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






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






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






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






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






6. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






7. 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






8. 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






9. Probability= Favorable Outcomes/Total Possible Outcomes






10. 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






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






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






13. 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






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






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






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






17. Part = Percent x Whole






18. 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






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






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






21. 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






22. Add the exponents and keep the same base






23. Combine like terms






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






25. 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






26. 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






27. 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






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






29. 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






30. The whole # left over after division






31. 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






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






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






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






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






36. Factor out the perfect squares






37. Subtract the smallest from the largest and add 1






38. 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






39. 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






40. pr^2






41. Volume of a Cylinder = pr^2h






42. 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






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. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






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






46. 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






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






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






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