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






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






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






5. 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






6. 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






7. 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






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






9. 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






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






11. Combine like terms






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






13. 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






14. 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






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






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






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






18. 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






19. Factor out the perfect squares






20. 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)






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






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






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






24. Part = Percent x Whole






25. 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






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






27. 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






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






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






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






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






32. 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






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






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






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






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






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






38. Volume of a Cylinder = pr^2h






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






40. 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






41. 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






42. pr^2






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






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






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






46. 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






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






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






49. 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






50. To solve a proportion - cross multiply