A
Which of the following statements correctly describes the Cartesian coordinate plane?
A. It is a two-dimensional plane divided into four quadrants by two perpendicular lines called the x-axis and y-axis.
B. It is a three-dimensional plane used to plot points in space, divided by three axes: x, y, and z
C. It is a single axis used to represent positive and negative values of a variable
D. It is a graphing system that uses a circular grid to represent points based on angles and distances from the center
A. It is a two-dimensional plane divided into four quadrants by two perpendicular lines called the x-axis and y-axis.
Which quadrant contains points where both x and y coordinates are negative?
A. Quadrant I B. Quadrant II C. Quadrant III D. Quadrant IV
C. Quadrant III
A triangle has sides 8 cm, 15 cm, and 17 cm. Use the converse of the Pythagorean Theorem to classify the triangle.
A. Acute B. Obtuse
C. Right D. Not a Triangle
C. Right
Which of the following sets of side lengths can form a triangle?
A. 2, 2, 5 B.3, 4, 8
C.5, 5, 5 D. 6, 10, 15
C. 5, 5, 5
Which of the following statements is the Triangle Inequality Theorem?
A. The sum of the angles in a triangle is 180°
B. A triangle is equilateral if all three sides are equal.
C. The square of the hypotenuse is equal to the sum of the squares of the other two sides. D. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
D. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
A student is exploring the volume of pyramids with different base shapes but identical base areas and heights. Which of the following factors directly influences the volume of a pyramid?
A. The material used to construct the pyramid
B. The shape of the base (e.g., triangle, hexagon)
C. The number of edges and vertices of the base D. The area of the base and the height of the pyramid
D. The area of the base and the height of the pyramid
A triangular pyramid and a hexagonal pyramid have the same height, and their base areas are equal. What conclusion can you draw about their volumes?
A. The triangular pyramid has a smaller volume because its base has fewer sides.
B. The hexagonal pyramid has a greater volume because its base is more complex.
C. The volumes cannot be compared because the shapes of their bases are different. D. Both pyramids have the same volume because the volume depends only on base area and height.
D. Both pyramids have the same volume because the volume depends only on base area and height.
A 1-liter bottle of detergent costs Php 58, while a 3-liter bottle costs Php141. Which option gives the best value?
A. 1-liter bottle B. 3-liter bottle C. Both have the same value D. Neither
B. 3-liter bottle
How is a point represented in the Cartesian coordinate system?
A. As a quadrant
B. As a straight line
C. As a single number
D. As an ordered pair (x,y)
D. As an ordered pair (x,y)
A laptop costs Php 60,000. If bought on an installment plan, it requires a Php 10,000 down payment and Php 5000 per month for 12 months. How much more expensive is the installment plan compared to paying cash?
A. Php 5000 B. Php 8000 C. Php 10000 D. Php 12000
C. Php 10000
How would you plot the point (-3, -2) on the Cartesian plane?
A. Move 3 units left and 2 units up from the origin.
B. Move 3 units right and 2 units up from the origin.
C. Move 3 units left and 2 units down from the origin.
D. Move 3 units right and 2 units down from the origin.
C. Move 3 units left and 2 units down from the origin.
A ramp is constructed with a height of 3m and a base of 4 m. What is the length of the ramp?
A. 4.5 m B.5 m
C. 5.5 m D. 6 m
B. 5 m
If a triangle has sides measuring 5 cm, 7 cm, and 10 cm, does it satisfy the Triangle Inequality Theorem?
A.Yes, because the difference between the sides is less than the third side.
B.Yes, because 5 + 7 > 10, 7 + 10 > 5, and 10 + 5 > 7
C. No, because 5 + 7 < 10
D. No, because 5 + 10 < 7.
B.Yes, because 5 + 7 > 10, 7 + 10 > 5, and 10 + 5 > 7
A cone and a sphere have the same radius r and height ℎ = 2𝑟. Which of the following is true about their volumes?
A.The cone's volume is half the sphere's volume. B.The cone's volume is equal to the sphere's volume.
C. The cone's volume is twice the sphere's volume. D. The cone's volume is one-third the sphere's volume
A.The cone's volume is half the sphere's volume.
One leg of a right triangle measures 9 cm, and the hypotenuse measures 15 cm. Find the length of the other leg.
A. 10 cm B.12 cm
C. 13 cm D. 14 cm
B.12 cm
If you plot the points (3,0) and (0,−2), which axes do they lie on?
A. Both lie on the x-axis B. x-axis and y-axis respectively
C. Both lie on the y-axis D. y-axis and x-axis respectively
B. x-axis and y-axis respectively
Consider a triangular pyramid, a pentagonal pyramid, and a hexagonal pyramid, each with the same base area and height. Which of the following is true about their volumes?
A. The hexagonal pyramid has the largest volume. B.The triangular pyramid has the largest volume.
C. The pentagonal pyramid has the smallest volume. D. All three pyramids have the same volume.
D. All three pyramids have the same volume.
A line segment has endpoints R(-3, 2) and S(7, 10). What is the length of the line segment?
The length of the line segment is SQUARE ROOT OF 164 or approximately 12.81 units.
A student claims that doubling the base area of a triangular pyramid will double its volume, while doubling its height will quadruple its volume. Is this claim correct?
A. Yes, the claim is correct.
B. No, doubling the height will only double the volume
C. No, neither part of the claim is correct. D. No, doubling the base area has no effect on the volume.
B. No, doubling the height will only double the volume
A sphere is placed inside a cylinder with the same height and diameter as the sphere. What fraction of the cylinder’s volume is occupied by the sphere?
A. 1/2 B. 2/3 C. 3/4 D. 1
B. 2/3
If x = 4 and y = 2, what is the value of
x2 + 2(y)?
20
A water tank is shaped like a cone with a height of 10 m and a base radius of 3m. How much water can the tank hold when full?
A. 94.2 m3 B. 125.6 m3
C. 188.4 m3 D. 314 m3
A. 94.2 m3
The endpoints of a line segment are (4, -2) and (-6, 8) on the Cartesian coordinate plane. What is the distance between points P and Q? What are the coordinates of the midpoint of the line segment PQ?
Distance: 14.14; Midpoint: (-1, 3)
If the midpoint of the line segment joining points P(1, -2) and Q(5, 4) What are the coordinates of the midpoint?
(3, 1)
If a hexagonal pyramid has a base area of 90 cm2 and a height of 10 cm, what is its volume?
A. 150 cm3 B. 300 cm3
C. 450 cm3 D. 900 cm3
B. 300 cm3