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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 Cylinder = pr^2h






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






3. Part = Percent x Whole






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






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






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






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






8. 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






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






10. 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






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






12. To solve a proportion - cross multiply






13. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






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






19. 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






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






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






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. Add the exponents and keep the same base






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






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






26. 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






27. 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






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






29. 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.






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






31. 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






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






33. 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






34. 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)






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






36. 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






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






38. 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






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






40. 2pr






41. 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






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






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






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






45. 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






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






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






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. 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)






50. 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