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COMPETENCY TEST CHAPTER
( Operations on Algebraic Expressions )

I. For each problem numbered 1 to 20, choose the right answer !
1. The coefficient of x in 5x2 – 7x + 9 is ….
a. -7 c. 7
b. 5 d. 9
2. The like terms in 7ab2 – 4a2b + 5ab2 – a2b2 are ….
a. -4a2b and 5ab2 c. 7ab2 and –a2b2
b. 7ab2 and 5ab2 d. -4a2b and -a2-b2
3. The expanded form of 7p  (-3pq)  (-2qr) is …
a. -42pqr c. 42pqr
b. -42p2q2r d. 42p2q2r
4. The expanded form of -6ab (4ab2 + 2a2b – 3ab) is …
a. -24a2b2 + 2a2b – 3ab c. -24a2b2 + 2a3b2 – 18a2b2
b. -24a2b3 + 2a2b – 3ab d. -24a2b3 – 2a3b2 + 18a2b2
5. The simplest form of 3 (2a – 4y) – 5 (2x – 3y) is …
a. 4x + 27y c. -4x + 27y
b. 4x – 27y d. -4x – 27y
6. The product of 8a2 – 6a – 5 and 4a2 + 7a + 9 is …
a. 12a2 + a + 4 c. 12a2 – 13a + 4
b. 12a2 + a – 4 d. 12a2 – 13a – 4
7. The difference between -5(3p + q) and 2p – 3q is …
a. -17p – 8q c. 17p – 8q
b. -17p – 2q d. 17p + 2q
8. The least common multiple (LCM) of 144 and 108 is …
a. 36 c. 144
b. 108 d. 432
9. The greatest common divisor (GCD) of 24, 54, and 90 is …
a. 6 c. 30
b. 12 d. 60
10. The LCM of 9p2q3, 12p4q2, and 18p3q4 is …
a. 3p2q2 c. 18p2q4
b. 9p2q2 d. 24a2b3c4
11. The GCD of 8a2b3c3 and 12ab2c4 is ….
a. 4ab2c3 c. 18p3q4
b. 9p2q2 d. 36p4q4

12. (-p6q4r2) : (-p3q2r) = ….
a. –p2q2 c. p2q2
b. –p3q2r d. p3q3r
13.
a. c.
b. d.
14.
a. c.
b. d.
15. The expanded form of -2(4a2b3) is …
a. -128a6b9 c. 128a6b9
b. -128a5b6 d. 128a5b6
16. The expanded form of
a. c.
b. d.
17. The expanded form of (3x + 2) (2x – 4) is …
a. 6x2 – 12x – 8 c. 6x2 – 8x – 8
b. 6x2 + 8x + 8 d. 6x2 – 8x + 8
18. A rectangle has a length of (5x – 2) cm and a width of (4x – 7) cm. The area of the rectangle is ….
a. (20x2 – 27x + 14) cm2 c. (20x2 – 27x – 14) cm2
b. (20x2 – 43x + 14) cm2 d. (20x2 – 43x – 14) cm2
19. The expanded form of (3a – 4b)2 is …
a. 9a2 – 24ab – 16b2 c. 9a2 + 24ab + 16b2
b. 9a2 + 24ab – 16b2 d. 9a2 – 24ab +16b2
20. The expanded from of (3b – 2)2 – (b – 3)2 is ….
a. 8b2 + 6b + 5 c. 8b2 – 6b + 5
b. 8b2 – 6b – 5 d. 8b2 + 6b – 5


II. For the following problems, answer them completely !
1. The length of a rectangle is (3x + 2) cm and the width of it is (2x – 1) cm.
If the perimeter of the rectangle is 60 cm, then :
a. Form an equation in terms of x which gives the length of the perimeter,
b. Find the value of x,
c. Find the area of the rectangle !
2. Expand :
a. (2a2 + 5b2) (4a2 – 7b2)
b. (4x + 3y) (16x2 – 12xy + 9y)2
c. (4x – 3y)2 – (3x – 4y)2
3. Simplify the fractions below !
a.
b.
c.
4. A car traveled from city A to city B at an average speed of v km/hour for 2 hours. Then it continued the journey to the city C at speed of 4 km/hour faster than v for 1.5 hours.
a. Find the total distance from the city A to city C in terms of v !
b. Find the total distance if v = 60 !
5. By using an appropriate identity, find the value of :
a. 4  247
b. 8  509
c. 632 – 372
d. 9742 – 262