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






2. 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






3. 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






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






5. 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)






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






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






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






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






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






12. 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






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






14. 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






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






16. 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






17. 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






18. 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






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






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






21. Combine like terms






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






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






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






25. Volume of a Cylinder = pr^2h






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






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






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






29. 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






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






31. 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






32. 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)






33. 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






34. Multiply the exponents






35. 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






36. 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






37. 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






38. 2pr






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






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






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






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






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






44. 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






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






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. 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






49. 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






50. 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