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






2. 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






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






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






5. 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






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






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






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






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






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






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






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






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






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






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






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






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






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






19. 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






20. Part = Percent x Whole






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






22. 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






23. 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






24. Add the exponents and keep the same base






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






26. 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






27. Subtract the smallest from the largest and add 1






28. Volume of a Cylinder = pr^2h






29. 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






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






31. 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






32. 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






33. pr^2






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






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






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






37. Factor out the perfect squares






38. 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






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






40. 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






41. 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






42. 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






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






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






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






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






47. 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






48. Multiply the exponents






49. 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






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