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






2. Combine like terms






3. Factor out the perfect squares






4. 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






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






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






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






8. Volume of a Cylinder = pr^2h






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






10. 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.






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






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






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






14. 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






15. 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






16. 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






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






18. 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






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






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






21. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






22. 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






23. 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






24. 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






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






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






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






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






29. 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






30. Add the exponents and keep the same base






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






32. Part = Percent x Whole






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






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






35. Probability= Favorable Outcomes/Total Possible Outcomes






36. Multiply the exponents






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






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






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






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






41. 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






42. 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






43. 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






44. pr^2






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






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






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






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






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






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