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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 whole # left over after division






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






3. Part = Percent x Whole






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






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






6. 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






7. 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






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






9. Factor out the perfect squares






10. 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






11. Probability= Favorable Outcomes/Total Possible Outcomes






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






13. 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






14. 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






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






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






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






18. 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






19. 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






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






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






22. 2pr






23. 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






24. 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






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






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






27. 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






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






29. 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)






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






31. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






32. 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






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






34. 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






35. 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






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






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






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






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






40. 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)






41. 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






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






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






44. Volume of a Cylinder = pr^2h






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






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






47. To solve a proportion - cross multiply






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






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






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