1. Which of the following shows a pattern?

A.3, 2, 3, 2, 5, 2
B. 5, 7, 2, T, G, Y
C. A, D, G, J, M
D. smooth, long, wall, sing

2. Which set of numbers are the first three terms of the sequence an = 10n-7?
A. 3, 10, 27 B. 3, 13, 23 C. 3, 17, 13 D. 3, 20, 37

3. Which of the following is a correct description of an arithmetic sequence?

A. A term is obtained by multiplying a constant number from the preceding term.
B. A term is obtained by squaring the preceding term.
C. A term is obtained by adding a constant number to the preceding term.
D. A term is obtained by extracting the square of the preceding term.

4. Which of the following is NOT an arithmetic sequence?

A. 1, 2, 3, 4,… B. 3, 9, 27, 81,… C. 4.5, 5.0, 5.5, 6.0,… D. 13, 2, -9, -20,
…

5. Find the fourth term of a sequence with a common ration of -3 and the first term is 3.
A. 81 B. 27 C. -27 D. -81

6. Which of the following presents a geometric sequence?

25 27
A. 12, -12, -12, -12, … B. 32, 8, 2, ½,… C. 12, , 13, ,… D. 1, 2, 3, 5, 8
2 2

7. During a free-fall, a skydiver jumps 16 feet, 48 feet and 80 feet on the first, second, and third
fall, respectively. If he continues to jump at this rate, how many feet will we have jumped during
the tenth fall?
A. 304 B. 336 C. 314,928 D. 944,784

8. A hall has 30 rows. Each successive row contains one additional seat. If the first row has 25
seats, how many seats are in the hall?
A. 1,185 B. 1,780 C. 1,815 D. 1, 970

9. Determine the 12th term of the geometric sequence 1, 2, 4,…

A. 512 B. 1, 024 C. 1,112 D. 2, 048

10. The first term of a geometric sequence is 2, and the second term is 10, what is the fifth term?
A. 100 B. 250 C. 500 D. 750

11. If a sixth-degree polynomial is divided by a fourth-degree polynomial, find the degree of the
quotient.
A. 1 B. 2 C. 3 D. 4

12. What will be multiplied to (x + 3) to get (3x3 + 9x2 – x – 3)?

A. x – 3 B. 3x – 1 C. 3x2 – 1 D. 3x2 – 3

13. What is the quotient when P(x) = (x3+ 6x2+ 2x – 12) is divided by (x + 2).
A.x2–4x– 6 B.x2–4x+6 C. x2+4x+6 D.x2+4x–6

14. If one factor of(x3–2x2–11x-20) is (x –5), what is theother factor?

A. x2+3x+4 B.x2- 3x+4 C.x2+3x-4 D.x2-3x–4
15.The following are polynomials, EXCEPT
A.x2–4x+5 C.3x4–5x3+2x–1
B.4x-3+8x-2+10x–7 D.x3–y3

16. Which of the following is NOT a polynomial function?

−2 3 1
A. f ( x )=x 3 B. f ( x )= x +1 C. f ( x )=−x+ √5 x 3 D. f ( x )=x 5 −2 x 2
3

17. What are the end behaviors of the graph of f(x) = 3x5+x3-2x-4?
A. rises to the left and falls to the right C. rises to both directions
B. falls to the left and rises to the right D. falls to both directions

18. The coordinates of the vertices of a square are H (3,8), I (15,8), K(15,-4), and E(3,-4). What is
the length of the diagonals of the square?
A. 4 B. 8 C. 12 D. 12√2

19. What are the coordinates of the midpoint of a segment whose endpoints are (-1, -3) and (11,
7)?
A. (2,5) B. (6,5) C. (−5,−2) D. (5,2)

20. A map is drawn on a grid where 1 unit is equivalent to 1 km. On the same map, the
coordinates of the point corresponding to San Vicente is (4,9). Suppose San Vicente is 6 km
South of San Luis. Which of the following could be the coordinates of the point corresponding to
San Luis?
A. (4,3) B. (−2,3) C. (−2,9) D. (−6,9)

21. Which of the following situations involve permutation?

A. Matching tops and skirts
B. Winning the “suertres lotto” combination in the PCSO
C. Choosing four of your classmates to attend in your birthday party
D. Finding the lines formed by connecting the given points on a plane

22. In how many ways can 7 people be seated around a circular table?
A. 6 B. 24 C. 120 D. 720

23. Find the number of distinguishable permutations of the word PILIPINAS.

A. 30, 240 B. 30, 420 C. 32, 400 D. 34, 200

24. In how many ways can 5 girls be seated in a row of 5 seats?

A. 95 B. 120 C. 105 D. 100

25. From a class of 32 girls and 18 boys, how many study groups of 3 girls and 2 boys can be
formed?
A. 438,880 B. 478,880 C. 638,880 D. 758,880
 b c
1. If ab + cd = 12 ad, and ad ≠ 0, then + = ¿.
d a ¿
a. ab + cd b. 12 c. 12a + 12d d. 12 ac

