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






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






5. Part = Percent x Whole






6. 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)






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






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






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






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






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






13. 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






14. pr^2






15. Combine like terms






16. 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






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






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






19. 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






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






21. Add the exponents and keep the same base






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






23. 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






24. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






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






26. 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






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






28. 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






29. Multiply the exponents






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






31. 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






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






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






34. 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






35. 2pr






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






37. 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






38. 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






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






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






41. 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.






42. 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






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






44. Subtract the smallest from the largest and add 1






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






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






47. The whole # left over after division






48. 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






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






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