Rapid Mathematics Assessment for Grade 8

Assessment Instructions:
Your score on this test will help your teacher determine your readiness to
learn the mathematics required at your grade level. You have ninety (90)
minutes to complete this test.

Only the Questionnaire and Answer Sheet provided to you should be on

your desk. Write all your solutions and answers, including any scratch
work, directly on the Answer Sheet.

Before answering each question, double-check that the question numbers

on your Answer Sheet match those on the Questionnaire to avoid
misplaced answers. Please review your answers carefully before
submitting your paper.

i. For multiple-choice questions:

 Some multiple-choice questions may require selecting more

than one answer. In such cases, write the letters of all your
chosen options.

ii. For short-answer questions:

Provide clear and complete answers in the designated space

provided on the Answer Sheet. Show all necessary calculations or
explanations. You may write your explanations in English, Filipino, or
Taglish.

Formulas you may find helpful:

 Perimeter of a triangle: 𝑃 = 𝑎 + 𝑏 + 𝑐

 Area of a triangle: 𝐴 = ½ × 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡

 Circumference of a circle: 𝐶 = 2𝜋𝑟

 Area of a circle: 𝐴 = 𝜋𝑟²

 Volume of a cylinder: 𝑉 = (𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑎𝑠𝑒) × ℎ𝑒𝑖𝑔ℎ𝑡

Refer to the number expressions in Box 1 to answer items 1 to 5.
Box 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 × 4 − 5 × 3.
2. What must be the next number expression to 5 × 5 − 6 × 4 in Box 1?

The powers of 2 are given in Table 1. Use this information to answer items 6 to
8.
Table 1
Exponential Form Expanded Form Power of 2

22 2×2 4

23 2×2×2 8

24 2×2×2×2 16

25 2×2×2×2×2 32

3. Which of the following algebraic expressions represents the set of

number expressions in Box 1?
a. (𝑛)(𝑛) − (𝑛 + 3)(𝑛 + 1) d. 𝑛2 −
3𝑛(1)
b. (𝑛)(𝑛) − [(𝑛 + 1)(𝑛 − 1)]
e. 𝑛2 − 𝑛 −
1
c. (𝑛 − 1)(𝑛 − 1) − 𝑛(𝑛 − 2)
4. Explain or show why you think you have chosen the correct algebraic
expressions for the set of number expressions in Box 1.
5. What does 𝑛 represent in your chosen expression in item 3?

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

7. Write the exponential form of 1024.

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.

9. Is there a number between 0.998 and 0.999? If YES, give one

example. If NO, explain why you think so.

10. Show how you will subtract 0.998 from 0.999.

3
11. Is there a fraction that is greater than but less than 1? If YES, give
4
one example.

If NO, explain why you think so.

Refer to the following information to answer items 12 to 14.

The graph shows the relationship between student absences and overall
academic grade across all subjects in the Masipag section, a special class
for arts and design, for two academic quarters. Each point on the graph
represents an individual student
Figure 1
12. How many students had an overall academic grade below 84? [Refer
to Figure 1]

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

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.

Refer to Table 2 below to answer items 17, 18, 20.

Malaya High School organized music and sports activities to celebrate

the school’s foundation day. Table 2 shows the participation of the Grade
7 students.

Table 2
 Did not
Participated in
participate in Total
sports activity
sports activity
Participated in
18 31 49
music activity
Did not
participate 42 19 61
in music
activity

Total 60 50 110

17. How many students participated in the music activity?

18. How many students did notparticipate in any of

the two activities?

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

Refer to Figure 3 to answer items 21 to 22.

A number describes the position of a point on a number line. The picture

below is part of a number line.
Figure 3

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.

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

Use the following information to answer items 23 to 28.

An ordered pair of numbers describes the position of a point on a Cartesian
plane. This position is called the coordinates of the point. The first number
in the ordered pair is called the 𝑥-coordinate and the second number is
called the 𝑦-coordinate.

Figure 4

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

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)
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,
b. (𝑥, −2𝑥+1) −𝑥+1)
c. (𝑥, −𝑥) e. (𝑥,
−𝑥+2)

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.

Copy of Figure 4
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?

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

29. If 𝒓 is an integer, select all possible values that can be represented by 2𝑟 − 1.

−5 -27 -82 99 46 122

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
3n
b. cost =
100
c. cost =100 n
100 n
d. cost =
3
e. 3 :100=n: cost

In Box 2 below, let 𝑎 represent the number in the first blank space, and 𝑏 represent
the number in the second blank space.

Box 2

17 + ___ = ___ + 3

31. Write two possible values for 𝑎 and 𝑏 that will make the equation in Box 2 true.
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.
33. Shown below is the solution to the given linear equation.

5y − 8 = 14−3y ---- ①

5y + 3y – 8 = 14 ---- ②

8y – 8 = 14
8 y=14 +8
8 y=22

11
y= ∨2.75
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.

Use the information below to answer items 34.

The cost of renting a tricycle per day is shown in the graph and formula below.

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

Use the information below to answer items 38 to 39.

Lines f, g, and h intersect at points 𝑃, 𝑄 and 𝑅, forming a triangle. The measures of

𝑝, 𝑞 and 𝑟. The picture below is part of the
plane that shows the triangle 𝑃𝑄𝑅.
the angles in degrees are represented by

Copy of Figure 6

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. q = 10 and r = 130
c. q = 110 and r = 30
d. q = 100 and r = 80
 e. q = 100 and r = 50

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.

Use the following information to answer items 41.

Carlos built a house for his dog, Brownie. The lower part of the dog house serves as
a sleeping area, while a small portion on top is used for toy storage. The base of the
toy storage, which measures 25 centimeters, is parallel to the floor. The dog house
is triangular with sides in the ratio of [Link]. The shortest side measures 1 meter.

Figure 7

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.

Use the information below to answer items 44.

Circumference of a circle: 𝐶 = 2𝜋𝑟

Area of a circle: 𝐴 = 𝜋𝑟2

Figure 8 (top view of the pool)

A public park has a circular pool with a

diameter of 10 meters. The park
management decided to build a sidewalk
around the pool to allow people to walk
around it safely. The sidewalk has a uniform
width of 1 meter all around the pool.

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.

Refer to the information below to answer items 46.

A wheel with a diameter of 60 cm is rolled along a straight path.

Figure 10
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. 10 π ( 2.1 ) cubic meters

b. 25 π (2.1 ) cubic meters
10 π (2.1)
c. cubic meters
2
25 π (2.1)
d. cubic meters
2
100 π ( 2.1)
e. cubic meters
2

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

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