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






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






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






4. 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






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






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






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






8. 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






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






10. 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






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






12. 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






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






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






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






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






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






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






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






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






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






22. 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






23. Add the exponents and keep the same base






24. Probability= Favorable Outcomes/Total Possible Outcomes






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






26. 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






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. 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






29. 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






30. 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






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






32. Part = Percent x Whole






33. Subtract the smallest from the largest and add 1






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






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






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






37. 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






38. 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






39. 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






40. 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






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






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






43. 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






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






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






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






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






48. Multiply the exponents






49. 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






50. 2pr