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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 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






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






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






4. The whole # left over after division






5. 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






6. 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






7. 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)






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. 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






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






11. Probability= Favorable Outcomes/Total Possible Outcomes






12. 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






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






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






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






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






17. 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






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. To divide fractions - invert the second one and multiply






20. 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






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






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






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






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






25. To solve a proportion - cross multiply






26. 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






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






28. Volume of a Cylinder = pr^2h






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






30. 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






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






32. Factor out the perfect squares






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






34. 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






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






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






37. 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






38. 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






39. 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






40. 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






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






42. Add the exponents and keep the same base






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






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






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






46. 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






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






48. pr^2






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






50. 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