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






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






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






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






5. 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)






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






7. 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






8. The whole # left over after division






9. 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






10. 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






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






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






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






14. 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






15. To solve a proportion - cross multiply






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






17. 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






18. 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






19. 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






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






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






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






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






24. Combine like terms






25. 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






26. 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






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






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






29. 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






30. 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






31. 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






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






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






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






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






37. Factor out the perfect squares






38. pr^2






39. 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






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






41. 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






42. Subtract the smallest from the largest and add 1






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






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






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






46. Part = Percent x Whole






47. Volume of a Cylinder = pr^2h






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






49. 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






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