Division Unified Test in Secondary Mathematics Grade 10

TABLE OF SPECIFICATION
Second Grading Examinations
SY 2018-2019

Easy Average Difficult

Item (60%) (30%) (10%)

UNDERSTANDING
REMEMBERING

ANSWER KEY
Competency

EVALUATING
ANALYZING

CREATING
APPLYING
1 4
Performs division of polynomials using long division and synthetic division 2 3
3 1
4 3
5 1
Proves the Remainder theorem 6 2
7 1
Proves the Factor Theorem 8 3
9 3
Factors Polynomials 2
10
Illustrates polynomial equations 11 4
Proves Rational Root Theorem 12 4
13 1
Solves polynomial Equations 14 2
15 4
16 1
Solves problems involving polynomial equation
17 3
Illustrates polynomial functions 18 4
19 1
20 2
21 3
Graphs polynomial functions.
22 4
23 1
Solves problems involving polynomial functions.
24 2
25 1
Derives inductively the relations among chords, arcs, central angles and
inscribed angles.
26 1
27 4
Proves theorems related to chords, arcs, central angles and inscribed angles. 28 3
29 2
30 4
31 3
32 2
Illustrates secants, tangents, segments and sectors of a circle. 33 1
34 4
Proves theorems on secants, tangents and segments. 35 1
Solves problems on circles. 36 2
Proves theorems on secants, tangents and segments. 37 3
Performs division of polynomials using long division and synthetic division 38 1
39 2
Solves problems on circles.
40 2
TOTAL 12 12 6 6 3 1 40

DIVISION OF DAVAO DEL NORTE

 Division Unified Test in Secondary Mathematics Grade 10
SECOND QUARTERLY EXAMINATION
SY: 2018-2019
Name: _______________________________ Grade/ Section: ______________ Score: ________

Directions: Read and analyze each item carefully. Select and shade the number that
corresponds to your answer. You have one hour to answer the test. GOOD LUCK!

1. Each of the following is a polynomial expression EXCEPT;

① x3 – 2x + 8x – 3 ② 3x3 – √ 2x + 8x2 ③ 5x3 – 4x + 9x4 −3
④ +3
5x
For items No. 2 – 4. Refer to the illustration on long division that follows:
Divide: (x3 – 12x2 + - 42) ÷ (x– 3)

2nd line

2. What is the quotient?

① x– 3 ② x3 – 12x2 – 42 ③ x 2 – 9 x – 27 ④ - 123

3. Which of the following is the first step in dividing the given problem?
① Arrange the dividend in descending order and supply the missing term
② Arrange the divisor in descending order and supply the missing term
③ Arrange the dividend in ascending order and supply the missing term
④ Arrange the divisor in ascending order and supply the missing ter
4. What is the process used to obtain the 2nd line?
① Adding (x2) by ( x - 3) ③ Multiplying (x2) by ( x - 3)
② Subtracting (x2 - 9x) from (x3- 12x) ④ Dividing ((x2 - 9x) by x – 3)
For items number 5 – 8 . Refer to the problem given below.
Divide: ( 3x4 – 6x2 + 1 ) by( x+ 3)
5. What is the synthetic divisor of the problem given above?
① –3 ② -1 ③ 3 ④ x+3

6. Which of the following choices show the correct division sentence for finding the quotient of the problem
① – 3Ι 3 –6 1 ③ 3Ι 3 0 –6 1
–9 45 9 27 57
3 – 15 46 3 9 19 58
② – 3Ι 3 0 –6 0 1
–9 27_ – 63 189 ④ 3Ι 3 0 –6 0 1
3 –9 21 – 63 190 –9 –27_ – 99 –297
3 –9 – 33 – 99 - 296

7. What is the quotient of the given problem?

①3x3 – 9x2 + 21x - 63 ③ 3x4 – 9x3 + 21x2 – 63x+ 190 8..
② 3x2 – 15x + 46 ④ 3x3 – 9 x2 – 33 x – 99
Which of the following will show the correct solution for finding the remainder of the division problem above using the
Remainder theorem?
① 3( 3)4 – 6( 3)2 + 1 ③ 3(– 3)4 – 6(– 3)2 + 1
4 3 2
② 3(– 3) + (– 3) – 6(– 3) + (– 3)+ 1 ④ (– 3)4 – 6(– 3)2 + 1

9.What is the remainder when 4x4 – 3x2 + 2 is divided by x – 2 ?

① 299 ② 54 ③ 34 ④3

10. If 2x4 – mx3 + 7x – 2 is divided by x + 2, the remainder is 8, what is the value of m?

 ① –2 ② –1 9 ④6
③
2
11.. Which of the following will determine if x + 2 is a factor of 3x + 5x2 – 2x + 9?
4

① P(2) = 3(2)4 + 5(2)2 – 2(2) + 9 ③ 3(2)4 + 5(2)2 –2(2) + 9 = 0

② P(–2) = 3(–2)4 + 5 (–2)2 –2(–2) + 9 ④ 3(–2)4 + 5(–2)2 –2(–2) + 9 =0

12. Which of the following is NOT a factor of x3– 7x + 6?

①x–2 ② x–1 ③ x+ 3 ④x+2
13. Find the value of b so that x – 2 is a factor of 2bx 5 – 4bx3 – 8x –16.
① 1 1 ③ –1 ④–8
②
3
14. Find a polynomial equation whose roots are – 2, -1, and 3

① x3 – 6x2 -– 7x – 6 = 0 ② x3 – 7x – 6 = 0 ③ x3 + 7x – 6 = 0 ④ x3 – 6x2 – 7x –6 = 0
15. Which of the following is a possible rational roots of 2x 3 – x2 – x + 6 = 0 ?

