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






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






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






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






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






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






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






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






9. 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






10. 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






11. To solve a proportion - cross multiply






12. 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






13. 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






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






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






16. Multiply the exponents






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






18. 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






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






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






21. 2pr






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






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






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






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






26. 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)






27. Combine like terms






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






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






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






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






32. 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






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






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






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






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






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






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






39. Probability= Favorable Outcomes/Total Possible Outcomes






40. 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






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






42. 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






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






44. 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






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






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






47. 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






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






49. 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)






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






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