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






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






3. 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






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






5. 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






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






7. 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)






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






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






10. 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






11. 2pr






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






13. 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)






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






15. 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






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. 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






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






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






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






21. Part = Percent x Whole






22. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






25. pr^2






26. 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






27. To solve a proportion - cross multiply






28. 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






29. 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






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






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






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






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






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






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






36. 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






37. 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






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






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






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






41. 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






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






43. 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






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






45. 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






46. 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






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






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






49. 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






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