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WorksheetsREVIEWER IN MATHEMATICS 8
Total questions: 50
Worksheet time: 25mins
A city planner uses a Cartesian coordinate grid to design a new public park. The x-axis represents east–west streets and the y-axis represent north–south streets. The origin is the city hall. On the city planner’s map, what does the point (0, 0) represent?
The park entrance
The marketplace
The main road
The city hall
A city planner uses a Cartesian coordinate grid to design a new public park. The x-axis represents east–west streets and the y-axis represent north–south streets. The origin is the city hall. The planner marks the following locations:
Playground at (3, 4), Fountain at (0, –3),
Parking lot at (–5, 2).
Which of the following correctly describes these locations?
Playground in QI; Parking lot in QII; Fountain on x-axis
Playground in QII; Parking lot in QIII; Fountain on y-axis
Playground in QI; Parking lot in QII. Fountain on y-axis
Playground in QI; Parking lot in QII. Fountain on x-axis
A treasure map is drawn on a Cartesian grid where each square represents 1 meter. The (0,0) marks the campsite in the center of the map. On the treasure map, the coordinate origin is marked at (0,0). Why does this point represent the campsite?
It is the reference point for other locations.
It is the farthest of all landmarks.
It always lies on the axes.
It shows the treasure’s spot.
A treasure map is drawn on a Cartesian grid where each square represents 1 meter. The (0,0) marks the campsite in the center of the map. The treasure hunter marks these points: Waterfall at (–3, 4), Cave at (–4, –2), and Tree at (3, 0). Which illustration is correct?
A treasure map is drawn on a Cartesian grid where each square represents 1 meter. The (0,0) marks the campsite in the center of the map. The hunter walks 6 meters east and 2 meters north from the campsite. Which coordinate shows the hunter’s new location?
(6, 2)
(–6, 2)
(–2, –6)
(2, –6)
A treasure map is drawn on a Cartesian grid where each square represents 1 meter. The (0,0) marks the campsite in the center of the map. The hunter starts at the campsite (0, 0), walks to the Cave (–5, 2), then to the Tree (0, –3). Which path shape best describes the movement?
A. A right-angle path
B. A straight line only
C. A square path
D. A triangle path
A treasure map is drawn on a Cartesian grid where each square represents 1 meter. The (0,0) marks the campsite in the center of the map. The hunter marks the four points of a square at (4, 4), (–4, 4), (–4, –4), and (4, –4). He wants to bury a marker at the square’s center. By analyzing the coordinates, which location is correct and why?
(0, 0), because it is equidistant from all four corners
(2, 2), because it is halfway between (4, 4) and (–4, 4) only
(–2, –2), because it is closer to the negative coordinates
(0, 4), because it lies on the y-axis of the square
A city planner uses a Cartesian grid map (1 unit = 1 meter) to design a park. Landmarks such as fountain, benches, and gates are marked as points on the plane. The bench is at (–3, 4) and the fountain at (0, 0). What formula will be used to find the distance between the bench and the fountain?
d=∣x2−x1∣
d=∣x2−x1∣
d=(2x1+x2,2y1+y2)
d=(x2−x1)+(y2−y1)
A city planner uses a Cartesian grid map (1 unit = 1 meter) to design a park. Landmarks such as fountain, benches, and gates are marked as points on the plane. The bench is at (–3, 4) and the fountain at (0, 0). What is their distance apart?
7 units
5 units
3 units
1 unit
A city planner uses a Cartesian grid map (1 unit = 1 meter) to design a park. Landmarks such as fountain, benches, and gates are marked as points on the plane. The east and west gates are at (6, 2) and (–2, –4). What is the midpoint between them?
(2, –1)
(4, –1)
(2, –2)
(–4, –1)
A city planner uses a Cartesian grid map (1 unit = 1 meter) to design a park. Landmarks such as fountain, benches, and gates are marked as points on the plane. Which is farther from the fountain (0, 0): the bench at (–3, 4) or the gate at (6, –2)?
The bench, 5 units away
The gate, √40 ≈ 6.3 units away
Both are the same distance
Cannot be determined
A city planner uses a Cartesian grid map (1 unit = 1 meter) to design a park. Landmarks such as fountain, benches, and gates are marked as points on the plane. The city wants to place a drinking fountain halfway between the playground at (–4, 2) and the picnic area at (2, –6). Where should it be located?
