Rapid Mathematics Assessment for Grades 7 to 10
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?
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?
2
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
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.
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.
3
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.
4
Refer to the following information to answer items 15 to 16.
Barangay San Mateo is planning to provide financial assistance for its two puroks.
They surveyed the monthly family incomes in Purok 1 and Purok 2. The data collected
is presented in Figure 2.
Figure 2
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.
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?
5
Refer to Table 2 below to answer items 17 to 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
Participated in
sports activity
Did not
participate in
sports activity
Participated in
music activity
18
31
49
Did not
participate in
music activity
42
19
61
60
50
110
Total
Total
17. How many students participated in the music activity?
18. How many students did not participate in any of the two activities?
19. What is the probability of selecting a student who participated in both music and
sports activities?
20. Write a question that can be answered using the information in Table 2.
6
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?
7
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)
b. (1, -2)
c. (2, 3)
d. (3, 2)
e. (4, 7)
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)
b. (𝑥, −2𝑥+1)
c. (𝑥, −𝑥)
d. (𝑥, −𝑥+1)
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.
8
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 =
b. cost =
c. cost = 100𝑛
100𝑛
3
d. cost =
3𝑛
e. 3: 100 = 𝑛: cost
3
100
9
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
8y = 14 + 8
8y = 22
11
y=
or 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.
10
Use the information below to answer items 34 to 37.
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]
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.
36. In Figure 5, what does the number 200 in the formula represent?
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
11
Use the information below to answer items 38 to 40.
Lines f, g, and h intersect at points 𝑃, 𝑄 and 𝑅, forming a triangle. The measures of
the angles in degrees are represented by 𝑝, 𝑞 and 𝑟. The picture below is part of the
plane that shows the triangle 𝑃𝑄𝑅.
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
12
Copy of Figure 6
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.
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.
13
Use the following information to answer items 41 to 43.
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 3:3:2. 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.
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.
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.
14
Use the information below to answer items 44 to 45.
Circumference of a circle: 𝐶 = 2𝜋𝑟
Area of a circle: 𝐴 = 𝜋𝑟 2
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.
Figure 9 (auxiliary view of the pool)
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. 10𝜋(2.1) cubic meters
b. 25𝜋(2.1) cubic meters
c.
10𝜋(2.1)
2
cubic meters
d.
e.
25𝜋(2.1)
2
100𝜋(2.1)
2
cubic meters
cubic meters
15
Refer to the information below to answer items 46 to 47.
A wheel with a diameter of 60 cm is rolled along a straight path.
Figure 10
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]
16