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






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






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






5. Subtract the smallest from the largest and add 1






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






7. 2pr






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






9. 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






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






11. 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






12. 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.






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






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






15. 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






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






17. pr^2






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






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






20. Part = Percent x Whole






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






22. 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






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






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






25. 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






26. 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






27. 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






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






29. 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






30. To divide fractions - invert the second one and multiply






31. 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






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






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






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






35. 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






36. 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






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






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






39. 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






40. 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






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






42. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






43. Domain: all possible values of x for a function range: all possible outputs of a function






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






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






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






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






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






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






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