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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. 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.






3. 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






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






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






6. Subtract the smallest from the largest and add 1






7. 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






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






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






10. 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






11. 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






12. pr^2






13. Multiply the exponents






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






15. 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






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






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






18. Add the exponents and keep the same base






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






20. 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






21. Factor out the perfect squares






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






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






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






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






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






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






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






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






30. 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






31. 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






32. 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)






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






34. 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






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






36. 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






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






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






39. 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






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






41. 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






42. 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






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






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






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






46. 2pr






47. 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






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. 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






50. To solve a proportion - cross multiply