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






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






4. 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






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






6. 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






7. 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






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






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






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






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






12. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






16. 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






17. 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






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






19. 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






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






21. Part = Percent x Whole






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






23. 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






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






25. 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)






26. Subtract the smallest from the largest and add 1






27. 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






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






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






30. To solve a proportion - cross multiply






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






32. 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






33. 2pr






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






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






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. Factor out the perfect squares






38. 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






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






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






41. 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






42. 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






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






44. Combine like terms






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






47. 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






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






49. 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






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