“Slope” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Rise over run. Rise to your whY, run from your eX. Key Idea: Slope The slope measures the steepness of a line on a coordinate plane. General Rule: slope = rise / run = change in y / change in x “Rise” is the vertical change (change in y). “Run” is the… Continue reading “Slope” Explained
“Slant Height” Explained https://www.youtube.com/watch?v=XHOmBV4js_E For pyramids and cones the slant height is the slanted height of the face. Found with pythagorean theorem applied to height and generally half of the base. Key Idea: Slant Height For pyramids and cones, the slant height is the distance along the face from the base to the apex (tip).… Continue reading “Slant Height” Explained
“Sine (sin)” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Side opposite of angle / hypotenuse. Key Idea: Sine (sin) In a right triangle, the sine of an angle is the ratio of the side opposite the angle to the hypotenuse. General Rule: sin(θ)=Opposite Side / Hypotenuse Only applies to right triangles. Helps find missing side lengths or angles when combined… Continue reading “Trigonometric Ratios” Explained
“Scaling Area” Explained https://www.youtube.com/watch?v=XHOmBV4js_E When scaling area, the scale factor is multiplied twice or squared. Key Idea: Scaling Area When a figure is scaled, its area changes according to the square of the scale factor. General Rule: If the linear scale factor is k=, the area scale factor is k^2. Formula: New Area = (Scale… Continue reading “Scaling Dimensions” Explained
“Pythagorean Theorem” Explained https://www.youtube.com/watch?v=XHOmBV4js_E a^2+b^2=c^2 Key Idea: Pythagorean Theorem The Pythagorean Theorem relates the side lengths of a right triangle:the square of the hypotenuse equals the sum of the squares of the two legs. General Rule: For any right triangle: a^2+b^2=c^2 where a and b are the legs, and c is the hypotenuse (the side… Continue reading “Pythagorean Theorem” Explained
“Probability” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Number of target outcomes / number of total outcomes. Key Idea: Probability Probability measures how likely an event is to occur. It compares the number of desired outcomes to the number of possible outcomes. General Rule: P(event)=Number of target / outcomesNumber of total outcomes Why this matters for the SAT: Probability questions… Continue reading “Probability” Explained
“Prism” Explained https://www.youtube.com/watch?v=XHOmBV4js_E A 3d shape where whatever comes before the word prism tells you the shape of the base stretched straight up with a height. Ex. A “circular prism” is like a tube. A circle with a straight height. Key Idea: Prism A prism is a 3D solid formed by extending a 2D shape… Continue reading “Prism” Explained
“Perimeter” Explained https://www.youtube.com/watch?v=XHOmBV4js_E All the side lengths added up. “Peri” means outside. “Meter” means measure. Key Idea: Perimeter The perimeter is the total distance around a shape, found by adding up all the side lengths.The word comes from Greek: “peri” = around, “meter” = measure. General Rule: Perimeter=Sum of all side lengths Why this matters… Continue reading “Perimeter” Explained
“One Solution (Quadratic System)” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Discriminant (b^2-4ac) is equal to zero. Key Idea: One Solution (Quadratic System) A quadratic system has one real solution when the quadratic and the line (or another curve) touch at exactly one point — typically where the line is tangent to the parabola. General Rule: Use the discriminant: Δ=b^2−4ac… Continue reading “Quadratic Systems” Explained
“One Solution (Linear System)” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Different slopes. One intersection. Key Idea: One Solution (Linear System) A linear system has one solution when the two equations represent lines with different slopes, meaning they intersect at exactly one point. General Rule: Slopes are different. One point of intersection exists. This single point satisfies both equations simultaneously.… Continue reading “Linear Systems” Explained
