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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 20 minutes. 2 minutes extra for reading the instructions.
  • 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. 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






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






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






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






5. 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






6. 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






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






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






9. 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






10. Probability= Favorable Outcomes/Total Possible Outcomes






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






12. 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






13. 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






14. 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






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. 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






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






18. 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






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






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






21. 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






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






23. Part = Percent x Whole






24. pr^2






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






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






27. 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)






28. Add the exponents and keep the same base






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






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






31. 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






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






33. 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






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






35. 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






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






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






38. 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






39. 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






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






41. 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)






42. Multiply the exponents






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






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






45. Combine like terms






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






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






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






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






50. Factor out the perfect squares