Republic of the Philippines

DEPARTMENT OF EDUCATION
Florida National High School
Florida, Butuan City
SY 2015-2016
NAT REVIEWER IN MATHEMATICS – SET B
Name: ___________________________________ Score: ____________________
Grade / Section: ___________________________ Date: _____________________
Direction: Choose and encircle the letter of the best answer.
1. Which of the following is the sum of all the multiples of 3 and 15 to 48?
a. 315 b. 360 c. 378 d. 396
2. Find the 8th term of a geometric sequence where the third term is 27 and the common ratio is 3.
a. 2187 b. 6561 c. 19 683 d. 59 049
3. What is the next term in the Fibonacci sequence 1, 1, 2, 3, 5, 8, … ?
a.13 b.16 c.19 d. 20
4. The first term of an arithmetic sequence is 2 while the 18th term is 87. Find the common difference of the sequence.
a.7 b. 6 c. 5 d. 3
2 2
5. What is the 6 term of the geometric sequence , , 2, 10, … ?
th
25 5
a. 25 b. 250 c. 1250 d. 2500
6. Find 𝑘 so that the numbers 2𝑘 + 1, 3𝑘 + 4, 𝑎𝑛𝑑 7𝑘 + 6 form a geometric sequence
a. 𝟐; −𝟏 b. −2; 1 c. 2; 1 d. −2; −1
3 9 27 81
7. What is the sum of the infinite geometric series − + − +⋯
4 16 64 256
3 𝟑
a. 3 b. 1 c. d.
4 𝟕
8. Find 𝑝 so that the numbers 7𝑝 + 2, 5𝑝 + 12, 2𝑝 − 1, … form an arithmetic sequence.
a.−8 b.−5 c. −13 d. −𝟐𝟑
9. What is the 𝑛𝑡ℎ term of the arithmetic sequence 7, 9, 11, 13, 15, 17, …?
a. 3𝑛 + 4 b. 4𝑛 + 3 c. 𝑛 + 2 d. 𝟐𝒏 + 𝟓
𝑛2 −1
10. What is the 7th term of the sequence whose nth term is 𝑎𝑛 = ?
𝑛2 +1

𝟐𝟒 23 47 49
a. b. c. d.
𝟐𝟓 25 50 50
2
11. How many real roots does the quadratic equation 𝑥 + 5𝑥 + 8 = 0 have?
a. 0 b. 1 c. 2 d. 3
12. The equation (3𝑥 + 5)(𝑥 − 1) = −2 is a quadratic equation but is not written in standard form. What is the standard form of
these equation?
