Mathematics

Question 1

1. Your classmate said that each of the four expressions in Box 1 is equivalent to 1.
   Verify what your classmate said by showing your computation for the number expression 4 x 4 - 5 x 3

Answer 1

16-15=1

Question 2

2. What must be the next number expression to 5 x 5 - 6 x 4 in Box 1?

Answer 2

6 x 6 - 7 x 5

Question 3

3. Which of the following algebraic expressions represents the set of number expressions in Box 1?

a. (n)(n) - (n + 3)(n + 1)

d. n ^ 2 - 3n(1)

b. (n)(n) - [(n + 1)(n - 1)]

e. n ^ 2 - n - 1

c. (n - 1)(n - 1) - n(n - 2)

Answer 3

b and c

Question 4

4. Explain or show why you think you have chosen the correct algebraic expressions for the set of number expressions in Box 1.

Answer 4

(n)(n) - [(n + 1)(n - 1)]
= n ^ 2 - (n ^ 2 - 1) = n ^ 2 - n ^ 2 + 1
= 1
or
(n - 1)(n - 1) - n(n - 2) = n ^ 2 - 2n + 1 - (n ^ 2 - 2n) = n ^ 2 - 2n + 1 - n ^ 2 + 2n = 1

Question 5

5. What does n represent in your chosen expression in item 3?

Answer 5

b = 1st number
c = 3rd number

Question 6

6. Show that 1024 is a power of 2. [Refer to Table 1]

Answer 6

2x2x2x2x2x2x2x2x2x2=1024

Question 7

7. Write the exponential form of 1024

Answer 7

2¹⁰

Question 8

8. Find a number that is a power of 2 that meets BOTH of these conditions:

The number is a multiple of 16.

The number is also more than 50 but less than 200.

Answer 8

64 or 128

Question 9

9. Is there a number between 0.998 and 0.999? If YES, give one example. If NO, explain why you think so.

Answer 9

Yes, with a correct example.

Any number starting with 0.998, followed by one or more digits, with at least one non-zero digit. Examples: 0.99801, 09984, 0.998000005

Question 10

10. Show how you will subtract 0.998 from 0.999.

Answer 10

0.999
0.998
0.001

Question 11

11. Is there a fraction that is greater than 3/4 but less than 1? If YES, give one example. If NO, explain why you think so.

Answer 11

YES, 7/8

Question 12

12. How many students had an overall academic grade below 84? [Refer to Figure 1]

Answer 12

5 students

Question 13

13. Explain why you think your answer in item 12 is correct based on the information shown in the graph in Figure 1.

Answer 13

There are five points with y-coordinates below 84.

Question 14

14. Which of the following can be a correct interpretation of the data presented in the graph in Figure 1?

a. As the number of absences increases, the overall academic grade also increases.

b. As the number of absences decreases, the overall academic grade increases.

c. As the number of absences increases, the overall academic grade decreases.

d. As the number of absences decreases, the overall academic grade also decreases.

Answer 14

B and C

Question 15

15. Based on the graph in Figure 2, which of the two puroks shows more diversity in monthly family income? Explain or justify your answer.

Answer 15

Mentioned that Purok 1 is more vaned or diverse and the explanation 2 here uses technical statistical terms and/or the statistics represented.

Because the range of Purok 1 (40-8=32) is greater than that of Purok 2 (24-15-9).

Because the difference between the maximum monthly income and minimum monthly income of Purok 1 is greater than that of Purok 2.

Because the differences of the monthly income of Purok 1 from the center value or average of the monthly income of Purok 1 are greater than the differences of the monthly income of Purok 2 from the center value of the monthly income of Purok 2

Question 16

16. The average monthly income of the families in Purok 1 and Purok 2 are equal. Should both purok be given the same amount of financial aid? What information in the graph in Figure 2 did you base your decision on?

Answer 16

The explanation must mention VARIABILITY and information that can be read or interpreted from the graph. Some examples of references to the statistical graph are the following:

Purok 1’s monthly family incomes are farther from the average compared to those in Purok 2. As a result, the monthly average doesn’t reflect the incomes of most families in Purok 1. This means many families may get more or less than they actually need.

