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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 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






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






3. The whole # left over after division






4. 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






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






6. 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






7. Probability= Favorable Outcomes/Total Possible Outcomes






8. Multiply the exponents






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






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






11. 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






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






13. 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






14. 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






15. 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






16. 2pr






17. 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






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






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






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






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






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






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






24. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






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






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






27. 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






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






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






30. 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






31. Combine like terms






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






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






34. 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






35. 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






36. To solve a proportion - cross multiply






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






38. pr^2






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






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






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






43. Subtract the smallest from the largest and add 1






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






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






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






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






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






49. 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






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