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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. 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)






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






3. Add the exponents and keep the same base






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






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






6. 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






7. 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






8. 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)






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






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






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. 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






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






14. 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






15. Volume of a Cylinder = pr^2h






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






17. Part = Percent x Whole






18. pr^2






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






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






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






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






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






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






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






26. 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






27. 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






28. 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






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






30. 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






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






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






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






34. The whole # left over after division






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






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






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






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






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






40. Combine like terms






41. 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






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






43. Probability= Favorable Outcomes/Total Possible Outcomes






44. 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






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






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






47. To solve a proportion - cross multiply






48. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






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






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