I see that the minimum family income eamers are in Purok 1, but the highest family income earners are also in Purok 1. The financial aid must be given to families below a certain income cutoff instead, whether that family is in Purok 1 or Purok 2

Question 17

17. How many students participated in the music activity?

Answer 17

49

Question 18

18. How many students did not participate in any of the two activities?

Answer 18

19

Question 19

19. What is the probability of selecting a student who participated in both music and sports activities?

Answer 19

18/100 or 9/55

Question 20

20. Write a question that can be answered using the information in Table 2.

Answer 20

Questions that presented a logical and relevant scenario requiring a transformation of the values provided in the table.

E.g. If a new student joins the school and participates in both activities, how would this affect the number of students who did not participate in either activity?

Question 21

21. What is the position of point F in Figure 3?

a. Point F is at -500.

b. Point F is at -400.

c. Point F is at -300.

d. Point F is at -200.

e. Point F is at 50.

Answer 21

C

Question 22

22. What is the position of point G in Figure 3?

Answer 22

0

Question 23

23. What are the coordinates of Point C in Figure 4?

Answer 23

(4,4)

Question 24

24. A line is drawn passing through points B and C in Figure 4. Select two ordered pairs that represent the coordinates of points that are also in this line.

a. (1,-1)

d. (3, 2)

b. (1,-2)

e. (4, 7)

c. (2,3)

f. (5,6)

Answer 24

b d f

Question 25

25. Draw a line through points A and B in Figure 4. Which of the following ordered pairs represent all the points that are on this line? a. (x, - 2x) d. (x, - x + 1) b. (x, - 2x + 1) e. (x, - x + 2) c. (x, - x)

Answer 25

e

Question 26

26. In Figure 4, connecting the points A, B and C will form a triangle, called triangle ABC. What is the area of triangle ABC? Show your method for getting the area.

Answer 26

A=1/2bh =1/2(6)(4) =12 sq. units

Question 27

27. A point represents position. Suppose in Figure 4, point A represents the position of your house, point B represents the position of your school and point C represents the position of the barangay hall. There is a straight road that you can take to the school and the barangay hall from your house. Which is the shorter walk from your house, going to the school or to the barangay hall?

Answer 27

School B or Point

Question 28

28. Show or explain how you determined your answer in item 27.

Answer 28

use distance formula which is 5.66units AB and 6 units AC

Question 29

29. If r is an integer, select all possible values that can be represented by 2r-1. -5 -27 -82 99 46 122

Answer 29

-5, -27 and 99

Question 30

30. At a fruit stand, apples are priced at 3 for Php100. Which of the following expressions can be used to find the amount to be paid (cost) for any number of apples? Select the correct answers. 100 a. cost = 3 3η b. cost = 100 c. cost=100n 100n d. cost = 3 e. 3:100= n: cost

Answer 30

d and e

Question 31

31. Write two possible values for a and b that will make the equation in Box 2 true.

Answer 31

a=1, b=15 and a=0, b=14

Question 32

32. Which statement is always true about a and b? [Refer to Box 2] a. a is greater than b. b. The sum of a and b, (a + b) is 20. c. The difference between b and a, (b - a) is 14. d. a and b can take any value.

Answer 32

c

Question 33

33. Shown below is the solution to the given linear equation. 5y - 8 = 14 - 3y 5y+3y-814 8y-8 = 14 8y = 14 + 8 8y = 22 or 2.75 y = 11/4 What reason can we use to transform equation 1 into equation 2? a. If we subtract 3y from both sides of equation 1, the equation will remain true. b. If we subtract 8 from both sides of equation 1, the equation will remain true. c. If we add 3y to both sides of equation 1, the equation will remain true. d. If we divide both sides of equation 1 by 8, the equation will remain true.

Answer 33

c

Question 34

34. How much does it cost to rent the tricycle for 5 days? [Refer to Figure 5]

Answer 34

P1250

Question 35

35. What does the number 250 in the formula represent? [Refer to Figure 5] a. The daily cost of renting the tricycle. b. The number of days the tricycle is rented. c. The fixed cost of renting the tricycle. d. The total cost of renting for one day.

