TARLAC STATE UNIVERSITY
COLLEGE OF ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
Practice Problems - Algebra
1. A type of Inequality that is true only for some intervals of x
a. Algebraic Inequality
c. Absolute Inequality
b. Conditional Inequality
d. Recursive Inequality
13. Find the domain of 𝑓(𝑥) = √3𝑥 − 1
a. [1/3, ∞)
c. [0, ∞)
b. (1/3, ∞)
d. [−1/3, ∞)
2. A type of Inequality that is true for all real numbers
a. Algebraic Inequality
c. Absolute Inequality
b. Conditional Inequality
d. Recursive Inequality
14. Solve the inequality
3. Analysis of the nature of and algebraic solutions of algebraic
equation or polynomial.
a. Theory of Equations
b. Fundamental theorem of algebra
c. Remainder theorem
d. Rational Roots theorem
For the partial fraction;
𝑥 4 − 𝑥 3 + 14𝑥 2 − 2𝑥 + 22
𝐴
𝐵𝑥 + 𝐶
𝐷𝑥 + 𝐸
=
+
+
(𝑥 + 1)(𝑥 2 + 4)(𝑥 2 − 2𝑥 + 5) 𝑥 + 1 𝑥 2 + 4 𝑥 2 − 2𝑥 + 5
4. If a polynomial f(x) is divided by x-k until the remainder is a
constant, then this remainder is f(k)
a. Rational zeroes theorem
c. Remainder theorem
b. Factor theorem
d. Quadratic surd
5. A number of the form ±√𝑎, where 𝑎 is a positive rational number
which is not the square of another rational number.
a. Pure Quadratic Surd
c. Rational zeroes theorem
b. Factor theorem
d. Mixed Quadratic Surd
6. It states that every equation which can be put in the form with
zero on one side of the equal-sign and a polynomial of degree
greater than or equal to one with real or complex coefficients on
the other has at least one root which is a real or complex number.
a. Remainder Theorem
b. Rational Zeros theorem
c. Factor Theorem
d. Fundamental Theorem of Algebra
1
𝑥−2
>0
c. (−∞, +∞)
d. (2, +∞)
a. [2, +∞)
b. (−2, +∞)
15. Which of the following gives the value of A.
a. 1
b. -4
c. -9
d. 5
16. Which of the following gives the value of C
a. 3
b. -2
c. 0
d. 2
17. Which of the following gives the value of D
a. 0
b. -1
c. 1
d. 4
18. Which of the following gives the value of E
a. 1
b. 3
c. 6
d. -9
19. Which of the following is an upper bound for the roots of
𝑥 4 − 𝑥 3 − 2𝑥 2 − 4𝑥 − 24 = 0
a. -1
b.1
c. 2
d. 3
20. Find the 11th term of (𝑥 +
2
√𝑦
15
)
𝑥5
𝑥6
a. 3075082 𝑦5
c. 3075082 𝑦4
𝑥6
7. Which of the following gives the value of k so that 𝑥 − 3 is a
factor of 𝑥 4 − 𝑘 2 𝑥 2 − 𝑘𝑥 − 81.
a. -7/3
b. -5/3
c. 2
d. -1/3
8. Which of the following is a possibility for the roots of
𝑥 4 + 2𝑥 3 + 3𝑥 2 + 4𝑥 + 5 = 0.
a. 4 positive real number
b. 3 positive real root and 1 negative real root
c. 2 negative real number and 2 positive real number
d. 4 negative real number
9. Form a quartic equation with real coefficients having 1-2i and
3+i as roots.
a. (𝑥 2 − 4𝑥 + 2)(𝑥 2 − 𝑥 + 10)
b. (𝑥 2 + 2𝑥 + 5)(𝑥 2 − 6𝑥 + 11)
c. (𝑥 2 − 2𝑥 + 5)(𝑥2 − 6𝑥 + 10)
d. (𝑥 2 − 𝑥 + 1)(𝑥 2 − 𝑥 + 10)
𝑥+7
10. Solve the inequality 𝑥+3 ≥ 0
a. (−∞, −7) ∪ (−3, ∞)
b. (−∞, −7] ∪ [−3, ∞)
c. (−∞, −7] ∪ (−3, ∞)
d. (−∞, −7) ∩ (−3, ∞)
11. Solve the inequality −2𝑥 2 < −11𝑥 + 5
1
1
a. (−∞, 2) ∪ [6, ∞)
c. (−∞, 2] ∪ (6, ∞)
1
1
b. (−∞, ) ∪ (6, ∞)
2
14
2
3
14
a. 3 ≤ 𝑥 ≤
c. 3 < 𝑥 <
3
d. 3075072 𝑦5
1 11
21. Find the term containing 𝑥 9 in the expansion of (𝑥 3 + 𝑥)
a. 123𝑥 9
b. 550𝑥 9
c. 233𝑥 9
d. 462𝑥 9
22. Find the sum of the coefficients (𝑥 2 + 3𝑦 − 2𝑧 3 )10
a. 1678999
c. 60466176
b. 1024
d. 124444
23. Ninety people at a Superbowl party were surveyed to see what
they ate while watching the game. The following data was
collected: 48 had nachos. 39 had wings. 35 had a potato skins. 20
had both wings and potato skins. 19 had both potato skins and
nachos. 22 had both wings and nachos. 10 had nachos, wings and
potato skins. How many had nothing?
a. 19
b. 12
c. 18
d. 14
24. Suppose Walter’s online music store conducts a customer
survey to determine the preferences of its customers. Customers
are asked what type of music like. They may choose from the
following categories: Pop (P), Jazz (J), Classical (C), and none of
the above (N). Of 100 customers some of the results are as
follows: 44 like Classical 27 like all three 15 like only Pop 10 like
Jazz and Classical, but not Pop How many like Classical but not
Jazz?
a. 12
b. 7
c. 11
d. 10
d. (−∞, ] ∪ [6, ∞)
2
12. Solve the inequality. −5 ≤
𝑥5
b. 3075072 𝑦4
2
4−3𝑥
2
25. From the equation 5x2 + (3k – 2)x – 4k – 1 = 0, determine the
value of k so that the sum and product of the roots are equal.
a. 2
b. - 3
c. 1
d. 2
<1
2
14
2
3
14
c. 3 > 𝑥 >
d. 3 < 𝑥 ≤
3