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






2. To solve a proportion - cross multiply






3. 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






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. 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






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






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. 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






9. 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






10. Combine like terms






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






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






13. 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






14. 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






15. 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






16. 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






17. 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






18. 2pr






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






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






21. 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






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






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






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






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






26. 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






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






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






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






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






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






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






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






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






35. 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






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






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






38. Multiply the exponents






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






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






41. 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






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






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






44. Part = Percent x Whole






45. To multiply fractions - multiply the numerators and multiply the denominators






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






47. 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)






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. Probability= Favorable Outcomes/Total Possible Outcomes






50. 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