a. 3𝑥 2 − 3𝑥 + 5𝑥 − 5 + 2 = 0 c. 3𝑥 2 − 8𝑥 + 8 = 0
b. 3𝑥 2 − 2𝑥 + 3 = 0 d. 𝟑𝒙𝟐 + 𝟐𝒙 − 𝟑 = 𝟎
13. Which of the following is a polynomial?
1
i. 4𝑥 3 + 9𝑥 − 5𝑥 2 + 7 ii. 2𝑥 −5 + 𝑥 −2 + 𝑥 −3 + 2𝑥 + 5 iii. 2
𝑥 +3𝑥+6
a.i only b. ii only c. i and ii d. i and iii
14. The following are examples of polynomials, EXCEPT
a. 𝑥 2 − 4𝑥 + 5 b. 𝟒𝒙−𝟑 + 𝟖𝒙−𝟐 + 𝟏𝟎𝒙 − 𝟕 c. 3𝑥 4 − 5𝑥 3 + 2𝑥 − 1 d. 𝑥 3 −𝑦 3
15. What is the quotient when 𝑥 2 − 25 is divided by 𝑥 − 5 ?
a. 𝑥 − 5 b. 𝑥 − 25 c. 𝒙 + 𝟓 d. 𝑥 + 25
16. Which expression gives the remainder when P(x) = 4𝑥 2 + 2𝑥 − 5 is divided by 𝑥 − 2?
5
a. 𝑃(−5) b. 𝑃(−2) c. 𝑷(𝟐) d. 𝑃( )
4
17. Which of the following polynomials is exactly divisible by (3𝑥 + 1) ?
a. 6𝑥 2 + 17𝑥 + 5 b. 9𝑥 2 + 6𝑥 + 1 c. 3𝑥 3 + 4𝑥 2 − 8𝑥 − 3 d. all of the above
18. Which of the following is the factored form of 𝑥 3 + 3𝑥 2 − 10𝑥 − 24 ?
a. (𝒙 + 𝟒)(𝒙 − 𝟑)(𝒙 + 𝟐) c. (𝑥 − 4)(𝑥 − 3)(𝑥 + 2)
b. (𝑥 − 4)(𝑥 − 3)(𝑥 − 2) c.(𝑥 + 4)(𝑥 + 3)(𝑥 − 2)
19. Factor 8𝑥 3 − 729 completely.
a. (2𝑥 − 9)(4𝑥 2 − 18𝑥 + 81) c. (2𝑥 + 9)(4𝑥 2 + 18𝑥 + 81)
2
b.(2𝑥 + 9)(4𝑥 − 18𝑥 + 81) d. (𝟐𝒙 − 𝟗)(𝟒𝒙𝟐 + 𝟏𝟖𝒙 + 𝟖𝟏)
20. What is the sum of the measures of the central angles of a circle with no common interior points?
a. 120 b. 240 c. 360 d. 480
21. A dart board has a diameter of 40cm and is divided into 20 congruent sectors. What is the area of one of the sectors?
a. 20𝜋 𝑐𝑚2 b. 40𝜋 𝑐𝑚2 c. 80𝜋 𝑐𝑚2 d. 800𝜋 𝑐𝑚2
22. Catherine designed a pendant. It is a regular hexagon set in a circle. Suppose the opposite vertices are connected by line
segments and meet at the center of the circle. What is the measure of each angle formed at the center?
a. 22.5° b. 45° c. 60° d. 72°
23. If an inscribed angle of a circle intercepts a semicircle, then the angle is ________
a. Acute b, right c. obtuse d. straight
24. Calculate 𝑃(12, 4)
A. 40,320 B. 𝟏𝟏, 𝟖𝟖𝟎 C. 990 D. 495
25. Find 𝐶(18, 4)
A. 2,400 B. 𝟑, 𝟎𝟔𝟎 C. 4,896 D. 73,440
26. If 𝑃(9, 𝑟) = 504, 𝑤ℎ𝑎𝑡 𝑖𝑠 𝑟?
A. 7 B. 6 C. 5 D. 𝟑
27. If 𝑃(𝑛, 4) = 17,160, 𝑡ℎ𝑒𝑛 𝑛 = ______
A. 9 B. 11 C. 𝟏𝟑 D. 14
28. If 𝐶(𝑛, 5) = 252, 𝑡ℎ𝑒𝑛 𝑛 = ______
B. 7 B. 8 C. 9 D. 𝟏𝟎
29. In how many different ways can 7 potted plants be arranged in a row?
A. 𝟓, 𝟎𝟒𝟎 B. 2,520 C. 720 D. 210
30. In how many different ways can 10 different-colored horses be positioned in a carousel?
A. 504 B. 4 032 C. 𝟑𝟔𝟐 𝟖𝟖𝟎 D. 3 628 800
31. Which of the following represents the distance d between the two points (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) ?
A. 𝑑 = √(𝑥2 + 𝑥1 )2 +(𝑦2 + 𝑦1 )2 C. 𝒅 = √(𝒙𝟐 + 𝒙𝟏 )𝟐 −(𝒚𝟐 + 𝒚𝟏 )𝟐
B. 𝑑 = √(𝑥2 − 𝑥1 )2 +(𝑦2 − 𝑦1 )2 D. 𝑑 = √(𝑥2 − 𝑥1 )2 −(𝑦2 − 𝑦1 )2
32. Point L is the midpoint of 𝐾𝑀̅̅̅̅̅. Which of the following is true about the distances among K, L, and M?
A. 𝐾𝑀 = 𝐾𝑀 B. 𝐿𝑀 = 𝐾𝑀 C. 𝑲𝑳 = 𝑳𝑴 D. 2|𝐾𝑀| = 𝐾𝐿 + 𝐿𝑀
33. A map is drawn on a grid where 1 unit is equivalent to 2km. On the same map, the coordinates of the point corresponding to
San Rafael is (1, 4). Suppose San Quintin is 20 km away from San Rafael, which of the following could be the coordinates of the
point corresponding to San Rafael?
A. (17, 16) B. (17, 10) C. (𝟗, 𝟏𝟎) D. (−15, 16)
34. If the coordinates of M and N are (5, 7) and (5, -4), which of the following would give the distance between two points?
A. |7 − 4| B. |7 − 5| C. |−𝟒 − 𝟕| D. |−4 − 5|
35. The distance between two points 𝑀 (𝑥, 5) 𝑎𝑛𝑑 𝐶 (5, −1) is 10 units. What is the x-coordinate of M if it lies in the second
quadrant?
A. −7 B. −𝟑 C. −1 D. 13
36. Which of the following equation describes a circle on the coordinate plane with a center at (2, −3) and a radius of 5 units?
