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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. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






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






3. Combine like terms






4. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






5. 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






6. Volume of a Cylinder = pr^2h






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






8. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






9. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






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






11. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






12. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






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






14. 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






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






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






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






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






19. 2pr






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






21. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






22. 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






23. 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






24. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






25. 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






26. Subtract the smallest from the largest and add 1






27. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






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






29. For all right triangles: a^2+b^2=c^2






30. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






31. Add the exponents and keep the same base






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






33. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






34. 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






35. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






36. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






37. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






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






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






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






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






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






43. 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






44. Multiply the exponents






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






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






47. To divide fractions - invert the second one and multiply






48. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






49. The whole # left over after division






50. To solve a proportion - cross multiply