Transformations
What are the 4 transformations in math?
translation, rotation, reflection and dilation.
A cube has sides of length 6 cm. What is its volume?
Volume = side³ = 6³ = 216 cm³
A circle has a radius of 5 cm. What is its diameter?
10 cm
Calculate the mean of the following dataset: 12, 15, 18, 22, 25, 30.
(12 + 15 + 18 + 22 + 25 + 30) / 6 = 20.33.
A rectangle has a length of 8 cm and a width of 5 cm. What is its area?
40 cm²
A triangle has vertices A(1, 2) B(3, 5), and C(2, 1). If the triangle is translated 4 units to the right and 1 unit down, what are the new coordinates of the vertices?
A'(5, 1), B'(7, 4), C'(6, 0)
A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 3 cm. What is its volume?
Volume = length × width × height = 10 × 5 × 3 = 150 cm³
What is the formula for the circumference of a circle, using the radius?
C = 2πr
Find the median of the following dataset: 5, 10, 12, 18, 20, 25, 30.
18
A parallelogram has a base of 12 cm and a height of 6 cm. What is its area?
72 cm²
Rotation: Point E is at (-2, -3). Rotate it 180 degrees around the origin. What are the coordinates of E'?
E'(2, 3)
A triangular prism has a base triangle with a base of 8 cm and a height of 5 cm. The prism's height is 12 cm. What is its volume?
(1/2) × base × height (of triangle) × height (of prism) = (1/2) × 8 × 5 × 12 = 240 cm³
A circle has a radius of 7 meters. Calculate its circumference. (Use π ≈ 3.14)
43.96 meters
The heights (in inches) of 5 students are: 65, 68, 72, 69, 71. Calculate the range and standard deviation of the heights.
72 - 65 = 7
A rectangular garden is 15 feet long and 8 feet wide. What is the area of the garden in square yards?
13.33 sq yd
Quadrilateral DEFG has vertices D(-4, 2), E(-1, 4), F(1, 2), and G(-2, 0). Reflect the quadrilateral across the y-axis. What are the coordinates of the vertices of D'E'F'G'?
D'(4, 2), E'(1, 4), F'(-1, 2), G'(2, 0)
A square pyramid has a base with sides of 6 cm and a height of 9 cm. What is its volume?
Volume = (1/3) × base area × height = (1/3) × 6² × 9 = 108 cm³
A cylinder has a volume of 785 cubic centimeters and a height of 10 cm. What is the radius of the cylinder? (Use π ≈ 3.14)
5 cm
A dataset of test scores is: 75, 80, 92, 68, 88, 79, 85. Calculate the mean, median, and mode of the test scores.
Mean: Add all scores and divide by the number of scores. (75 + 80 + 92 + 68 + 88 + 79 + 85) / 7 = 81.
Median: Sort the scores in ascending order: 68, 75, 79, 80, 85, 88, 92. The median is the middle value, which is 80.
Mode: The mode is the value that appears most frequently. In this dataset, no value repeats, so there is no mode.
A circle has a diameter of 14 cm. What is the area of the circle (use π ≈ 3.14)?
153.86 cm²
Point C is at (4, 2). Reflect it across the y-axis. What are the coordinates of C'?
C'(-4, 2)
A storage container is shaped like a rectangular prism with a smaller cube on top. The prism has a length of 8 ft, a width of 5 ft, and a height of 4 ft. The cube has sides of 3 ft. What is the total volume of the container?
Volume of prism = 8 × 5 × 4 = 160 ft³. Volume of cube = 3³ = 27 ft³. Total volume = 160 + 27 = 187 ft³
If you double the radius of a sphere, how does the volume change?
The volume increases by a factor of 8
A bag contains 5 red marbles and 3 blue marbles. If you pick one marble randomly, what is the probability of picking a blue marble?
The total number of marbles is 5 + 3 = 8. The number of blue marbles is 3. Therefore, the probability of picking a blue marble is 3/8.
A rectangle has an area of 48 square inches. If its length is twice its width?
Width = 4 inches, Length = 12 inches