78 Questions
What is the formula for the surface area of a sphere?
4πr^2
What is the formula for the volume of a cylinder?
πr^2 h
What is the formula for the surface area of a rectangular prism?
2lw + 2lh + 2wh
What is the formula for the volume of a cube?
s^3
What is the formula for the surface area of a cone?
πr(l + r)
What is the formula for the volume of a rectangular pyramid?
1/3 lwh
What is the formula for the surface area of a triangular prism?
bh + 2ls + lb
What is the formula for the area of a circle?
πr^2
What is the definition of a translation in transformation geometry?
A transformation that moves every point of a shape the same distance in the same direction.
What is the notation for a translation in transformation geometry?
(x, y) → (x + a, y + b)
What is the key element of a rotation in transformation geometry?
All of the above
What is the formula for a 90° counterclockwise rotation about the origin in transformation geometry?
(x, y) → (-y, x)
What is the definition of a reflection in transformation geometry?
A transformation that flips a shape over a line.
What is the formula for a reflection over the x-axis in transformation geometry?
(x, y) → (x, -y)
What is the key element of a dilation in transformation geometry?
Both A and B
What is the formula for a dilation from the origin with a scale factor of k in transformation geometry?
(x, y) → (kx, ky)
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What happens to the perimeter of a shape when you double one of its dimensions?
The perimeter is doubled
What is the formula for the area of a triangle?
A = 1/2 * base * height
What is the effect of doubling both dimensions of a shape on its area?
The area is quadrupled
What is the formula for the area of a circle?
A = πr^2
What happens to the area of a shape when you double one of its dimensions?
The area is doubled
What is the formula for the circumference of a circle?
C = 2πr
What is the formula for the area of a parallelogram?
A = base * height
What is the formula for the perimeter of a square?
P = 4s
What is the formula for the area of a kite?
A = 1/2 * d1 * d2
What is the surface area of a cylinder with radius 4 cm and height 10 cm?
160π cm²
What is the volume of a triangular prism with base length 6 cm, height 8 cm, and length 10 cm?
180 cm³
What is the surface area of a rectangular pyramid with length 8 cm, width 6 cm, and height 10 cm?
168 cm²
What is the volume of a sphere with radius 6 cm?
324π cm³
What is the surface area of a cone with radius 4 cm and height 12 cm?
96π cm²
What is the volume of a cube with side length 8 cm?
256 cm³
What is the surface area of a rectangular prism with length 10 cm, width 8 cm, and height 6 cm?
188 cm²
What is the volume of a cylinder with radius 3 cm and height 15 cm?
165π cm³
If (x, y) is rotated 90° counterclockwise about the origin, what is the resulting coordinate?
(-y, x)
What is the formula for the perimeter of a trapezium?
P = a + b + c + d
What is the effect of doubling both dimensions of a shape on its perimeter?
The perimeter is doubled.
What is the formula for the area of a rhombus?
A = 1/2 × d_1 × d_2
If (x, y) is reflected over the line y = x, what is the resulting coordinate?
(y, x)
What is the formula for the area of a kite?
A = 1/2 × d_1 × d_2
What is the effect of doubling one dimension of a shape on its area?
The area is doubled.
What is the formula for the perimeter of a parallelogram?
P = 2(a + b)
What is the formula for the area of a trapezium?
A = 1/2 × (side_1 + side_2) × height
What is the effect of doubling both dimensions of a shape on its area?
The area is quadrupled.
What is the result of translating a point (x, y) by a vector (-3, 2)?
(x - 3, y + 2)
What is the effect of a 180° rotation about the origin on a point (x, y)?
(x, y) → (-x, -y)
What is the result of reflecting a point (x, y) over the line y = x?
(x, y) → (y, x)
What is the effect of a dilation with a scale factor of 2 from the origin on a point (x, y)?
(x, y) → (2x, 2y)
What is the result of translating a point (x, y) by a vector (4, -2) and then rotating it 90° counterclockwise about the origin?
(x + 4, y - 2) → (-y + 4, x - 2)
What is the result of reflecting a point (x, y) over the x-axis and then translating it by a vector (2, 3)?
(x, y) → (x, -y) → (x + 2, y + 3)
What is the result of rotating a point (x, y) 270° counterclockwise about the origin and then dilating it by a scale factor of 3 from the origin?
(x, y) → (y, -x) → (3y, -3x)
What is the result of reflecting a point (x, y) over the line y = x and then rotating it 90° counterclockwise about the origin?
(x, y) → (y, x) → (-x, y)
What is the result of rotating a point (x, y) by 90° counterclockwise about the origin?
(-y, x)
What is the formula for the area of a parallelogram?
base × height
What happens to the perimeter of a shape when you double one of its dimensions?
It doubles
What is the formula for the perimeter of a trapezium?
side_1 + side_2 + side_3 + side_4
What is the result of reflecting a point (x, y) over the x-axis?
(x, -y)
What is the formula for the area of a kite?
(1/2) × d_1 × d_2
What is the effect of doubling both dimensions of a shape on its area?
It quadruples
What is the formula for the perimeter of a rectangle?
2 × (l + w)
What is the result of dilating a point (x, y) from the origin with a scale factor of 2?
(2x, 2y)
What is the formula for the circumference of a circle?
2 × π × r
What is the surface area of a cube with side length 5 cm?
150 cm²
What is the volume of a cone with radius 3 cm and height 6 cm?
36π cm³
What is the surface area of a sphere with radius 4 cm?
128π cm²
What is the volume of a rectangular prism with length 6 cm, width 4 cm, and height 3 cm?
72 cm³
What is the surface area of a triangular prism with base length 5 cm, height 6 cm, and length 7 cm?
142 cm²
What is the volume of a cylinder with radius 2 cm and height 8 cm?
32π cm³
What is the surface area of a rectangular pyramid with length 6 cm, width 4 cm, and height 5 cm?
104 cm²
What is the volume of a cone with radius 2 cm and height 4 cm?
12π cm³
What is the effect of a translation on a shape?
It moves every point of the shape the same distance in the same direction.
What is the formula for a 270° counterclockwise rotation about the origin?
(x, y) -> (y, -x)
What is the line of reflection for the formula (x, y) -> (y, x)?
y = x
What is the effect of a dilation with a scale factor of k on a shape?
It changes the size of the shape but not its shape.
What is the result of translating a point (x, y) by a vector (a, b)?
(x, y) -> (x + a, y + b)
What is the center of rotation for a rotation?
The fixed point around which the shape is turned.
What is the formula for a reflection over the y-axis?
(x, y) -> (-x, y)
What is the result of rotating a point (x, y) 90° counterclockwise about the origin and then translating it by a vector (2, 3)?
(x, y) -> (-y + 2, x + 3)
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