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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. Combine like terms






2. 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






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






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






5. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






6. 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






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






8. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






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






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






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






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






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






14. 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






15. 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






16. 2pr






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






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






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






20. 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)






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






22. 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






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






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






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






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






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






29. 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






30. 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






31. 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






32. Probability= Favorable Outcomes/Total Possible Outcomes






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






34. 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






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






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






37. To solve a proportion - cross multiply






38. 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






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






40. 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






41. pr^2






42. 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






43. 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






44. 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.






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






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






47. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






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






49. Subtract the smallest from the largest and add 1






50. The whole # left over after division