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






3. 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






4. 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






5. 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






6. 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)






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






8. 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






9. 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






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






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






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






13. 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






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






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






16. Add the exponents and keep the same base






17. 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






18. 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






19. 2pr






20. 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






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






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






23. 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






24. Combine like terms






25. Volume of a Cylinder = pr^2h






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






27. Multiply the exponents






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






29. Domain: all possible values of x for a function range: all possible outputs of a function






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






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






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






33. To solve a proportion - cross multiply






34. 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






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






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






37. 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






38. 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






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






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






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






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






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






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






45. 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






46. Probability= Favorable Outcomes/Total Possible Outcomes






47. pr^2






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






49. 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






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