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






2. To solve a proportion - cross multiply






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






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






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






6. 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






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






8. 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






9. Combine like terms






10. 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






11. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






12. 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






13. 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






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






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






16. 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






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






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






19. The whole # left over after division






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






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






22. 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






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. Factor out the perfect squares






25. 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






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. 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






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






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






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






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






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






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






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






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






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






38. Add the exponents and keep the same base






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






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






41. 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






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






43. 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






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






45. 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






46. 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)






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






48. 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






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






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