(0, –2)
(–2, –2)
(–1, –2)
(1, –2)
A city planner uses a Cartesian grid map (1 unit = 1 meter) to design a park. Landmarks such as fountain, benches, and gates are marked as points on the plane. To give visitors equal walking distance, where is the better lamp post location?
Midpoint of east and west gates (2, –1)
Midpoint of north and south trees (0, 0)
At (2, –1), gates midpoint
At (0, 0), trees midpoint
Either location, same balance
Neither location works
The planner wants to add a rest area inside a rectangular park with corners at (4, 2), (4, 2), (4, –6), and (–4, –6). If you were tasked to design the most balanced spot for the rest area, which placement would you choose and why?
(0, –2), center of the park
(2, –2), near the right side
(0, –4), along the bottom
(–2, –2), near the left side
An architect is designing glass pyramids for a park, each with different polygonal bases (triangular, pentagonal, and hexagonal). The goal is to determine how their volumes compare to rectangular and square pyramids. What is the general formula for finding the volume of any pyramid?
V = Bh
V=31Bh
V = ½ Bh²
V = Bh²
The architect designed a triangular-based pyramid with an area of base 24m² and a height of 9m. What is its volume?
72m³
81m³
108m³
216m³
A relief organization is storing supplies in two pyramid-shaped containers. Container A has a triangular base with an area of 60m² and a height of 9m. Container B has a hexagonal base with an area of 120m² and a height of 4.5m. The organization wants to know which container can store more supplies. Which statement best describes the storage capacities of the two containers?
Container A and Container B can store the same amount of supplies.
Container A can store twice as much as Container B.
Container B can store twice as much as Container A.
Container A can store only half as much as Container B.
The SSLG officers will build a pyramid-shaped photobooth with a polygonal base. The officers want different design options before deciding. If you were part of the design team, what new mathematical question could you create to help the officers decide on the best design?
How does changing the base shape affect the volume?
What is the best material to use for the design?
What color should the photobooth be?
How tall are other photobooth in school?
For the upcoming Teachers’ Day Celebration, the school plans to build a pyramid-shaped stage backdrop at the center of the covered court. The backdrop will be made of lightweight materials, and the Math Club is tasked to help with design, cost, and efficiency by solving problems about the pyramid’s volume and surface area.
The stage backdrop is designed as a square pyramid with a base side of 6 m and a height of 9 m. How much space inside the pyramid structure will be occupied by the frame and decorations?
18 m³
108 m³
324 m³
648 m³
During the planning for the Teachers’ Day stage backdrop, the organizers are examining two possible pyramid designs: Design A: Square base with side 6m and height 9m. Design B: Rectangular base 8m by 5m and height 9m. By examining their volumes, what can you conclude about Design B in relation to Design A?
Both have the same volume.
Design B is 28 m³ smaller.
Design B is 28 m³ larger.
Design B has double the volume.
The Student Council plans pentagonal pyramid gift boxes (base area = 150 cm², height = 12 cm). Different solutions for the volume were suggested. Which option is the most reasonable, based on the correct formula for a pyramid?
600 cm³ – used Bh without ÷ 3
1,800 cm³ – correct formula Bh/3
1,200 cm³ – divided by 4 instead of 3
3,600 cm³ – doubled the base area first
The school will design a hexagonal pyramid-shaped lantern to hang on the stage. The lantern has base area 180 cm² and height 10 cm. Four students gave different answers for its volume. After evaluating their work, whose solution is correct?
Alvin: 500 cm³
Bea: 600 cm³
Cesar: 1,200 cm³
Dexter: 1,800 cm³
During the decoration process, the officers use different 3D shapes for the decorations. Which of the following is the best real-life example of a cone?
A. A party hat
B. A rectangular gift box
C. A cylindrical water bottle
D. A pyramid-shape flags
During the planning, a student recalls that the volume of a cone is related to the volume of a cylinder with the same base and height. Which statement correctly describes their relationship?
The cone has the same volume as the cylinder.
The cone’s volume is twice that of the cylinder.
The cone’s volume is one-third of the cylinder.
The cone’s volume is half of the cylinder.
The Math Club Officers ordered cone-shaped party hats for the students. Each hat has a base radius of 7 cm and a height of 15 cm. To find the volume of each hat, which formula should they use?
