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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 30 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. Combine like terms






2. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






3. 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






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






5. pr^2






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






7. 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






8. 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






9. 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






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






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






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






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






14. 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






15. 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






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






17. 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






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






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






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






21. 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






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






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






24. 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






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






26. The whole # left over after division






27. 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






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






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






30. 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.






31. Add the exponents and keep the same base






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






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






34. Factor out the perfect squares






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






36. 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






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






38. 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






39. Probability= Favorable Outcomes/Total Possible Outcomes






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






41. 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






42. Multiply the exponents






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






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






45. 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






46. 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






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






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






49. 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






50. 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