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






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






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. pr^2






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






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






7. The whole # left over after division






8. 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






9. 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






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






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 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






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






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






15. 2pr






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






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






18. 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






19. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






20. Part = Percent x Whole






21. Multiply the exponents






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






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






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






25. 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






26. Add the exponents and keep the same base






27. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






28. Subtract the smallest from the largest and add 1






29. Factor out the perfect squares






30. Volume of a Cylinder = pr^2h






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






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






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






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






35. 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






36. 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






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






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






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. 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






41. 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






42. 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






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






44. 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






45. 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






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






47. 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






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






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






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