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






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






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






4. Add the exponents and keep the same base






5. The whole # left over after division






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






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






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






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






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






11. 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






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






14. 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






15. 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)






16. 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






17. 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






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






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






20. 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.






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






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






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






24. 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






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






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






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






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






29. Multiply the exponents






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






31. 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






32. 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






33. Subtract the smallest from the largest and add 1






34. Probability= Favorable Outcomes/Total Possible Outcomes






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






36. 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






37. 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






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






39. Factor out the perfect squares






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






41. 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






42. Volume of a Cylinder = pr^2h






43. 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






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






45. 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






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






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






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






49. Part = Percent x Whole






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