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MATH 10 DIAGNOSTIC TEST

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Republic of the Philippines
Department of Education
National Capital Region
SCHOOLS DIVISION OFFICE
Quezon City, Metro Manila
DIAGNOSTIC TEST IN GRADE 10 MATHEMATICS SY 2018
–
2019
Directions: Choose the letter which corresponds to your answer from the given choices. Then write the letter of your choice on your answer sheet. 1. What do you call a sequence in which every term starting from the second term is obtained by multiplying the preceding term by the same nonzero real number? A. Arithmetic sequence C. Harmonic sequence B. Geometric sequence D. Fibonacci sequence 2.
If the exterior angles of a quadrilateral form a geometric sequence with a common ratio 3/2, find the smallest exterior angle. (Give your correct answer to 2 decimal places.)
A. 44.31˚
B. 66.46˚
C. 149.54˚
D. 224.31˚
3. What is the sum of all the odd integers between 8 and 26? A. 153 B. 151 C. 149 D. 148
4.
Which of the following is a quadratic equation whose roots are
–
2 and
–
4? A.
+ 6 + 8 = 0
C. x
2
+ 2x + 8 = 0 B.
6 + 8 = 0
D.
+ 2 8 = 0
5. Four days
before Cashton’s birthday, Shirley decided to give him marbles. On the
first day, she gave 1 marble, on the second day, she gave 3 marbles, on the third day, 5 marbles, and so on. How many marbles did he receive on his birthday? A. 15 B. 16 C. 25 D. 27 6. How many times will the graph of the polynomial function P (x) =
()( 2)²( + 3)
cross the x-axis? A. 1 B. 2 C. 3 D. 4 7. What is the remainder when the polynomial
2
+ 7
+ 2 3
is divided by (x
–
1)? A. 8 B. 4 C. 3 D. 5 8.
What is the next term of the sequence 3, 9, 15, 21…?
A. 26 B. 27 C. 28 D. 29
9. Express the repeating decimal 0.212121….... as a fraction in simplest form.
A.
307
B.
337
C.
10021
D.
92
10. Find k so that (x
–
1) is a factor of
k
x
2
+ x
–
3. A. 0 B. 1 C. 2 D. 3 11. Find the 8
th
term of a geometric sequence whose 3
rd
term is 27 and the common ratio is 3. A. 2187 B. 6561 C. 19683 D. 59049
12. Which of the following could be the graph of the polynomial function
f
(x) =
( 3)( + 2)
? A. B. C. D. 13.
A coin is tossed twice and the results are recorded, how many different outcomes are possible? A. 1 B. 2 C. 3 D. 4 14. A sequence wherein each succeeding term is obtained by adding a constant term is called ___________. A. Arithmetic B. Geometric C. Fibonacci D. Harmonic 15. AD is a diameter of a circle and AB is a chord. If AD= 34cm, AB = 30cm, find the distance of AB from the center of the circle. (See the figure at the right.) A. 17 cm B. 15 cm C. 4 cm D. 8 cm 16. Which of the following polynomials is exactly divisible by x+1? A.
2
+ 1
C. x
3
+ 2x
2
–
5x
–
6 B.
5
+ 6 + 1
D. All of the above 17. What are the coordinates of the midpoint of a line segment whose end points are at (2, 6) and (4, 8)? A. (3, 7) B. (6, 2) C. (0, 4) D. (6, 14) 18. Which of the following sequences describes an arithmetic sequence?
A. 0, 1, 3, 5…
B. 4, 9, 14, 19…
C. 3, 6, 12, 24…
D. 2, 3, 5, 8…
19. Jules bought salted peanuts at a nearby convenience store. It comes in three flavors: garlic, spicy and adobo. How many different ways can he open his snacks? A. 6 B. 5 C. 3 D. 1 20. What is the measure of the inscribed angle that intercepts a semi-circle ? A. 60
°
B. 90
°
C. 120
°
D. 180
°
21. Given line segment AC, one of its endpoints has coordinates (2, 2). If the midpoint B has coordinates (
–
1, 2), what are the coordinates of the other endpoint? A. (5, 2) B. (
–
4, 2) C. (½, 2) D. (½, ½) 22. What is the 6
th
term in a
n
=
n
2
–
3? A. 9 B. 3 C. 33 D. 12 23. Which of the following is a polynomial function? A. f(x) =
7
−
+ 5 + 1
C. h(x) =
/
3
+ + 1
B. g(x) =
7
+ 5 + √ 5
D. m(x) =
3
+
√
+ 1
24. A circle has the equation
+
= 16
. What is the radius of this circle? A. 256 B. 16 C. 8 D. 4 25. Write the formula described by
the sequence 3, 7, 11, 14…
A.
