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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. Probability= Favorable Outcomes/Total Possible Outcomes






2. 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






3. 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






4. 2pr






5. 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






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






7. pr^2






8. Add the exponents and keep the same base






9. 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






10. The median is the value that falls in the middle of the set - the mode is the value that appears most often






11. Part = Percent x Whole






12. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






13. Combine like terms






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






15. 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






16. To solve a proportion - cross multiply






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






18. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






19. Factor out the perfect squares






20. 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






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






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






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






24. Subtract the smallest from the largest and add 1






25. Multiply the exponents






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






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






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






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






30. 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.






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






32. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






33. 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






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






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






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






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






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






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






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






41. 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






42. Volume of a Cylinder = pr^2h






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






44. 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






45. 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






46. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






47. 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






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






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






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