math 10

​Division

Republic of the Philippines

Department of Education

REGION III-CENTRAL LUZON

REGIONAL MID-YEAR ASSESSMENT IN MATHEMATICS 10

Name: ___________________________________

Date: ____________

Section: __________________________________

Score: ___________

DIRECTIONS: Read and understand each item carefully. Choose the correct answer among

the given choices and write only the letter on your answer sheet.

___1. Which is true in the number pattern 3, 10, 17, 24, 31, 38?

A. The next term is obtained by adding 7

B. The next term is obtained by subtracting 7
C. The next term is obtained by multiplying by 7

D. The next term is obtained by dividing by 7

___2. In the arithmetic sequence -8, -11, -14 ... which term is -32?

A. 8th term

C. 10th term

B. 9th term

D. 11th term

For item number 3, study the problem inside the box below.

___3. How much will Mr. Santos save after a month? 2 months? After 3 months? 4 months?
Summarize your answer using the table below.

A. 2 500, 5 000, 7 500, 10 000
B. 5000, 7 500, 10 000, 12 500
C. 15 000, 17 500, 20 000, 22 500
D. 17 500, 20 000, 22 500, 25 000

Month No.

1

2

3

4

Savings

Mr. Santos is planning to buy a laptop for his teaching. To prepare for this, he

is thinking of saving P 2,500.00 every month starting next month. He has already saved
Php 15,000.00 for this purpose.

For item number 4, refer to the table below.

___4. What can you say about the numbers? Is there anything that you have noticed?

A. From the numbers, we can say that the 1st number added to itself and so with the next

remaining numbers.

B. From the numbers, we can say that the 1st number and the 2nd number added and so

with the next remaining numbers.

C. From the numbers, we can say that the second number is twice the first number and so

with the next remaining numbers.

D. From the numbers, we can say that the 1st number multiplied by 3 and so with the next

remaining numbers.

For item number 5, refer to the information below

___5. Using the given information, help Fiona to pin out the steps in solving the given tasked
to her in finding the arithmetic means between a certain number.

I.

Use the general formula an = a1 +(n-1) d

II.

Solve for d.

III.

Substitute the given values of an and a1.

IV.

Add the value of d, to the terms.

A. I, III, II, IV

C. I, III, IV, II

B. B. I, II, IV, III

D. I, II, III, I

___6. The geometric mean between the first two terms in a geometric sequence is 24. If the
third term is 8, find the first term.

A. 56

C. 72

B. 64

D. 256

DAY

NUMBER OF EGGS

1

6

2

12

3

24

4

48

5

56

Raising ducks is a good source of additional income specially when the
area is near the lowland rice field. Pau’s place is a perfect area for duck raising.
When Pau starts raising his ducks, he makes a record of the production of eggs
as his ducks starts laying eggs. He made a tally of the number of eggs his
ducks laid each day. The table below shows his tally.

One of the common tasks in studying arithmetic sequence is

finding the arithmetic means. The arithmetic means are the terms
between any two nonconsecutive terms of an arithmetic sequence.

___7. Zion was assigned by his teacher to get the 8th term of the geometric sequence 8, 12,
18, … but healready forgot the steps on how to solve it, let us help him to do this by
listing out the procedure.

I. Apply the Product law of exponents.
II. Get the product of a1 and the result of rn-1
III. Find the common ratio between two terms.
IV. Substitute the values for a1, n, and r in the formula.
V. Use the general formula for geometric sequence an = a1rn-1

A. I, II, III, IV, V

C. III, IV, V, I, II

B. I, II, IV, III, V

D. III, V, IV, I, II

___8. Find the sum of the numbers between 1 and 100 which are divisible by 6.

A. 618

C. 816

B. 714

D. 917

___9. If the first term is 19, and the last term is 96, the sum of the arithmetic series is
690, how many terms are there in a sequence?

A. 9

C.11

B. 10

D.12

___10. Grade 10 students are tasked to form a triangular pyramid out from 400 blocks. How
many layers of blocks can be made if there are 39 blocks in the bottom and only 1
block at the top of the pyramid?

A. 10

C. 30

B. 20

D. 50

___11. To practice social and physical distancing due to the COVID 19 pandemic,
students inside the classroom are arranged alternately as shown in the given
illustration below. The classroom can only accommodate four rows with at most 5
seats per row. If 5 seats are placed in the first row, how many seats are available in
the third row and how many students can use the classroom in every session?