V = πr²h
V = ½πr²h
V = ⅓πr²h
V = ¼πr²h
The Grade 8 students are preparing giant spherical balloons to decorate the school stage. Each balloon is perfectly round with a radius of r. However, the students realized they don’t know the exact formula for the volume of a sphere. Which formula should they use to find the volume of a sphere?
V = πr³
V = 1/2πr³
V = 2πr³
V = 4/3πr³
Each hat has a base radius of 7 cm and height of 15 cm. Three students solved the volume of the hat:
Abby: V = πr²h = (3.14)(7²)(15) = 2310 cm³
Bobby: V = ½πr²h = 2(3.14)(72)(15) = 1155 cm³
Cathy: V = ⅓πr²h = 3(3.14)(72)(15) = 770 cm³
Which student got the correct solution?
Abby
Bobby
Cathy
None of them
Grade 8 students realized they used the wrong formula for the volume of a sphere when inflating balloons with a radius of 3 m. If you were to design a corrected solution for your classmates, which of the following would be the best approach?
Simply memorize the correct formula V = 4/3πr³ without explaining the mistake.
Redraw the balloon as a cube and create a new formula for its volume.
Prepare a guide that compares the correct formula with the wrong ones, shows the correct calculation, and explains why using the wrong formula can cause problems.
Ignore the incorrect formulas and just state the final correct answer.
A 5-inch deep ice cream cone has a radius of 1 inch. A spherical scoop of ice cream also has a radius equal to 1 inch. If the ice cream melts in the cone, will it overflow?
The ice cream will overflow because the scoop’s volume is larger than the cone’s capacity.
The ice cream will not overflow because the cone’s volume is greater than the scoop’s volume.
The ice cream will fit exactly, filling the cone completely.
The cone will be only half-filled after the ice cream melts.
Lui’s conical hat has a diameter of 19 inches and a height of 7.5 inches. If you were asked to teach a classmate how to find its volume, which explanation would you create?
Multiply diameter by height
Use surface area formula
Find base area, then apply by height
Write the full solution using V = ⅓πr²h, substitute r = 9.5, h = 7.5, then solve.
A ladder leans against a wall. The bottom of the ladder is 9 ft away from the wall, and the ladder reaches a height of 12 ft on the wall.
In the right triangle formed by the ladder, wall, and ground, which side is the hypotenuse?
The wall
The ground
The ladder
Both the wall and ground
Which formula correctly applies the Pythagorean Theorem to find the length of the ladder?
a² + b² = c², a = 9, b = 12 and c as the ladder.
a² - b² = c², a = 9, b = 12 and c as the ladder.
a + b = c, a = 9, b = 12, and c as the ladder.
2a + b = c, a = 9, b = 12, and c as the ladder.
During their field trip to Intramuros, Grade 8 students apply the Pythagorean Theorem and its converse to measure distances between landmarks, classify triangular pathways, and evaluate exhibit designs at sites like San Agustin Church and Fort Santiago.
The students measure a right triangular pathway from the entrance of Fort Santiago to a nearby wall. The pathway has legs of 5 m and 12 m. What is the length of the hypotenuse (direct path across)?
A. 13 m
B. 14 m
C. 15 m
D. 17 m
Near the San Agustin Church, students examine a triangular support beam with sides 8 m, 15 m, and 17 m. They compare the square of the longest side with the sum of the squares of the other two sides to decide what type of triangle it forms. Which reasoning best supports their conclusion?
17² = 8² + 15², so it is a right triangle.
17² < 8² + 15², so it is an acute triangle.
17² > 8² + 15², so it is an obtuse triangle.
The sides only show it is scalene.
While mapping a grassy shortcut, the students note sides 6 m, 8 m, and 11 m. They compare 11² with 6² + 8². Which conclusion correctly analyzes the triangle?
11² = 6² + 8²—Right triangle.
11² < 6² + 8²—Acute triangle.
11² > 6² + 8²—Obtuse triangle.
The triangle cannot be classified.
A group designs an exhibit stand with sides 7 m, 24 m, and 25 m. If stability requires a right triangle, which evaluation is most accurate?
Accept, because 25² = 7² + 24².
Reject, because 25² > 7² + 24².
Accept, because the perimeter matches the space.
Reject, because angles are unequal.
For a proposed flag display with sides 9 m, 12 m, and 16 m, students must decide if the design should be approved as a right triangle. Which evaluation is best?
