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






2. 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






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






4. Part = Percent x Whole






5. 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






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






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






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






9. 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






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






11. 2pr






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. 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)






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






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






16. 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






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






18. Subtract the smallest from the largest and add 1






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






20. 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






21. Combine like terms






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






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






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






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






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






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






28. 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)






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






30. 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






31. 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






32. Probability= Favorable Outcomes/Total Possible Outcomes






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






34. 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






35. 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






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. To divide fractions - invert the second one and multiply






38. pr^2






39. 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






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. 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






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






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






44. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






45. 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






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






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






48. 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






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






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