A. 4 seats, 18 students

C. 4 seats, 20 students

B. 5 seats, 18 students

D. 5 seats, 20 students

___12. Because of air resistance, the length of each swing of a certain pendulum is 85% of
the length of the previous swing. If the first swing has a length of 60 cm, find the total
length the pendulum will swing before coming to rest.

A.

200 cm

C. 400 cm

B.

300 cm

D. 500 cm

___13. To build up endurance, you start an exercise program, you start 30 minutes on the
first day, 34 minutes on the second day, 38 minutes the third day, 42 minutes on the
fourth day, and so on, each day extending your exercise time by 4 minutes. If you
continue at this rate, ending at 2 hours and 30 minutes, what is the total time you
spend exercising?

A. 2,610 minutes

C. 2,790 minutes

B. 2,700 minutes

D. 2,880 minutes

___14. A farmer has eight baskets used in collecting chicken eggs from his poultry house.
He placed three eggs in the first basket, six eggs in the second, and twelve eggs in
the third. If he continues to put eggs on the next baskets in such a way that each has
twice the number of eggs as the basket before it, then how many eggs does the farmer
collect?

A. 80

C. 765

B. 410

D. 850

___15. Castor used synthetic division to look for the quotient of 6𝑦2+ 16𝑦 + 4𝑦3− 3 and
𝑦 − 2. He got 13 as a remainder. His solution is shown below.

What is the error?

I. The sign of the divisor was not changed.
II. The sum entries in the third row are incorrect.
III. The numerical coefficients of the first row were not properly written.
IV. The terms of the polynomial were not arranged according to decreasing

powers of y.

A. I and II only

C. II and IV only

B. I and IV only

D. III, and IV only

___16. You are tasked to evaluate (x2 + 10x + 21) ÷ (x + 7) using long division, what will be
steps are you going to follow for you to do the work correctly?

I. Subtract to get the remainder.
II. Multiply that term by the divisor.

III. Subtract and write the result to be used as the new dividend.
IV. Multiply that term and the divisor and write the result under the new dividends.
V. Divide the first term of the dividend by the first term of the divisor and write

the result as the first term of the quotient

VI. Divide the first term of this new dividend by the first term of the divisor and write

the result as the second term of the quotient.

A. I, II, VI, IV, V, III

C. V, II, III, VI, IV, I

B. I, V, II, IV, VI, III

D. V, III, II, VI, IV, I

-2

6

16

4

-3

-12

-8

16

6

4

-4

13

___17. Given P(x) = 2x4 + x3 –3x2 – x – 15. What is the value of P(2).

A. 9

C. 17

B. 11

D. 25

___18. In the expression x3 + 6x2 + 11x + 6 = 0 , If x = 1, the result is 24. What does this
imply?

A. 1 is a root of the equation

C. 1 is a factor of the equation.

B. 1 is not a root of the equation

D. 1 is not a factor of the equation.

___19. Nicole divides the polynomial (5𝑥2+ 14𝑥 − 24) 𝑏𝑦 (𝑥 + 4). using long method.
What is the process used to obtain the second line?

Use the illustration on long division that follows:

A. Adding 5x to (𝑥 + 4)

C. Multiplying 5x by (𝑥 + 4)

B. Subtracting 5x from (𝑥 + 4)

D. Dividing 5x by (𝑥 + 4)

___20. Consider the polynomial equation, x3 + 11x + 6x2 + 8 = 0. Using synthetic division,
we write the coefficients of the dividend in the first row as 1 11 6 8. Can
you spot an error entry of the coefficients?

A. No, since the coefficients are written in correct order.
B. Yes, constant must be arranged in descending order.
C. Yes, 6 must be written before 11 since exponents must be arranged in descending
order.
D. Yes, the last number must be negative since it will be written on the right side of
the equation.

___21. Which of the following polynomials can be easily solved by applying the zero-product
property?

A. 2x3 + 4x2 + 2x + 7 = 0

C. x2 + 2x + 1 = 0

B. x3 + 3x2 + 2x + 3 = 0

D. (x-2) (x+1) = 0

5𝑥 − 6

𝑥 + 4 )5𝑥2+ 14𝑥 − 24̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅

5𝑥2+ 20𝑥

−6𝑥 − 24

−6𝑥 − 24

0

___22. Supply the missing terms in the box by finding the roots of the given polynomial
equation x3 - 8x2 +5x + 14 = 0.

2

1

5

14

2

-12

1

-6

-7

0

A. -8, -14

C. -8, 14

B. 8, -14

D. 8, 14

___23. Which of the following is/arethe root/s of 𝑥(𝑥 − 2)(𝑥 − 2)(3𝑥 + 1) = 0?

I. −

1

3

II. 0

III.

