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






2. 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






3. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






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






5. The whole # left over after division






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






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






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






9. 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






10. 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






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






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






13. 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






14. 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






15. 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






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






17. 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






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






20. 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






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






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






24. Combine like terms






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






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






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






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






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






30. 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






31. 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






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






33. 2pr






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. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






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






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






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






39. 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)






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






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






42. Add the exponents and keep the same base






43. 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






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






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






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






47. Probability= Favorable Outcomes/Total Possible Outcomes






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






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. 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