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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. 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)






2. 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






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






4. 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






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






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






7. 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






8. Multiply the exponents






9. 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






10. Add the exponents and keep the same base






11. To solve a proportion - cross multiply






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






13. 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






14. Probability= Favorable Outcomes/Total Possible Outcomes






15. 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






16. 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






17. pr^2






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






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






20. 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






21. Factor out the perfect squares






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






23. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






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






25. 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.






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






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






28. 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






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






30. 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






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






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






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






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






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






36. 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






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






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






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






40. 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






41. 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






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






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






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






45. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






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






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






48. 2pr






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






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