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






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






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






4. 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






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






6. 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






7. 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






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






9. 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






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






11. 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






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






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






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






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






16. To solve a proportion - cross multiply






17. 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






18. Subtract the smallest from the largest and add 1






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






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






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






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






23. 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






24. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






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






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






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. 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






33. Factor out the perfect squares






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






35. Combine like terms






36. The whole # left over after division






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






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






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






40. 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






41. Add the exponents and keep the same base






42. 2pr






43. 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






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






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






46. 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






47. Volume of a Cylinder = pr^2h






48. 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)






49. Multiply the exponents






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