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This post is intended as a home for useful but orphaned math strategies. Included are Triangles Within Triangles, Avoid Fractions on the SAT/ACT, and Two Reactions to Right Triangles. Proceed to peruse these and other SAT/ACT math and general approach tips. [Note: “iff” means “if and only if.”]  Triangles Within Triangles   On the SAT, whenever a triangle appears inside another triangle, all triangles will be similar, and setting up and solving a proportion will solve the given problem. Avoid Fractions on the SAT/ACT It’s often best to entirely avoid fractions on the SAT/ACT. Instead, fractions can be converted to decimals to make numbers more intuitive and calculations, estimates, and comparisons easier. Two Reactions to Right Triangles Whenever encountering a right triangle in a math problem, immediately ask two questions: Could I use the Pythagorean theorem? Could I use SOH CAH TOA? Nine times out of ten one of those approaches will lead to the solution. No Solutions Que...

This post is intended as a home for useful but orphaned math strategies. Included are Triangles Within Triangles, Avoid Fractions on the SAT/ACT, and Two Reactions to Right Triangles. Proceed to peruse these and other SAT/ACT math and general approach tips. [Note: “iff” means “if and only if.”]  Triangles Within Triangles   On the SAT, whenever a triangle appears inside another triangle, all triangles will be similar, and setting up and solving a proportion will solve the given problem. Avoid Fractions on the SAT/ACT It’s often best to entirely avoid fractions on the SAT/ACT. Instead, fractions can be converted to decimals to make numbers more intuitive and calculations, estimates, and comparisons easier. Two Reactions to Right Triangles Whenever encountering a right triangle in a math problem, immediately ask two questions: Could I use the Pythagorean theorem? Could I use SOH CAH TOA? Nine times out of ten one of those approaches will lead to the solution. No Solutions Que...

This post is intended as a home for useful but orphaned math strategies. Included are Triangles Within Triangles, Avoid Fractions on the SAT/ACT, and Two Reactions to Right Triangles. Proceed to peruse these and other SAT/ACT math and general approach tips. [Note: “iff” means “if and only if.”]  Triangles Within Triangles   On the SAT, whenever a triangle appears inside another triangle, all triangles will be similar, and setting up and solving a proportion will solve the given problem. Avoid Fractions on the SAT/ACT It’s often best to entirely avoid fractions on the SAT/ACT. Instead, fractions can be converted to decimals to make numbers more intuitive and calculations, estimates, and comparisons easier. Two Reactions to Right Triangles Whenever encountering a right triangle in a math problem, immediately ask two questions: Could I use the Pythagorean theorem? Could I use SOH CAH TOA? Nine times out of ten one of those approaches will lead to the solution. No Solutions Que...

Analytic geometry is a core sub-topic in all algebra courses, blending geometry and algebra on a coordinate grid measured by x and y axes.  As the story goes, famous French polymath René Descartes came up with the idea after watching a fly crawl up a wall. These questions comprise a large fraction of SAT/ACT questions, and students must fully command key elements. Following is what you need to know.  - Equation of a line  y = mx+b. m = slope, b = y-intercept. Equation of a parabola Vertex form: y = a(x-h)^2 + k, vertex is (h,k). Standard form: y = ax^2+bx+c, vertex is (h,k) with h = -b/2a, k = f(h). Equation of a circle (x-h)^2+(y-k)^2 = r^2. Vertex is (h,k), radius = r. To write the equation of a line containing 2 given points (x,y): Use a Desmos table together with y1 ~ mx1+b to return m, b. - For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it unti...

Analytic geometry is a core sub-topic in all algebra courses, blending geometry and algebra on a coordinate grid measured by x and y axes.  As the story goes, famous French polymath René Descartes came up with the idea after watching a fly crawl up a wall. These questions comprise a large fraction of SAT/ACT questions, and students must fully command key elements. Following is what you need to know.  - Equation of a line  y = mx+b. m = slope, b = y-intercept. Equation of a parabola Vertex form: y = a(x-h)^2 + k, vertex is (h,k). Standard form: y = ax^2+bx+c, vertex is (h,k) with h = -b/2a, k = f(h). Equation of a circle (x-h)^2+(y-k)^2 = r^2. Vertex is (h,k), radius = r. To write the equation of a line containing 2 given points (x,y): Use a Desmos table together with y1 ~ mx1+b to return m, b. - For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it unti...

Analytic geometry is a core sub-topic in all algebra courses, blending geometry and algebra on a coordinate grid measured by x and y axes.  As the story goes, famous French polymath René Descartes came up with the idea after watching a fly crawl up a wall. These questions comprise a large fraction of SAT/ACT questions, and students must fully command key elements. Following is what you need to know.  - Equation of a line  y = mx+b. m = slope, b = y-intercept. Equation of a parabola Vertex form: y = a(x-h)^2 + k, vertex is (h,k). Standard form: y = ax^2+bx+c, vertex is (h,k) with h = -b/2a, k = f(h). Equation of a circle (x-h)^2+(y-k)^2 = r^2. Vertex is (h,k), radius = r. To write the equation of a line containing 2 given points (x,y): Use a Desmos table together with y1 ~ mx1+b to return m, b. - For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it unti...