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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






2. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






3. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






4. 1. Re-express them with common denominators 2. Convert them to decimals






5. 2pr






6. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






7. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






8. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






9. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






10. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






11. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






12. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






13. The whole # left over after division






14. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






15. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






16. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






17. Add the exponents and keep the same base






18. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






19. you can add/subtract when the part under the radical is the same






20. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






21. Change in y/ change in x rise/run






22. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






23. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






24. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






25. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






26. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






27. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






28. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






29. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






30. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






31. To multiply fractions - multiply the numerators and multiply the denominators






32. Surface Area = 2lw + 2wh + 2lh






33. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






34. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






35. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






36. Domain: all possible values of x for a function range: all possible outputs of a function






37. pr^2






38. (average of the x coordinates - average of the y coordinates)






39. The smallest multiple (other than zero) that two or more numbers have in common.






40. Volume of a Cylinder = pr^2h






41. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






42. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






43. A square is a rectangle with four equal sides; Area of Square = side*side






44. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






45. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






46. Combine equations in such a way that one of the variables cancel out






47. Sum=(Average) x (Number of Terms)






48. To find the reciprocal of a fraction switch the numerator and the denominator






49. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






50. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex