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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 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






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






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






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






5. The whole # left over after division






6. 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






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






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






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






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






11. Multiply the exponents






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






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






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






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






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






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






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






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






21. Volume of a Cylinder = pr^2h






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






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






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






25. 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






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






28. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






30. 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






31. 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






32. 2pr






33. Probability= Favorable Outcomes/Total Possible Outcomes






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






35. 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






36. 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)






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






38. 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






39. 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






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






41. 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






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






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






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






45. 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






46. 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






47. 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






48. To solve a proportion - cross multiply






49. 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






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