① 2 2 2 3
② ③ – ④–
3 3 2
For items no. 16 - 18. Given the equation: x 4 – x3 – 7x2 + x + 6 = 0
16. How many roots will the equation have?
① 4 ② 3 ③2 ④ 1
17. How many possible positive roots will there be?
① 4 ② 3 ③ 2 ④ none
18. Each of the following are roots of the given equation except;
① –2 ② –1 ③ 1 ④ 2
19. The edges of the box are 3, 4, 5 inches respectively. What equal increase in each dimension will increase the volume by
150 cubic inches?
① 2 inches ② 3 inches ③ 4 inches ④ 25 inches

20. Which of the following is an example of a polynomial function?

1
① f(x)=3 x 2+ 4 x 4 −2 5 3 2 ④ f(x) = 3−√2 x
② f(x) = x + √ 9 x -2 ③ f(x)= −2 x+ 5
8 3x
For items no. 21 – 23: Use the given polynomial function:
P(x) = (x2 – 2)(x2 – 1)2(1 – 3x)2(x + 2)
21. What is the degree of the polynomial function given above?
① 16 ② 11 ③ 9 ④ 8
22. What is the leading coefficient of the function given above?
① –9 ② –3 ③ 3 ④ 9
23. If you will be asked to graph the given function using its properties. Which of these would be the end behavior of the
graph?
① falls to the left and rises to the right ③ rises to the left and falls to the right
② falls to the right and rises to the left ④ rises to the right and falls to the left

For numbers 24 – 25
The profit P(in millions of pesos) for a siomai factory can be modeled by P(n)=−n3 +4 n2 +n ,where n is
the number of siomai produced (in millions) in a month.
24. What is the profit of the company for producing 2 million pieces. of siomai?
① 4M ② 10 M ③ 12 M ④ 26 M
25. If the company will produce 5 millions siomai, will they have more profit? Why?
① No, they will not earn profit because the result ia even.
② Yes, the more they produce the more profit.
③ No, because the result will be negative so no profit is guaranteed
④ Yes, but only a little amount because the products will not be sold out.
26. Refer to the graph below which statement is false?
① the degree equals the number of turning points
② the first coefficient is positive
③ the degree is even
④ it has a minimum value

For items no. 27 – 30. Refer to the Figure 1

27. Which of the following is NOT an inscribed angle?
① ∠BAC ③ ∠ ABC
② ∠ ACB ④ ∠ AOB

28. Each of the following is a major arc EXCEPT-

D
^
① CAB ③^
ACB Figure 1
② ^ABC ④ ^
ABD

BC= 70 , what is the measure of m ∠ ABC

29. If m ^
① 350 ② 550 ③ 1100 ④ 2900
30. If chord AC is 48 mm long and is 7 mm from the center of the circle. What is the radius of the circle?

① 7 mm ② 12 mm ③ 24 mm ④ 25 mm

For items no. 31 - 32. In figure 2, if m ∠ A = 3x + 10, m ∠B = 3x + 20 and m ∠C = 2x + 5 ,

find the measure of ∠ D . Figure 2
31. In solving the problem given above, which of the following equations will be used?
① 3x +10 + 3x + 20 = 180 ③ 3x +10 + 2x + 5 = 180
② 3x + 20 + 2x + 5 = 180 ④ 3x + 10+ 3x + 20 + 2x + 5 = 180

32. What is the measure of ∠ D ? Figure 2

① 330 ② 710 ③ 850 ④ 1090

For item nos. 33 – 37.. Refer to figure 3:

33. How do you call P´C?

① tangent ③ secant
② chord ④ diameter

34. If PB = 8 and BA = 10, then PC = __________________

① 64 ③ 36
② 46 ④ 12
Figure 3

35. If AO = 6, AC = 14, and EO = 12, then DO = ______________

① 4 ②7 ③8 ④ 16
36. If we will solve for the measure of ∠ DPA , which of the following equation will be used?
1 ^
① m ∠ DPA = ( m BE −m D
^ A)
2 ③ m ∠ DPA = (m B ^E +m ^DA )
1 ④ m ∠ DPA = (m DA−m B ^ ^E)
② m ∠ DPA = ( m ^ DA−m B ^ E)
2
37. If m ∠ APC =
0
^ = 100 , m CE
^ = 41 , m DA 0
^ = 68 , Find m EB
^ 0
500, m CD
0 0
① 78 ② 68 ③ 270 ④ 140

38. Which of the following statements is not true?

① Tangents of the same circle can intersect with each other inside and outside the circle.
② A circle can have infinite number of tangents.
③ Secants of the same circle can intersect with each other inside and outside circle.
④ A circle can have infinite number of secants.

39. Mon was asked to solve (2x3 - x – 6) ÷ (x – 2) using synthetic division. His solution was as follows:
2 / 2 1 2
4 10
2 5 12
2
Q(x) = 2x – 5x + 12
After showing his solution his teacher asked you to correct his solution. What will you do?

① I will tell him that his answer is correct since he follow the steps correctly.
② I will tell him that his answer is wrong. He should supply the missing term which is x 2
③ I will correct his work by changing the quotient to 2x – 5 , since 12 is the remainder
④ I will change the divisor into – 2.

40. A 24- cm chord subtends an arc measuring 100 0. .The radius of the circle is 24 cm. long. What is the area of the triangle
formed by the radii of the circle and the chord?
① 144√ 2 cm2 ②144√ 3 cm2 ③ 144 cm2 ④ 288√ 3 cm2

Good Luck!!!!