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






2. Part = Percent x Whole






3. Combine like terms






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






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






6. 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)






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






8. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






12. Subtract the smallest from the largest and add 1






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






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






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






16. 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






17. 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






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






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






20. 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






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






22. 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






23. 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






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






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






26. 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






27. 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)






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






29. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






30. Factor out the perfect squares






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






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






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






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






35. 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






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






37. Volume of a Cylinder = pr^2h






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






39. 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






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






41. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






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






43. 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






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






45. 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






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






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






48. 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






49. 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






50. 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