1

3 IV. 2

A. I and IV only

C. I, III and IV only

B. I and II only

D. I, II and IV only

___24. It is a sequence in which each term after the first can be obtained by multiplying the
preceding term by a fixed constant called the common ratior.

A. Arithmetic Sequence

C. Harmonic Sequence

B. Geometric Sequence

D. Fibonacci Sequence

___25. Pedro and Juan made a new box for the popcorn. They have designed a box with
the width 3 cm less than the length and the height are 6 cm greater than the length.
The volume of each box must be 40 cm3.What is the length of the box?

A. 4

C. 8

B. 5

D. 10

___26. What should be the value of n if 𝑓(𝑥) = 2𝑥𝑛− 11𝑥 + 2 is a polynomial function?

A.

1
4

C. 4

B. √4

D. -4

___27. What could be the graph of the function 𝑓(𝑥) = 3𝑥5− 6𝑥2+ 3?

A.

C.

B. D.

___28. The profit P, in pesos, of a garments factory can be modeled by the polynomial

equation 𝑃(𝑥) = 0.00105𝑥3+ 𝑥 − 10 where x represents the number of bundles of T-
shirts sold. What is the profit when x = 3000?

A. 28,352,990

C. 27,993,150

B. 28,350,000

D. 27,000,000

___29. Quadrilateral LOVE is inscribed in a circle. If the m of ∠Lis 60°, m of ∠O is 150°,
m of ∠V is 120°, what is the m of ∠E?

A. 30°

C. 60°

B. 45°

D.150°

___30. In ʘ C, line AB is a diameter. If point D is on ʘ C, what is the m of ∠ D if ⊿ ADB is
inscribed inside ʘ C?

A. 45°

C. 180°

B. 90°

D. 360°

___31. In ʘ O, chords AB and FG are congruent. What can be said about 𝐴𝐵⏜ and 𝐹𝐺⏜?

A. 𝐴𝐵⏜ is congruent to 𝐹𝐺⏜ .

B. 𝐴𝐵⏜ is half the size of 𝐹𝐺⏜.

C. 𝐴𝐵⏜ is twice the size of 𝐹𝐺⏜.

D. 𝐴𝐵⏜ and 𝐹𝐺⏜ are equal to 180°.

___32. Given that ʘ C ≅ ʘ D.

∠𝐴𝐶𝐵 ≅ ∠𝐸𝐷𝐹

Prove that: arc AB≅ arc EF

What could be the reason for statement 5?

A. Definition of congruent arcs.

C. Congruent angles have equal arcs.

B. Definition of congruent circles.

D. Congruent parts of congruent

triangles are congruent.

___33. In figure 1, which is the chord?

A. FE
B. AB
C. GH
D. CD

___34. It is the angle on the circle formed by any two chords which is half the measurement
of the arc bounded by the said chords.

A. interior angle

C. exterior angle

B. inscribed angle

D. central angle

___35. Given: 𝐸𝑆̅̅̅̅ is a diameter of ʘ𝑈 and perpendicular to 𝐺𝑁̅̅̅̅ at 𝐼.

Prove that: 𝑁𝐼̅̅̅̅ ≅ 𝐺𝐼̅̅̅

What could be the reason for statement number 3?

A. Right angles are congruent.

C. Definition of perpendicular lines.

B. Definition of congruent angles.

D. Perpendicular lines are congruent.

___36. In proving theorems on secants, tangents, and segments, given that

𝐴𝑁̅̅̅̅ 𝑎𝑛𝑑 𝐽𝑁

̅̅̅̅ 𝑎𝑟𝑒 𝑟𝑎𝑑𝑖𝑖 𝑜𝑓 ʘ𝑁 , what could be the reason to say that 𝐴𝑁̅̅̅̅ ≅ 𝐽𝑁

̅̅̅̅?

