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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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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. 2pr






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






3. 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






4. 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)






5. 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






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






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






8. 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






9. 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






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






11. Factor out the perfect squares






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






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






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






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






16. 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






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






18. 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






19. 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






20. 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






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






22. 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






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






24. To solve a proportion - cross multiply






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






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






27. Volume of a Cylinder = pr^2h






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






29. 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






30. 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






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






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






33. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






36. 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






37. 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






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






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






40. 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






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






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






43. Add the exponents and keep the same base






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






45. Multiply the exponents






46. 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






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






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






49. The whole # left over after division






50. 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)







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