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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. Part = Percent x Whole






2. 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)






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






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






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






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






7. 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






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






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






10. 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






11. Volume of a Cylinder = pr^2h






12. 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






13. 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






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






15. 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.






16. To solve a proportion - cross multiply






17. 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






18. 2pr






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






20. Probability= Favorable Outcomes/Total Possible Outcomes






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






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. 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






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






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






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






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






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






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






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






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






32. Combine like terms






33. 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






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






35. 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






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






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






38. 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






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






40. 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






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. Add the exponents and keep the same base






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






44. pr^2






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






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






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






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






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






50. 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