^(-1) such that
A·A^(-1) = I (identity matrix)
30. Q: What is integration by parts? ANSWER ∫u dv = uv - ∫v du
, 31. Q: What is a probability density function? ANSWER Function
describing the probability distribution of a continuous random variable
32. Q: What is standard deviation? ANSWER Measure of spread of data
from the mean, σ = √(variance)
33. Q: What is a harmonic function? ANSWER A function satisfying
Laplace's equation ∇²f = 0
34. Q: What is the mean value theorem? ANSWER f'(c) = [f(b)-f(a)]/(b-a)
for some c in [a,b]
35. Q: What is Simpson's rule? ANSWER Numerical integration method
using parabolic approximations
36. Q: What is a vector space? ANSWER A set with defined addition and
scalar multiplication operations
37. Q: What is linear independence? ANSWER Vectors where no vector can
be written as a linear combination of others
38. Q: What is the rank of a matrix? ANSWER The maximum number of
linearly independent rows or columns
39. Q: What is a conformal mapping? ANSWER A transformation that
preserves angles locally
40. Q: What is the residue theorem? ANSWER Method for evaluating
complex contour integrals
41. Q: What is a Laurent series? ANSWER Power series that includes
negative powers
42. Q: What is the Cauchy-Riemann equations? ANSWER Conditions for a
complex function to be analytic
43. Q: What is Stokes' theorem? ANSWER Relates surface integral of curl to
line integral around boundary
44. Q: What is a Bessel function? ANSWER Solutions to Bessel's differential
equation, common in cylindrical problems
45. Q: What is the convolution theorem? ANSWER Convolution in time
domain equals multiplication in frequency domain
46. Q: What is a Jacobian matrix? ANSWER Matrix of first-order partial
derivatives of a vector function
