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






2. 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






3. 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






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






5. 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






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






7. 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






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






9. 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






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






11. 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






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






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. 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






15. 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






16. 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






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






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






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






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






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






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






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






24. 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






25. Multiply the exponents






26. 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.






27. 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






28. The whole # left over after division






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






30. 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)






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






32. 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






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






34. 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






35. 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






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






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






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






39. 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






40. 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






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






42. To solve a proportion - cross multiply






43. Volume of a Cylinder = pr^2h






44. 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






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






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






47. Part = Percent x Whole






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






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






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