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






2. 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






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






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






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






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






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






8. Factor out the perfect squares






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






11. 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






12. Add the exponents and keep the same base






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






14. 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






15. 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






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






17. The whole # left over after division






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






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






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






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






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






23. 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






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






25. 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






26. Part = Percent x Whole






27. pr^2






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






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






30. Multiply the exponents






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






32. 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






33. 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






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






35. 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






36. 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






37. 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






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






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






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






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






42. 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






43. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






49. 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






50. 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