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






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






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






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






5. Probability= Favorable Outcomes/Total Possible Outcomes






6. 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)






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






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






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






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






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






12. 2pr






13. The whole # left over after division






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






15. 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






16. pr^2






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






18. 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






19. Combine like terms






20. 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






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






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






23. 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)






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






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






26. 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






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






28. Add the exponents and keep the same base






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






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






31. 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






32. Factor out the perfect squares






33. 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






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






35. 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






36. 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.






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






38. 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






39. 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






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






41. 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






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






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






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






46. 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






47. 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






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






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






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