2. What must be the value of x in the arithmetic progression x – 7, x – 2, x + 3 so that its 10 th term
will be 40?
a. 3 b. 2 c. 1 d. 4
3. The average of m and n is 9, and p = 12. What is the average of m, n, and p?
a. 7 b. 21 c. 10 d. 18

1 2 1 1
4. What is the value of x in + − = ?
2 3 x 6
a. 2 b. 3 c. 1 d. 4

5. M varies inversely as N. If M = 25 when N = 2, what is M when N = 5?

a. 16 b. 10 c. 5 d. 2

6. A falling body strikes to the ground with a velocity V, which varies directly as the square root of
the distance d it falls. If a body that falls 100 feet strikes the ground with a velocity of 80 ft./sec.,
with what velocity will a ball dropped from a height of 550 ft. strike the ground?
a. 150 ft./sec. b. 190 ft./sec. c. 170 ft./sec. d. 188 ft./sec.

8
7. The same number is subtracted from the numerator and denominator of the fraction . If the
11
2
resulting fraction is equivalent to , what is the number subtracted?
3

a. 5 b. 2 c. 3 d. 4
8. If 3x = 81 and 4y = 64. What is (x – y)?
a. 17 b. 1 c. 0 d. -1

9. Which of the following equation is parallel to 3x – 2y = 4 and has a y – intercept of -3?

a. y = 2x – 3 b. 2x – 3y = 6 c. 2x – 3y = 4 d. 3x – 2y = 6
10. What is the slope of the line passes through (-1, 2) and (3, -4)?
3 −3
a. b. 3 c. 2 d.
2 2

11. P is 7 less than the square of the sum of the quotient of x and y and the product of x and y.
which equation express this relationship?

( ) ( )
2 2
x x
a. P= 7− + xy c. P=7− + xy
y y

( ) ( )
2 2
x x
b. P= + xy −7 d. P= + xy −7
y y
12. Determine the equation of the parallel to 3x – 8y + 11 = 0 and passing through (8, 10).
a. 8x – 3y – 34 = 0 c. 3x – 8y – 104 = 0
b. 3x – 8y + 56 = 0 d. 3x + 8y + 56 = 0

13. One end of a line segment is P(1, -2). If the midpoint of the segment is (4, 3), find the
coordinate of the other endpoint of the segment.
a. (6, 9) b. (6, 7) c. (5, 8) d. (7, 8)
14. What is the equation of the line through (4, 1) and parallel to the line through (7, 3) and (5, -1)?
a. x – 4y = 0 b. 3x + y = 13 c. 2x – y = 7 d. 5x – 6y = 14
−6
15. What is the equation of the line with slope and passes through C(4, 9)?
11
a. 6x + 11y – 75 = 0 c. 6x – 11y – 123 = 0
b. 11x + 6y + 10 = 0 d. 6x + 11y – 123 = 0

16. How long is the diameter of x2 + y2 – 10x + 14y = -10?

a. 128 units b. 16 units c. 8 units d. 64 units

17. In the graph of y = 2 – 2x2 – 4x, what is the highest point?

a. (1, -4) b. (4, -1) c. (-4, 1) d. (-1, 4)

18. The president of the senior class is authorized to appoint a committee of 5 from 4 elected
males and 8 elected females. How many different committees are possible if 3 elected males
are to be members?
a. 32 b. 112 c. 120 d. 220

19. How many distinct permutations can be made for the letters o the word INFINITY if all the
letters are to be taken?
A. 3540 B. 4512 C. 3360 D. 3124
20. A card is selected at random from a box of 20 cards numbered 1 to 20. What is the probability
that the number is multiple of 3?
7 3 5 3
a. b. c. d.
20 20 20 10
21. Solve for x: x = √18 - √72 + √50

A. -2√2 B. 2√2 C.4 D. 4√3

22. Find the value of x that will satisfy the following expression: √x – 2 = -√x + 2

A. x = 3/2 B. 18/6 C. 9/4 D. 4/9

23. Simplify: (a-2 b3 ) 2

a2b-1
2 2 6 6
a a a a
A. 7 B. 5 C. 7 D. 5
b b b b

24. Simplify the following:

√5−√ 3
√ 5+ √3
A. 4 + √ 15 B. 4 - √ 15 C. 8 + √ 8 D. 8−√ 8

25. If x < o and (3x-2)2 = 25, then 2x2 + 1 is _____.

A. – 1 B. 2 C. 7/3 D. 3
1. How do you write √ 2 x 3 y 5 in rational exponent form?
1 3 5 3 5 3 5
A. 2 2 x 2 y 2 B. 2 x 2 y 2 C. 2 xy D. x 2 y 2

1
2. Express (ab) 2 in radical form?
A. √ ab B. (ab)2 C. √ ab2 D. a 2 b 2

3. When do you say that two radicals are alike?

A. when their indices are the same. C. when their integral exponents are the same.
B. when their radicands are the same. D. when their indices and radicands are the same.

