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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. 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






2. 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






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






4. 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






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






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






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






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






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






10. The whole # left over after division






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






12. 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






13. 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






14. Probability= Favorable Outcomes/Total Possible Outcomes






15. Volume of a Cylinder = pr^2h






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






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






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






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






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






21. 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






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






24. 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)






25. Combine like terms






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






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






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






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






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






31. 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






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






33. 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






34. 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






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






36. 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






37. 2pr






38. 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






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






40. 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






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






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






43. Subtract the smallest from the largest and add 1






44. 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






45. Multiply the exponents






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






47. 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






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






49. 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






50. Add the exponents and keep the same base