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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 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. Volume of a Cylinder = pr^2h






2. 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






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






4. 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






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






6. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






8. 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






9. 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






10. 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)






11. 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






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






13. To solve a proportion - cross multiply






14. Part = Percent x Whole






15. 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






16. Multiply the exponents






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






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






20. 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






21. 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






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






23. Combine like terms






24. 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






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






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






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






28. 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






29. 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






30. 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






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






32. 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






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






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






35. 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)






36. 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






37. Add the exponents and keep the same base






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






39. 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






40. Sum=(Average) x (Number of Terms)






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






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






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






44. 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






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






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






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






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






49. 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






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






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