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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. 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






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






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






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






5. 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






6. To solve a proportion - cross multiply






7. Combine like terms






8. Part = Percent x Whole






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






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






11. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






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






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






14. 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)






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






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






17. 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






18. 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






19. 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






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






21. Add the exponents and keep the same base






22. 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






23. 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.






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






26. 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






27. 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






28. The whole # left over after division






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






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






31. 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






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






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






34. 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






35. 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






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






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






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






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






40. 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






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






42. Multiply the exponents






43. 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






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






45. 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






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






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






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. Volume of a Cylinder = pr^2h






50. 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