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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. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






2. 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






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






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






5. 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






6. 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.






7. 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






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






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






10. 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






11. 2pr






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






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






14. Part = Percent x Whole






15. Probability= Favorable Outcomes/Total Possible Outcomes






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






17. 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






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






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






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






21. 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






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






23. 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






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






25. 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






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






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






29. 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






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






31. 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)






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






33. Multiply the exponents






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






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






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. 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






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. Factor out the perfect squares






40. To solve a proportion - cross multiply






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






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






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






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






45. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






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. 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






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






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






50. 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