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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. 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






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






3. 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)






4. Multiply the exponents






5. pr^2






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






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






8. 2pr






9. To solve a proportion - cross multiply






10. 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






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






12. 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)






13. Volume of a Cylinder = pr^2h






14. 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






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






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






17. 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






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






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






20. 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






21. 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






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






23. Factor out the perfect squares






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






25. 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






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






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






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






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






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






31. 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






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






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






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






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






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






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






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






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






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






41. 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






42. 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






43. 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






44. Probability= Favorable Outcomes/Total Possible Outcomes






45. 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






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






47. Subtract the smallest from the largest and add 1






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






49. 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






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