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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 whole # left over after division






2. 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






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






4. 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






5. 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






6. Volume of a Cylinder = pr^2h






7. 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






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






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






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






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






12. To solve a proportion - cross multiply






13. 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






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






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






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






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






18. 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






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






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






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






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






24. 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






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






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






27. 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






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






29. Part = Percent x Whole






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






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






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






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






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






35. 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)






36. 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






37. 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






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






39. 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






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






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






42. 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






43. 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






44. 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






45. Combine like terms






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






47. 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






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






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






50. Probability= Favorable Outcomes/Total Possible Outcomes