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






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






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






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






5. 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






6. Combine like terms






7. The largest factor that two or more numbers have in common.






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






9. 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






10. 2pr






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






12. 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)






13. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






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






15. To solve a proportion - cross multiply






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






17. 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






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






19. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign






20. The whole # left over after division






21. Multiply the exponents






22. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






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






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






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






26. pr^2






27. 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






28. 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






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






30. 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






31. Volume of a Cylinder = pr^2h






32. Part = Percent x Whole






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






34. 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






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






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






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






38. 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






39. 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






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






41. 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






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






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






44. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






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






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






47. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






50. 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