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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. 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






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






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






4. Volume of a Cylinder = pr^2h






5. Add the exponents and keep the same base






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






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






8. 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






9. To solve a proportion - cross multiply






10. 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






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






13. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






14. Combine like terms






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






16. 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






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






18. 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






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






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






21. 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






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. Change in y/ change in x rise/run






24. 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






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






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






27. Probability= Favorable Outcomes/Total Possible Outcomes






28. pr^2






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






30. 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






31. 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






32. 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






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






34. 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






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






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






37. 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






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






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






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






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






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






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






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






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. 2pr






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






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






49. 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






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