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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. 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)






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






3. 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






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






6. 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






7. 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






8. 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






9. Combine like terms






10. 2pr






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






12. 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






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






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






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






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






17. 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






18. The whole # left over after division






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






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






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






22. Multiply the exponents






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






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






25. 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






26. Subtract the smallest from the largest and add 1






27. 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






28. 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






29. 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






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






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






32. 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






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






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






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






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






37. 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






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






39. Part = Percent x Whole






40. 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






41. pr^2






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






43. 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






44. 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






45. To solve a proportion - cross multiply






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






47. 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






48. 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






49. 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






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