Proceed to peruse these and other SAT/ACT math and general approach tips.
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
Questions referencing equations or systems with “no solutions” are common on the SAT/ACT math tests. They mainly come in two flavors: quadratic equations, and linear/non-linear systems.
SAT/ACT questions involving quadratic equations with no solutions can be solved using the Discriminant: D = b^2–4ac. There are no real solutions to a quadratic equation iff D < 0, and this inequality will usually solve the given problem.
In general, linear or non-linear systems with no solution produce graphs with no points of intersection. Linear systems have no solutions iff the lines graphed are parallel iff slopes are equal. Desmos can be employed to draw the graphs of both equations, and see what needs to be done (e.g. with sliders) to ensure required conditions are met.
40 Top Tips for Taking Standardized Tests
Click here to read my collected musings and battle-tested general approach tips for improving scores on standardized assessments like the SAT and ACT.
[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
Questions referencing equations or systems with “no solutions” are common on the SAT/ACT math tests. They mainly come in two flavors: quadratic equations, and linear/non-linear systems.
SAT/ACT questions involving quadratic equations with no solutions can be solved using the Discriminant: D = b^2–4ac. There are no real solutions to a quadratic equation iff D < 0, and this inequality will usually solve the given problem.
In general, linear or non-linear systems with no solution produce graphs with no points of intersection. Linear systems have no solutions iff the lines graphed are parallel iff slopes are equal. Desmos can be employed to draw the graphs of both equations, and see what needs to be done (e.g. with sliders) to ensure required conditions are met.
40 Top Tips for Taking Standardized Tests
Click here to read my collected musings and battle-tested general approach tips for improving scores on standardized assessments like the SAT and ACT.
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