Republic of the Philippines

Republic of the Philippines

DEPARTMENT OF EDUCATION
CARAGA ADMINISTRATIVE REGION B. 40
Division of Agusan Del Sur C. 53
Aurora National High School D. 54

FIRST QUARTERLY EXAMINATION

MATHEMATICS G10

Name: _______________________________________ Score: ________

1. What is the next shape?

, , ,
, , _ ___.

7. The arithmetic mean between two terms in an

A. arithmetic sequence is 39. If one of these terms is
32, find the other term.
B. A. 38
B. 46
C. C. 69
D. D. 71
n−4 8. It is the indicated sum of the terms of an arithmetic
2. Given the general terma n= , finda 2.
n sequence.
E. A. Arithmetic series
A. – 4 B. Arithmetic Means
B. – 1 C. Geometric Sequence
C. 1
D. Geometric Series
D. 4
3. Which of the following illustrates an arithmetic 9. What do you call a sequence of numbers in which
sequence? each term is obtained from the previous by
A. 3, 6, 12, 24, … multiplying the same value called the common
B. 2, 4, 6, 8, … ratio(r)?
C. 1, 1, 2, 3,5, … A. Arithmetic Means
1 1 1 1 B. Arithmetic series
D. , , , ,…
2 4 6 8 C. Geometric Sequence
D. Geometric Series
4. Given an arithmetic sequence 1, 10. Which of the following sequences illustrate a
6 10 geometric sequence?
, 2 , , 3 , … find the common difference.
4 4 A. 5, 10, 15, 20,…
1 B. 10, 7, 4, 1,…
A.
4 C. 8, 5, 8, 5, …
1 D. 1, 2, 4, 8, . .
B.
2
3 11. Jose got 6 rabbits to raise on his farm. From the
C.
4 following month forward, the rabbit population
3
D. doubled every month.
2
5. What is the first term of the arithmetic Let g(n), be the number of rabbits in Jose’s farm in
sequence __,-6, -9, -10, -13? the nth month since he got the rabbits.
A. -3 What kind of sequence is it?
B. -2 A. Arithmetic
C. 2
B. Fibonacci
D. 3
C. Geometric
D. Harmonic
12. A writer wrote 920 words on the first day, 810 on
6. The first term of an arithmetic sequence is 8 and the second day and 700 words on the third day. If
the last term is 100. What is the second term? the pattern continues, how many words did the
A. 31 writer write on the fifth day?
 A. 480 B. 59 594
B. 500 C. 58 595
C. 1180 D. 58 596
D. 2430 20. Which of the following defines a Fibonacci
13. Which of the following is a finite geometric sequence?
sequence? A. It is a sequence such that the reciprocals of the
A. 2, 6, 18, 54, … terms form an arithmetic sequence.
B. 24, 12, 6, 3, … B. It is a sequence where every term after the first is
1 1 1 1 obtained by adding a constant called the
C. , , , ,… common difference.
3 3 6 12
1 1 1 1 C. It is a sequence where its first two terms
D. , , , …,. is either both 1, or 0 and 1; and each
2 4 8 512
term, thereafter, is obtained by adding
14. What is the geometric mean between 2 and 18?
the two preceding terms.
A. 6
D. It is a sequence where each term after the first is
B. 10
obtained by multiplying the preceding term by a
C. 20
nonzero constant called the common ratio.
D. 36
15. Find the 6th term in the geometric
21. Which of the following describes the nth term of the
sequence 3,12,48,...
harmonic sequence
A. 36
1 1 1 1
B. 576 , , , , …?
C. 1728 4 8 12 16
D. 3072 1
A.
16. Find the eighth term of the geometric sequence n+1
where the third term is 27 and the common ratio is 1
3. B. 2
n +1
A. 2 187
1
B. 6 561 C.
C. 19 683 4n
C. 59 049 1
D.
4 n−2
22. Twelve days before Valentine’s Day, Carl decided
to give Nicole flowers according to the Fibonacci
17. Find the sum of the first 8 terms of the geometric
sequence. On the first day, he sent one red rose,
series if a1=1 and r=2. on the second day, two red roses, and so on. How
A. 15 many roses did Nicole receive during the tenth
B. 16 day?
C. 255 A. 10
D. 256 B. 55
18. Calculate the sum of the terms of the following C. 89
