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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. 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






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






3. 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






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






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






6. Multiply the exponents






7. 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






8. 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






9. 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






10. 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






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






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






13. 2pr






14. 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






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






16. 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






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






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






19. 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






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






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






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






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






24. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






27. Volume of a Cylinder = pr^2h






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






29. Factor out the perfect squares






30. 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






31. 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






32. 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)






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






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






35. 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






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






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






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






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






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






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






42. 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






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






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






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






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






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






48. 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






49. 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






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