A. (𝑥 − 2)2 + (𝑦 + 3)2 = 252 C. (𝑥 − 3)2 + (𝑦 + 2)2 = 252
2 2 2
B. (𝑥 + 2) + (𝑦 − 3) = 5 D. (𝒙 − 𝟐)𝟐 + (𝒚 + 𝟑)𝟐 = 𝟓𝟐
37. Which of the following would give the coordinates of the midpoint of (−6, 13)𝑎𝑛𝑑 𝑄(9, 6) ?
−6+13 9+6 −𝟔+𝟗 𝟏𝟑+𝟔 −6−13 9−6 −6−9 13−6
A. ( , ) B. ( , ) C. ( , ) D. ( , )
2 2 𝟐 𝟐 2 2 2 2
38. The endpoints of a segment are (−5, 2)𝑎𝑛𝑑 (9, 12) respectively. What are the coordinates of its midpoint?
A. (7, 5) B. (𝟐, 𝟕) C. (−7, 5) D. (7, 2)
39. The coordinates of the vertices of a rectangle are 𝑊(−2, 6), 𝐼(10, 6), 𝑁(10, −3), 𝐷(−2, −3). What is the length of a diagonal of
a rectangle?
A. 7. 5 B. 9 C. 12 D. 𝟏𝟓
40. Harry Potter likes to wear colored shirts. He has 10 shirts in the closet. Three of these are blue, four are in different shades of
red, and tdhe rest are of mixed or different colors. What is the probability that he will wear a blue or a red shirt?
7 4 3 4 3 7 7 4
A. + B. + C. + D. −
10 10 10 10 10 10 10 10
41. The spinner on the right is spun. What is the probability of a spin that results in an even number or a number less than 4?
1 3 4 5
A. B. C. D.
4 8 8 8
42. Jerson has four cans of juice – one can of orange, one of pineapple, one of calamansi, and one of guyabano. He chooses three of
these cans to take to school. If she chooses calamansi, what is the probability she also chooses pineapple?
7 3 2 3
A. B. C. D.
8 4 3 8
43. Noel tosses a fair coin eight times, and observes whether the toss yields a head (H) or a tail (T). Which of the following
sequences of outcomes yields a head (H) on his next toss? (I) T T T T T T T T
(II) H H T H T T H H
A. I B. II C. Neither I nor II D. Either I or II
44. A baby has 5 blocks in a box. One block is red, one is yellow, one is green, one is blue, and one is black. The baby pulls out a
block, looks at it, and puts it in the box. If he does this 4 times before he gets bored and crawls away, what is the probability that
the 4 blocks selected are all of the same color?
5 1 4 2
A. 4 B. 4 C. 4 D. 4
5 5 5 5
45. A box contains 4 red balls and 6 blue balls. A second box contains 16 red balls and an unknown number of blue balls. A single
ball is drawn from each box. The probability that both balls are of the same color is 0.44. How many blue balls are there in the
second box?
A. 4 b. 20 C. 24 D. 44
46. A family has two children. Suppose that he birth of each child is an independent event that it is equally likely to be a boy or a
girl. Let C denote the event that the family has one boy and one girl. Let D denote the event that the family has at most one girl.
Which of the following must be true about events C and D?
A. C and D are independent events C. C and D are not independent events
B. C occurs given that D does not occur. D. C and D are mutually exclusive events
47. A married couple agreed to continue bearing a new child until they get two boys, but not more than 4 children. Assuming that
each time that a child is born, the probability that it is a boy is 0.5, independent from all other times. Find the probability that the
couple has at least two girls.
1 5 5 4
A. B. C. D.
2 16 8 15
48. The probability that a visit to the school clinic is neither due to dental reasons nor medical reasons is 35%. Of those coming to
the clinic, 30% are due to medical reasons and 40% are due to dental reasons. What is the probability that a visit to the school
clinic is due to both dental and medical reasons?
A. 0.05 B. 0.12 C. 0.18 D. 0.25
49. A public health researcher examines the medical records of a group of 9937 men who died in 1999 and discovers that 210 of
the men died from causes related to heart disease. Moreover 312 of the 937 men had at least one parent who suffered from heart
disease, and of these 312 men, 102 died from causes related to heart disease. Determine the probability that a man randomly
selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease.
102 108 312 414
A. B. C. D.
625 625 625 625
50. There are four batteries, and one of them is defective. Two are to be selected at random for use on a particular day. Find the
probability that the second battery selected is not defective, given that the first was not defective.
2 1 1 1
A. B. C. D.
3 4 3 2

Prepared by: JACuarterosfeb2016