D. 144
geometric sequences.
23. There are 20 rows of seats in a concert hall with 20
1 1 1 1 seats in the first row, 21 seats in the second
1, , , , ,…
2 4 8 16 row, 22 seats in the third row, and so on.
In total, how many seats are there in the concert
hall?
1 A. 83
A.
32 B. 166
1 C. 375
B. D. 590
2
24. A scientist observes that the population of a certain
C. 1 colony of ants triples after every week. If 75 ants
D. 2 were present initially, approximately how many
weeks would it take for the population of the ants
to become 6075?
A. 3
19. Find the sum of the geometric sequence where the B. 4
C. 6
first term is 3, the last term is
D. 8
46 875, and the common ratio is 5.
A. 58 593
Please refer to the illustration below on long division to
answer item 25-26. 30. Find the remainder when x2 + 6x – 17 is divided
by x – 1.
A. – 17
Divide (25x2 – 50x + 25) by (5x-5) B. – 10
C. 6
5x – 5 D. 23
2
31. If f(3) = 0, which of the following statements
5x – 5 25x – 50x + 25 about f(x) is true?
25x2 – 25x 2nd line A. x + 3 is a factor of f(x)
- 25x + 25 B. – 3 is a root of f(x) = 0
- 25x + 25 C. 0 is the least value of f(x)
D. 3 is a zero of f(x)
0 32. If x – c is a factor of p(x),
25. What is the remainder? then p(c) = _____.
A. – 5 A. - 1
B. 0 B. 0
C. 5 C. 1
D. 25 D. 2
26. Which is the divisor?
A.0 33. Find g(2) if g(x) = 2x3 – 5x2 + 6x – 11
B. 5x – 5 A. – 24
C.5x + 5 B. – 11
D. 25x2 – 50x + 25 C. –3
27. A student is trying to use synthetic division to D. 4
solve
(3x3 – 4x2 – x + 1) ÷ (x + 1).
What value should go in the box next? 34. What must be a value of t that will make t + 2
a factor of 3x3 + 5x2 + tx – 10?
-1 3 -4 -1 1 A. –7
7 -6 B. 5
3 C. 6
A. – 1 D. 7
B. – 3 35. . Given the polynomial equation
C. 1 (x + 1) 2 (x – 5) = 0. What is the degree of the
D. 3 given equation?
28. Andy divided x4 + 3x2 – 4x – 2 A. 0
by x – 2 using synthetic division. Her work is B. 1
shown below. Identify her mistake. C. 2
D. 3
2 1 3 -4 -2
2 10 12 36. Suppose that when a polynomial p(x) is divided
1 5 6 10 by x – 5, the quotient is 3x4 – 5x2 + 2x – 5 with
the remainder of 4. We may conclude that…
10 A. x – 4 is a factor of p, and 4 is a zero of p.
X3 + 5x2 + 6x +
x−2 B. x + 5 is not a factor of p, and – 5 is not a
zero of p.
A. Andy wrote the remainder incorrectly. C. x – 5 is a factor of p, and 5 is a zero of p.
B. Andy did not use a zero place holder D. x – 5 is not a factor of p, and 5 is not a zero
for the x3 term. of p.
C. Andy added instead of subtracting the 37. A polynomial has degree 5. Which of the
rows. following is NOT a possible combination for its
D. Andy should have used – 2 as his roots?
division since the divisor is A. 5 real roots
x – 2. B. 3 real roots and 2 complex roots
29. If the remainder after dividing polynomial ( C. 1 real root and 4 complex roots
3 2 D. 2 real roots and 3 complex roots
5 x −3 x + k ¿ by (x+ 1) is 4, which of the
following must be the value of k? For items 38-40, find the quotient and remainder in
A. 10 each of the following.
B. 11
C. 12
38. ¿) ÷ ( x -2)
D. 13
 Quotient : ____________________
Remainder: __________________

39. ¿) ÷ ( x + 1)
Quotient : ____________________
Remainder: __________________

40. ¿) ÷ ( 2x + 1)

Quotient : ____________________
Remainder: __________________
 26. B
27. B
28. B
29. C
30. B
31. D
32. A
33. B
34. C
35. A
36. D
37. B
38. D
39. D
40. D
41. B
42. C
43. A
44. B

I.
A. 1. 448

B. 52428800
C. 51
D. Chickens- 31
E. 41ft.

DAYS OF 1 2 3 4 …
PROMOTION
POSTERS 500 496 492 488 …
REMAINING

ANSWER KEY

1. D
2. B
3. B
4. B
5. A
6. D
7. B
8. A
9. C
10. D
11. C
12. A
13. D
14. A
15. D
16. B
17. C
18. D
19. A
20. C
21. C
22. C
23. D
24. B
25. B