= 3 1
B.
= 4 1
C.
= 4 + 3
D.
= 3 4
26. Given circle F at the right, find the measure of
ERG if
EFG is 76
0
. A. 34
0
B. 38
0
C. 56
0
D. 124
0
27. In how many ways can 5 students arrange themselves in a row for a pictorial? A. 24 B. 48 C. 60 D. 120 28. What is the first term of the arithmetic sequence with
= 5 and
= 11? A. 1 B.
–
1 C. 2 D. 5 29. Evaluate:
8
P
4
A. 1700 B. 1686 C. 1400 D. 1100 30. The following are all prime factors of the polynomial
1
except A. (x+1) B. (x
–
1) C.
(
1)
D.
+ 1
31. It is an arrangement of distinct objects where order is not important. A. Fundamental counting principle C. Combination B. Permutation D. Probability 32. How many possible rational roots does the given polynomial equation
2
5
+ 7 3
= 0 have? A. 8 B. 7 C. 6 D. 5 33. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, 5 without repetition? A. 125 B. 100 C. 60 D. 30 34. If your percentile rank in an exam is 90. What is your
score’s position?
A. upper 10% B. lower 10% C. upper 90% D. lower 99% 35. The length of a rectangle is (4x
–
1) meters and its width is (2x + 3) meters. Find its area. A. (8
10 3)²
C. (8
10 + 3)²
B. (8
+ 10 + 3)²
D. (8
+ 10 3)²
36. Which of the following is a polynomial function of degree 3? A.
= (
-3) (
+ 1)²
C.
=
3+ ( 3)
B.
=
+ 1 (
+2)
D.
= (
–
3) (
+ 1)²
37. What is the geometric mean between a and 4a? A. 5a B.
±2
C. a D. 4a 38. In how many ways can 3 red notebooks, 2 violet notebooks and 1 green notebook be arranged in a bag? A. 1 B. 6 C. 36 D. 720 39. What figure is formed when points B (1, 3), E (2, 6), T (4, 7) and H (5, 5) are connected consecutively? A. parallelogram B. trapezoid C. square D. rectangle 40. The measure of position that divides a distribution into four equal parts is ________. A. median B. quartile C. decile D. percentile 41. What is the measure of the inscribed angle if it intercepts an arc that measures 48
°
? A. 24
°
B. 48
°
C. 90
°
D. 96
°
42.
Which theorem states that “if a polynomial P(x) is divided by (x –
r), then the remainder is P(r). A. Factor Theorem C. Remainder Theorem B. Rational Root Theorem D. Intermediate Zero Theorem 43. The equation of a circle is (x + 3)
2
+ (y
–
1)
2
= 4. Which of the following statements is FALSE? A. The x
–
coordinate of the center is
–
3. B. The radius of the circle is 2. C. The y
–
coordinate of the circle is
–
1. D. The point (
–
3,
–
1) is on the circle. 44. The weather bureau announced that the probability that it will rain today is 0.8. What is the probability that it will not rain today? A. 0.2 B.1.8 C. 1.2 D. 0.8 45. One card is drawn from a set of cards numbered 1 to 10. Find the probability of drawing out an odd number or a multiple of 3. A.
45⁄
B.
25⁄
C.
15⁄
D.
35⁄
46. The numbers 1 to 15 are placed in a box, and a number is selected. What is the probability that the number is 4 given that it is known to be an even number? A.
115⁄
B.
17⁄
C.
12⁄
D. 1/8 47. If a circle is divided into four equal parts, what is the measure of the central angle? A. 45
°
B. 90
°
C. 100
°
D. 120
°
48. A single card is selected from a deck of 52 cards. What is the probability that it is a king or a jack? A.
B.
C.
D. 1 49. If you roll a six sided die, what is the probability of rolling an even number? A.
B.
C.
D.
50. From a deck of 52 playing cards, how many numbered cards are there? A. 36 B. 40 C. 48 D. 52

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