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






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






3. 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






4. Combine like terms






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






6. 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






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






8. Factor out the perfect squares






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






10. 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






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






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






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






14. 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






15. Probability= Favorable Outcomes/Total Possible Outcomes






16. 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






17. 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






18. 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






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






20. 2pr






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






22. Add the exponents and keep the same base






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






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






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






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






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






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






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






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






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






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






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






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






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






36. 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






37. 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






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






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. 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






41. 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






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






43. 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






44. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






45. Part = Percent x Whole






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






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






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






49. 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






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