FEU Institute of Technology
Engineering Mathematics 1 Reviewer
1. Which of the following law states that the factors of a product may be grouped in any manner
without affecting the result?
A. Commutative Law
B. Associative Law
Answer: B
C. Distributive Law
D. Inverse Law
2. If a, b and c are rational numbers and if 𝑏2 – 4𝑎𝑐 is positive but not perfect square, then the
roots of the quadratic equation 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 are
A. real, irrational and unequal
B. real, rational and unequal
Answer: A
C. real, rational and equal
D. real, irrational and unequal
3.
A.
B.
C.
D.
In the equation 𝑥2 + 𝑥 = 0, one root is x equal to
1
5
Answer: D
1/4
-1
4.
A.
B.
C.
D.
The simplest form of √162 + √50
5.
A.
B.
C.
D.
Translate the given phrase “the sum of the squares of a and b” into its mathematical symbol/s.
𝑎𝑏2 + 𝑎2𝑏
(𝑎 + 𝑏)2
Answer: C
𝑎2 + 𝑏2
(𝑎 + 𝑏)2 + (𝑎 + 𝑏)2
√212
53√2
14√2
2√14
Answer: C
6. Which of the following can be classified as a linear equation?
A.
B.
C.
D.
1
√2
1
√2𝑥
1
√2
1
3
𝑥 − √10𝑦 2 +
3
− √10𝑦 +
3
− √10𝑥𝑦 +
√2𝑦
3
𝑥
1
𝑥
1
𝑥
1
= −𝑦
= 0
= −1
− √10𝑥 = −𝑥
Answer: A
FEU Institute of Technology
Engineering Mathematics 1 Reviewer
7.
A.
B.
C.
D.
Describe the nature of the roots of the quadratic equation 25𝑥2 − 30𝑥=9.
Imaginary
Irrational and distinct
Answer: B
Real and equal
Rational and distinct
8. Which of the following is true?
A. √𝑎2 + 𝑏 2 = 𝑎 + 𝑏
B. (𝑎 + 𝑏)2 = 𝑎2 + 𝑏2
𝑎
𝑎
𝑎
C.
= −
D.
𝑏−𝑐
√𝑎4
9.
A.
B.
C.
D.
The sum of two numbers is 35 and their product is 15. Find the sum of their reciprocals.
7/2
9/2
Answer: C
7/3
7/5
−
𝑏
𝑐
2𝑎3
+ 𝑎2 = 𝑎2 − 𝑎
Answer: D
10. Ten less than four times a certain number is 14. Determine the number.
A. 2
B. 4
Answer: C
C. 6
D. 8
11. Ten years ago, Jan was four times as old as Michael. Now he is only twice as old as Michael.
How old is Jan?
A. 28
B. 30
Answer: B
C. 32
D. 34
12. A pipe can fill a tank in 10 hours whereas a drain can empty its content in 15 hours. If I
accidentally opened both the pipe and the drain, how long will it take to fill the tank?
A. 22 hours
B. 25 hours
Answer: D
C. 27 hours
D. 30 hours
FEU Institute of Technology
Engineering Mathematics 1 Reviewer
13. Find the sum of the roots of 5x2 - 9x - 2=0
A. -5/9
B. -5/2
Answer: C
C. 9/5
D. 9/2
1
1
14. The roots of a quadratic equation are 3 and 4. What is the equation?
A.
B.
C.
D.
x2 + 7x + 2 = 0
x2 - 7x + 2 = 0
x2 + 7x + 1 = 0
x2 - 7x + 1 = 0
Answer: D
15. What is the remainder when x4 - 10x2 - 9x - 20 is divided by 𝑥 − 4?
A. 40
B. 42
Answer: A
C. 44
D. 46
16. Which of the following is the graph of 5 > x + 3?
A.
Answer: B
B.
C.
D.
17. Given the following functions: 𝑓(𝑥) = 𝑥 + 2 and 𝑔(𝑥) = 4𝑥 + 3, find (𝑓 + 𝑔)(𝑥)
A. 4𝑥 – 5
B. 4𝑥 + 5
Answer: D
C. 5𝑥 – 4
D. 5𝑥 + 5
FEU Institute of Technology
Engineering Mathematics 1 Reviewer
18. What is the inverse function of 𝑦 = 3𝑥 − 2?
A.
B.
C.
D.
𝑥+2
3
𝑥
Answer: A
2−3𝑥
3𝑥
2−𝑥
𝑥+3
2
3𝑥−37
19. Decompose (𝑥+1)(𝑥−4) into partial fraction.
A.
B.
5
𝑥+1
8
𝑥+1
−
8
𝑥−4
5
− 𝑥−4
5
Answer: B
8
C. − 𝑥+1 − 𝑥−4
D.
8
5
− 𝑥−4
𝑥+1
20. Resolve
A.
B.
C.
D.
7
𝑥+1
4
11𝑥+3
𝑥 2 −1
into partial fraction.
4
+ 𝑥−1
7
+ 𝑥−1
Answer: B
𝑥+1
4𝑥+7
𝑥 2 −1
7𝑥+4
𝑥 2 −1
21. Given the system of linear equations, 𝑥 + 𝑦 = 1 and 2𝑥 – 𝑦 = 2, what is the solution set?
A. {(1, 0)}
B. {(0, -1)}
Answer: A
C. {(-1, 0)}
D. {(3, 2)}
22. Simplify the logarithm below so that the result does not contain logarithm of products,
quotients or powers.
𝑥−2
𝑙𝑛√𝑥 2 √𝑥+3
A. 2 ln(𝑥) +
B. ln(𝑥) +
2
1
1
ln(𝑥 − 2) − 2 ln (𝑥 + 3)
1
ln(𝑥 − 2) − 2 ln (𝑥 + 3)
2
C. 2 ln(𝑥) −
D. ln(𝑥) +
1
1
4
1
4
1
ln(𝑥 − 2) + 4 ln (𝑥 + 3)
1
ln(𝑥 − 2) − 4 ln (𝑥 + 3)
Answer: B
FEU Institute of Technology
Engineering Mathematics 1 Reviewer
23. One leg of a right triangle is 20 cm and the hypotenuse is 10 cm longer than the other leg. Find
the length of the unknown leg.
A. 5 cm
B. 10 cm
Answer: C
C. 15 cm
D. 20 cm
24. The following positive angles are coterminal with 30° or -55° except
A. 390°
B. 750°
Answer: D
C. 1110°
D. 300°
25. You are standing 15 feet away from a tree, and you measure the angle of elevation to be 60°.
How tall is the tree? Assume you are 5 feet tall up to your eyes.
A. 10√3 ft
B. 7.5 ft
Answer: D
C. (15√3)/2 ft
D. 15√3 ft