4. The product of ¿ + 4)¿ - 4) is __________.

A. -34 B. 34 C. 26 D. -26

5. Which of the following set of radicals can be added or subtracted?

A. √ xy , 3 √ 5 x B. 2 √7 x , 3 √ 63 x C. 3 m √ n , m3 √ n D. √3 xy 2 , 3 √3 x2 y

6. Three of the radicals below can be expressed as similar radicals. Which of the following is NOT similar to the
other given radicals?
A. √ 44 B. √ 99 C. √ 110 D. √ 176

7. The combined form of 64 √ 3 - 4√ 48 - 5√ 48 is ________.

A. 3 √ 8 B. 28 √ 3 C. 8 √ 3 D. 3 √ 48

√
3
48 x3 y 7
8. Divide: 3 5
√8 x y
x √8 √6 x √6 x y √8
3 23 23 3
y x
A. B. C. D.
y x y x

9. What is the result after simplifying 2 √ 3+ 4 √ 3−5 √ 3 ?

A. −√ 3 B. √ 3 C. 11 √ 3 D. 21 √ 3

10. The length of a rectangle is 2 √ 50 meters and its width is3 √ 8meters. Find its area.
A. 5 √ 58 sq . meters B. 120 sq . meters C. 32 √ 2 sq . meters D. 124 sq . meters

11. Between what two consecutive whole numbers does √ 31 lie?

A. 4 and 5 B. 6 and 7 C. 5 and 6 D. 7 and 8

12. Evaluate and perform the operation of −3 √ 20 -√ 5.

A. −√ 5 B. −7 √ 5 C. −3 √ 15 D. already simplified
13. Find the perimeter of a triangle whose side lengths are 15 cm, 8√7 cm, and √112 cm. Give the answer as a
radical expression in simplest form.
A. (15 + 8√7 + √112)cm C. (15 + 24√7 )𝑐𝑚
B. (15 + 12√7) 𝑐𝑚 D. 27√7 cm

14. Simplify the expression√ 8 y + 5√ 50 y − 2 √ 18 y .

A. 13√ 2 y B. 21√ 2 y C. √ 8+ 5√ 50− 2 √ 18 √ y D.882 y

15. A square stepping stone in Atlanta’s Centennial Olympic Park measure 4√2 feet on a side. Which of the
following is TRUE of the area of the square stone?
A. The area is a indeterminate C. The area is an irrational number
B. The area is a rational number D. The area cannot be determined

16. The simplest form of √ 3

40 x 8 y 9 z 10 is
A. 2 x 2 y 3 z 3 √
3
5 x2 z B. 3 x 2 y 3 z3 √
3
5 x2 z C. 2 xyz❑ √
3
5 xyz D. C. 3 xyz ❑ √
3
5 xyz

17. Simplify the expression

A. 4 √ xz B. 2 x √ z
√ 28 x 3 y 2 z
7 xy
2

C. 2 √ xz D. 4 x √ z

4
18. Rationalize the denominator
3 √2 x
2 √2 x 2 2
A. B. c. x D.2 x
3x √x

√
19. Simplify 3 √2 x 24
A. √ x B. x 4 C. x √ x D. 12√ x

20. What is the simplified form of

√x
5
2 √x
5 4
√
5 32
x
?

A. B. C. 2x D. x
x x

21. Evaluate the expression √ 160 a5 b4

A. ab √ 80 B. 4 √ 10 a5 b 4 C. 4 √ a5 b4 D. 4 a2 b2 √ 10 a

22. Which of the following is equal with √ √3 64

A. √6 64 B. √3 64 C. √2 64 D. √2 8

23. It is the process of eliminating the radicals in the denominator of a fraction.

A. Elimination B. Rationalization C. Fractionalization D. Simplification

24. Which of the following needs to be rationalized?

a b √c
2 2 2 2
a b ab 2
a b
2
A. 2 √ c B. C. 2 √ c D.
c c
2
c √c

25.
1
√ 3 1
8
when simplify is equal to
1
A. B. 2 C. 4 D.
4 2