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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. 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






2. 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






3. 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






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






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






6. 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






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






8. 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






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






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






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






12. Factor out the perfect squares






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






14. 2pr






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






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






17. 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






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






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






20. Volume of a Cylinder = pr^2h






21. 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






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






23. 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






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






25. 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






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






27. 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






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






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






30. 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






31. Probability= Favorable Outcomes/Total Possible Outcomes






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






33. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






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






35. 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






36. 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






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






38. 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






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






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






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






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






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






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






45. 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)






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






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






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






49. 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






50. 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