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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. Multiply the exponents






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






3. 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






4. 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






5. 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






6. Factor out the perfect squares






7. 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






8. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






13. 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






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






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






16. 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






17. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






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






19. Subtract the smallest from the largest and add 1






20. 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)






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






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






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






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






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






26. 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






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






28. 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






29. Part = Percent x Whole






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






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






32. 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






33. 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.






34. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






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






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






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






38. 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






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






40. Volume of a Cylinder = pr^2h






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






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






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






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






46. The whole # left over after division






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






48. 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






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. pr^2