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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. 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






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






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






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






5. Combine like terms






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






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






8. 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)






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






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






11. Multiply the exponents






12. 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






13. Add the exponents and keep the same base






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






15. 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






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






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






18. 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






19. 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






20. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






21. Volume of a Cylinder = pr^2h






22. To solve a proportion - cross multiply






23. Factor out the perfect squares






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






25. 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






26. 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






27. 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






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






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






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






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






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






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






34. 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






35. 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.






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






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






38. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






39. The whole # left over after division






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






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






42. 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






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






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






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






46. Probability= Favorable Outcomes/Total Possible Outcomes






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






48. 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






49. 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






50. 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