Geometry and trigonometry Flashcards
What are area and volume problems?
Area and volume problems focus on using the relevant formulas for various two- and three-dimensional shapes. We’ll be expected to calculate the length, area, surface area, and volume of shapes, as well as describe how changes in side length affect area and volume.
How to know the volume formulas during the SAT? How To calculate the volume of a solid?
-At the beginning of each SAT math section, the following volume formulas are provided as reference. Top-right side of the screen
-Find the volume formula for the solid.
Plug the dimensions into the formula.
Evaluate the volume.
How To find an unknown dimension when the volume of a solid is given?
1-Find the volume formula for the solid.
2-Plug the volume and any known dimensions into the formula.
3-Isolate the unknown dimension.
What is The effect of changing dimensions on area and volume?
-When a linear dimension to the first power, e.g., the length of a rectangle or the height of a cylinder, changes by a factor, the area or volume changes by the same factor.
-However, when a linear dimension to the second power, e.g., the side length of a square or the radius of a cylinder or cone, changes by a factor, the area or volume changes by the square of the factor.
What are congruence, similarity, and angle relationship problems?
Congruence, similarity, and angle relationship problems ask us to solve for an unknown value using congruent angles, similar triangle, and intersections of lines.
What are right triangle trigonometry problems?
What are the Pythagorean triples?
-Right triangle trigonometry problems are all about understanding the relationship between side lengths, angle measures, and trigonometric ratios in right triangles.
-Pythagorean triples are integers a, b, and c that satisfy the Pythagorean theorem
Being able to recognize Pythagorean triples can save you valuable time on test day.
What are the 3 trigonometric ratios?
What is the mnemonic?
Sine= Opposite over Hypotenuse
Cosine= Adjacent over Hypotenuse
Tangent= Opposite over Adjacent
SOH CAH TOA
(provided in the SAT). What are special right triangles? Why is it useful?
Special right triangles are right triangles with specific angle measure and side length relationships. At the beginning of each SAT math section, the following two special right triangles are provided as reference (https://www.khanacademy.org/test-prep/v2-sat-math/x0fcc98a58ba3bea7:geometry-and-trigonometry-easier/x0fcc98a58ba3bea7:right-triangle-trigonometry-easier/a/v2-sat-lesson-right-triangle-trigonometry)
-This means when we see a special right triangle with unknown side lengths, we know how the side lengths are related to each other. For example, if we have a 30-60-90 triangle and the length of the shorter leg is 3, we know that the length of the hypotenuse is 2(3)=6 and the length of the longer leg is 3*sqrt{3}.
How are the sine and cosine of complementary angles are related?
sin(a)=cos(90-a)
What are circle theorems problems?
What is A central angle ?
-Circle theorems problems are all about finding arc lengths, sector areas, and angles in circles.
-A central angle in a circle is formed by two radii. This angle lets us define a portion of the circle’s circumference (an arc) or a portion of the circle’s area (a sector).
What is the proportional relationship between the central angle, the arc length and the sector area?
(central angle/360)= (arc length/circumference)= (sector area/circle area)
