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SAT Math: Concepts And Tricks

Subjects : sat, math
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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 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

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

3. Combine like terms

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

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

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

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

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

9. 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

10. 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.

11. 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

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

13. Probability= Favorable Outcomes/Total Possible Outcomes

14. 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

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

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

17. 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

18. Subtract the smallest from the largest and add 1

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

20. 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

21. 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

22. 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

23. 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

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

25. 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)

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

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

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

29. 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

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

31. Multiply the exponents

32. Volume of a Cylinder = pr^2h

33. 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

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

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

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

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

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

39. 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

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

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

42. 2pr

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

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

45. pr^2

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

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

48. 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

49. 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

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