Approve, since 16² = 9² + 12².
Approve, since all sides are integers.
Reject, since 16² > 9² + 12².
Reject, since the triangle inequality is violated.
A student draws segments of 4 cm, 6 cm, and 9 cm. Interpreting the Triangle Inequality Theorem, what should they conclude?
The longest side must equal the difference of the other two sides.
The sum of any two sides must be greater than the third side.
The product of two sides must equal the third side.
The longest side is always twice the shortest.
A student draws segments of 4 cm, 6 cm, and 9 cm. Interpreting the Triangle Inequality Theorem, what should they conclude?
These lengths can form a triangle since 4 + 6 > 9.
They cannot form a triangle because 4 + 6 = 10.
These lengths can form a triangle since 6 + 9 = 15.
They cannot form a triangle since 9 is too large compared to 4.
In a section of the park, a triangular flower bed has two sides measuring 7 m and 10 m. Apply the Triangle Inequality Theorem to find a possible third side.
2 m
3 m
8 m
18 m
A student is designing a triangular pathway using three concrete slabs with lengths 12 m, 18 m, and 30 m. Based on the Triangle Inequality Theorem, is this pathway possible to form a triangle?
Yes, because all lengths are whole numbers.
Yes, because the perimeter is 60 m.
No, because (12 + 18 = 30), which is not greater than the third side.
No, because 30 is too long compared to the other two sides.
A triangular picnic area in the Memorial Circle has sides measuring 11 m, 14 m, and 17 m. Which side is opposite the largest angle of this picnic area?
The side measuring 11 m.
The side measuring 14 m.
The side measuring 17 m.
All angles are equal, so no single largest side.
Students are observing a triangular art installation with sides 5 m, 8 m, and 10 m. Which side is opposite the smallest angle of this installation?
The side measuring 5 m.
The side measuring 8 m.
The side measuring 10 m.
All angles are the same size.
A group of students proposes building a new triangular mini-garden with sides 10 m, 15 m, and 26 m. After applying the Triangle Inequality Theorem, what is the best advice for this proposal?
Proceed with the design; it forms a valid triangle.
Redesign, as (10 + 15 = 25), which is not greater than 26 m.
Redesign, as 26 m is too close to the sum of the other two sides.
Proceed with the design, assuming the measurements are exact.
During a school trip, Grade 8 students visit Baclaran Market, a busy shopping place in Metro Manila. Their Math teacher challenges them to solve real-life financial problems about earning money, profit and loss, best buys, and installment plans. What does profit mean in business?
The total money used to buy products
The money earned after selling products
The extra money gained after subtracting costs from sales
The difference between the lowest and highest prices
A vendor in Baclaran Market buys slippers for ₱1,200 and sells them for ₱1,500. How should this situation be described?
A loss of ₱300
A profit of ₱300
No profit and no loss
A discount of ₱300
At Baclaran Market, a customer wants to know which laundry detergent pack is the better buy.
Deal A: 3 kg for ₱165
Deal B: 4 kg for ₱212
Using the unit price per kilogram, which deal should the customer choose?
Deal A, ₱55.00 per kg
Deal B, ₱53.00 per kg
Deal A, ₱53.00 per kg
Deal B, ₱55.00 per kg
Carlo compares two payment options for a cellphone:
• Cash price: ₱6,500
• Installment: ₱1,200 per month for 6 months
After analyzing the total costs, which option saves more money, and by how much?
Cash, cheaper by ₱200
Cash, cheaper by ₱700
Installment, cheaper by ₱200
Installment, cheaper by ₱700
A vendor in Baclaran buys t-shirts at ₱150 each and sells them at ₱200 each. If he sells 100 t-shirts, what should he conclude about his earnings?
He will not earn any profit
He will lose ₱5,000
He will gain a profit of ₱5,000
He will gain a profit of ₱10,000
Two rice stores in Baclaran Market offer promos:
• Store A: 25 kg of rice for ₱1,050
• Store B: 50 kg of rice for ₱2,150
If you were tasked to design a “Best Buy Poster” for shoppers, which recommendation would you create?
Store A, cheaper at ₱42.00 per kg
Store B, cheaper at ₱42.00 per kg
Store A, cheaper at ₱43.00 per kg
Store B, cheaper at ₱43.00 per kg
