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






2. 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






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






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






5. For all right triangles: a^2+b^2=c^2






6. 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






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






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






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






10. Volume of a Cylinder = pr^2h






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






12. pr^2






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






14. 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)






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






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






17. 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)






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






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






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. 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






22. 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






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






24. 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






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






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






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






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






30. The whole # left over after division






31. 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






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






33. 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






34. Factor out the perfect squares






35. 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






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






37. 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






38. 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






39. 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






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






41. 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






42. 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






43. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






44. Subtract the smallest from the largest and add 1






45. Part = Percent x Whole






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 divide fractions - invert the second one and multiply






48. Add the exponents and keep the same base






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






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