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






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






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






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. 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






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






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






8. 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






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






10. 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






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






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






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






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






15. 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






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






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. 2pr






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






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






21. 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






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






23. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






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






25. 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






26. 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






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






28. 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






29. 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






30. Factor out the perfect squares






31. 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






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






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






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






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. To divide fractions - invert the second one and multiply






37. Multiply the exponents






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






39. 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






40. Volume of a Cylinder = pr^2h






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






42. 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






43. 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






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






45. Subtract the smallest from the largest and add 1






46. To solve a proportion - cross multiply






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






48. 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)






49. The whole # left over after division






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