A. Definition of radii.

B. Definition of a circle.

C. Radii are all half of diameter.

D. Radii of the same circle are congruent.

___37. The monthly expenses of school A are Php 100,000.00. They spend Php 30,000 for
electricity, Php 20, 000 for utility and security guard, Php 10,000 for seminars and
training, and Php 40,000 for supplies and other operating expenses. What is the
measure of the central angle corresponding to supplies and other operating
expenses if you present the expenses in a pie graph?

A. 40°

C. 100°

B. 90°

D. 144°

___38. Given the monthly expenses of school A initem no. 37, what should be done by the
school to manage its budget more efficiently?

A. Do not turn on the lights and the electric fans to save enough budget from the

electricity expenses.

B. Cut the wages of the utility and security guard to have savings for the supplies and

other operating expenses.

C. Practice recycling and use water as well as electricity responsibly to avoid wastage of

resources and curtail expenses.

D. All the above.

___39. If the distance between two points (5, - 2) and (1, y) is 5, find the values of y.

A. 1, -5

C. 2, -3

B. -1, 5

D. -2, 3

___40. The coordinates of the vertices of a parallelogram are P (2,1), A (4,2), U (3,0) and L
(0,0). What is the length of the longer diagonal of the
parallelogram?

A. √5

C. 3

B. 3√2

D. 4

P

A

U

L

___41. What is the graph of the circle whose equation is given by 𝑥2+ (𝑦 − 4)2= 16?

A.

C.

B.

D.

___42. Which of the following is an equation of a circle whose center is at the origin with
radius 12 units?

A. 𝑥2+ 𝑦2= 12

C. 𝑥2+ 𝑦2= 24

B.𝑥2+ 𝑦2= 36

D. 𝑥2+ 𝑦2= 144

___43. Which of the following is an equation of a circle with a center at (7, -1) with radius
8 units?

A. (𝑥 + 7)2+ (𝑦 − 1)2= 8

C. (𝑥 − 7)2+ (𝑦 + 1)2= 8

B. (𝑥 − 7)2+ (𝑦 + 1)2= 64

D. (𝑥 + 7)2+ (𝑦 − 1)2= 64

___44. What is the center of the circle 𝑥2+ 𝑦2− 6𝑥 + 2𝑦 + 6 = 0?

A. (-3, 1)

C. (-3, -1)

B. (3, -1)

D. (3, 1)

___45. What is the equation of the circle whose radius has endpoints (2, 1) and (0, -2) and
whose center is in the first quadrant?

𝐴. (𝑥 − 1)2+ (𝑦 − 2)2= 13

C. (𝑥 − 2)2+ (𝑦 − 1)2= 13

𝐵. (𝑥 + 1)2+ (𝑦 + 2)2= 13

D. (𝑥 + 2)2+ (𝑦 + 1)2= 13

___46. The Google Map application shows that car A travelling at a speed of 60 kph is
located at a point whose coordinates are (120, 80). Behind car A is car, travelling in
the same direction at a speed of 80 kph, that is located at a point whose coordinates
are (20, 80). What is the distance between the two cars?

A. 60 km

C. 100 km

B. 80 km

D.120 km

___47. The coordinates of points C, O, M, and E are (2, 6), (6,6), (4,0) and (0,0)
respectively. What should you do if you want to prove that the figure created by
connecting these points is a parallelogram?

A. Plot the points in the coordinate plane and show that it forms a parallelogram.
B. Find all the midpoints between the points to show that their coordinates are equal.
C. Find the midpoints and compute for distances between them to show that they are

equal.

D. Compute the distances between the points to show that the pairs of parallel sides are

equal.

___48. Mang Jose cut a circular board with a diameter 80 cm. Then he divided the board
into 20 congruent sectors. What is the area of each sector?

A. 80 π 𝑐𝑚2

C. 800 π 𝑐𝑚2

B. 320 π 𝑐𝑚2

D. 1600 π 𝑐𝑚2

___49. Mary designed a pendant. It is a regular octagon 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°

C. 67.5 °

B. 45°

D. 135°

___50. Jose’s house which has coordinates (0,0) is surrounded by 4 convenience stores. If
store A is located at coordinates (9,4), store B at (3, 12), store C at (3,4) and store D
at (-3, 7), from which store should he buys milk if it is available in all stores and he
wants to conserve time?

A. Store A

C. Store C

B. Store B

D. Store D

Prepared by:

EVANGELINE T. DELA CRUZ

PAULINE GRACE G. QUERIJERO

Teacher III, SDO - Aurora

Teacher III, SDO - Aurora