Answer 35

c

Question 36

36. In Figure 5, what does the number 200 in the formula represent?

Answer 36

The cost/rate per day of renting the tricycle

Question 37

37. What aspect of the graph in Figure 5 represents the 200 in the formula? a. x-intercept b. y-intercept c. slope d. minimum point

Answer 37

c

Question 38

38. In Figure 6, if the measure of angle P is 30 degrees (that is, P = 30 ) which of the following are possible values for q and r? Choose 2 that are correct among the choices. Note that the triangle is not drawn to scale. a. q = 10 and r = 140 b. and r = 130 q = 10 c. q = 110 and r = 30 d. q = 100 and r = 80 e. q = 100 and r = 50

Answer 38

a and e

Question 39

39. In Figure 6, if the measure of angle R is 60 degrees (that is, r = 60) and the measure of the exterior angle at Q is 130, what is true about the values of p and q? Choose at least one true statement about p and q. NOTE: The exterior angle of a triangle forms a 180-degree angle with the adjacent interior angle. a. The sum of p and q is 130. b. p and q can have several values. c. The value of p is 70 and the value of q is 50. d. The value of p is 50 and the value of q is 70. e. The value of r plus p is 130.

Answer 39

c and e

Question 40

40. Which of the following statements about the properties of triangles will help determine the values of p and q in the preceding question? Choose those that are applicable. [Refer to Figure 6] a. Each angle of an equilateral triangle is 60 degrees. b. In an isosceles triangle, the base angles are equal. c. The exterior angle and one of the interior angles adjacent to it form a linear pair. d. The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles. e. There are six exterior angles in any triangle. f. The sum of all the exterior angles of a triangle is 360 degrees.

Answer 40

c and d

Question 41

41. What are the lengths of the other two sides of the triangular dog house? [Refer to Figure 7] a. The other two sides are 1.5 meters each. b. The other two sides are 2 meters and 3 meters. c. The other two sides are 3 meters each. d. The other two sides are 4 meters and 6 meters.

Answer 41

A

Question 42

42. In Figure 7, are the sides of the triangular dog house proportional to the sides of the triangular toy storage? Show your solution or explain your answer.

Answer 42

Yes. Since the base of the toy storage is parallel to the floor (which is the base of the dog house), their corresponding base angles are equal (or congruent). Then, by AA Similarity Theorem, the two triangles (toy storage and dog house) are similar. Corresponding sides of two similar triangles are proportional

Question 43

43. The base of the toy storage measures 25 centimeters. What are the lengths of its other two sides? [Refer to Figure 7] a. The other two sides are 37.5 centimeters each. b. The other two sides measure 50 and 75 centimeters. c. The other two sides are 75 centimeters each. d. The other two sides measure 100 and 150 centimeters.

Answer 43

A

Question 44

44. What is the area of the sidewalk in square meters surrounding the pool? Show your solution. [Refer to Figure 8] Use pi = 3.14

Answer 44

Apool= πr² Atotal= πr² = 3.14 x 5² =3.14 x 6² =78.5m² = 113.04m² Asidewalk=Atotal-Apool = 113.04m²-78.5m² = 34.54m²

Question 45

45. The park management decides to divide the pool into two equal parts. One part will be designated for adults and has a depth of 1.5 meters, while the other part will be designated for children and has a depth of 0.6 meters. Which of the following will give the total volume of water in the pool? [Refer to Figure 9] a. 10pi(2, 1) cubic meters b. 25pi(2.1) cubic meters c. 10π(2.1)/2 cubic meters d. 25pi(2.1)/2 cubic meters e. 100pi(2.1)/2 cubic meters

Answer 45

d

Question 46

46. The wheel in Figure 10 is rolled exactly 5 times. Show how you can compute the distance travelled by the wheel.

Answer 46

C=πx60 =60π D=5xC =5x60π D=300πm

Question 47

47. How many degrees did the wheel's pin rotate after 5 rolls? [Refer to Figure 10]

Answer 47

1800°