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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. 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






2. 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






3. 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






4. 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






5. 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






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






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






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






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






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. 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






12. Probability= Favorable Outcomes/Total Possible Outcomes






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






14. 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






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






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






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






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






20. The whole # left over after division






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






22. 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






23. 2pr






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






26. Combine like terms






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






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






29. 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






30. 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






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






32. 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)






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






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






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






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






37. Subtract the smallest from the largest and add 1






38. Part = Percent x Whole






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






40. pr^2






41. To divide fractions - invert the second one and multiply






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






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






44. Multiply the exponents






45. 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






46. 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






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






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






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






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