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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 divide fractions - invert the second one and multiply






3. 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






4. 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






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






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






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






8. 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






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






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






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






12. Volume of a Cylinder = pr^2h






13. 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






14. To solve a proportion - cross multiply






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






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






17. 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






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






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






20. 2pr






21. Combine like terms






22. 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






23. 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)






24. Part = Percent x Whole






25. 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)






26. 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






27. 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






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






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






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






31. Multiply the exponents






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






33. The whole # left over after division






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






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






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






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






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






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






40. 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






41. Subtract the smallest from the largest and add 1






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






43. 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






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






45. 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






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






47. 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






48. 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






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






50. 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