NCE 4101 – CE Integration 1 – Algebra Part 2
V. RELATIONS AND FUNCTIONS
16. What is the domain and range of
y=
√
x
?
17. What is the domain and range of
y=
√
9−x2
?
VI. THEORY OF EQUATIONS
18. if x^2 +2x +1 is divided by x – 3, compute
the remainder.
19. When you divide 2x^4 + ax^3 – x^2 + bx +1
by x – 2, the remainder is 13. When you
divide it by x -3, the remainder is 223. Find
the value of a.
20. Determine the value of k so that (3x + 2) is a
factor of 6x^3 – 5x^2 – 12x + k.
21. Investigate the possibilities that may exist
for the roots of 2x^3 – 5x^2 + 2x – 4 = 0.
22. What is the sum and product of roots of x^5
– 4x^4 – 7x^3 + x^2 – x + 4 = 0?
VII. BINOMIAL THEOREM
23. What is the middle term of (2x^2 +
3y^3)^10?
24. What is the constant term of (x – 2x^-1)^4?
25. What is the sum of coefficients of (3x + y -
2z)^5?
26. What is the sum of coefficients of (3x^2 + y -
2)^4?
27. What is the sum of exponent of (2x^3 –
y^5)^7?
VIII. INEQUALITIES
28. Find the solution set of
x3−7x2+36 ≥0
29. Find the solution set of
x2+10 x+25
x2−x−12 ≤0
30. Find the solution set of
|
3x+4
5
|
≥4
31. Find the solution set of
|
x−5
|
≤8
IX. PROPORTION AND VARIATION
32. Compute the mean proportional between 8
and 392.
33. Compute the third proportional between 16
and 12.
34. Compute the fourth proportional to 33, 22,
and 27.
35. If 2 typists can type 2 pages in 2 minutes, in
how many seconds will it take 5 typists to
type 19 pages?
