“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
“Perpendicular” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Flip the fraction and sign of the slope. Key Idea: Perpendicular Two lines are perpendicular if they intersect at a right angle (90°).Their slopes are negative reciprocals of each other. General Rule: If one line has slope mmm, the perpendicular line’s slope is: m_perpendicular=−(1/m) Why this matters for the SAT: Perpendicular slopes… Continue reading “Perpendicular” 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
“P% (Percent Form)” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Turn coefficient to percent form. Key Idea: p% (Percent Form) To express a decimal or coefficient as a percent, multiply it by 100 and add the percent symbol (%). General Rule: p%=coefficient×100 Why this matters for the SAT: Percent questions often use coefficients in equations (like growth rates or slopes).… Continue reading “P% (Percent Form)” 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 “One Solution (Quadratic System)” 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 “One Solution (Linear System)” Explained
“No Solution (Quadratic System)” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Discriminant (b^2-4ac) is less than zero (a negative number). Key Idea: No Solution (Quadratic System) A quadratic system has no real solution when the equation has no points of intersection. General Rule: Use the discriminant: Δ=b^2−4ac If Δ<0 (negative), the quadratic has no real solutions. Why this matters for the… Continue reading “No Solution (Quadratic System)” Explained
“No Solution (Linear System)” Explained https://www.youtube.com/watch?v=XHOmBV4js_E Parallel lines. Same slope. Key Idea: No Solution (Linear System) A linear system has no solution when the two equations represent parallel lines. General Rule: Both lines have the same slope. Lines have different y-intercepts. The lines never intersect, so no point satisfies both equations. Why this matters for… Continue reading “No Solution (Linear System)” Explained
“Model” Explained https://www.youtube.com/watch?v=XHOmBV4js_E An equation that represents a situation. Key Idea: Model A model is an equation or function that represents a real-world situation. General Rule: Variables represent quantities in the situation. Constants or coefficients define relationships or rates. The model can be used to predict, analyze, or describe the scenario. Why this matters for… Continue reading “Model” Explained
