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






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






3. Combine like terms






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






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






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






7. Part = Percent x Whole






8. 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)






9. 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






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






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






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






13. 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






14. Subtract the smallest from the largest and add 1






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






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






17. To solve a proportion - cross multiply






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






20. The whole # left over after division






21. 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






22. Volume of a Cylinder = pr^2h






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. Factor out the perfect squares






25. pr^2






26. 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






27. 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






28. 2pr






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






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






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






32. 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






33. 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






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






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






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






37. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






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






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. Change in y/ change in x rise/run






42. Add the exponents and keep the same base






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






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






45. 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






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






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






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






49. 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






50. 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.