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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 combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






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






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






4. 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






5. Part = Percent x Whole






6. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






7. 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)






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






9. 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






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






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






12. The whole # left over after division






13. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






16. 2pr






17. 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






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






19. 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






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






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






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






23. 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






24. 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






25. 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






26. 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






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






28. 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






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






30. 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)






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






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






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






34. 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






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






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






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






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






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






40. 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






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






42. 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.






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






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






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






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






47. Volume of a Cylinder = pr^2h






48. Multiply the exponents






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






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