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






2. 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






3. 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






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






5. 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






6. Volume of a Cylinder = pr^2h






7. 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






8. 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






9. 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






10. Factor out the perfect squares






11. 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






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






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






14. 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






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






16. Multiply the exponents






17. 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)






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






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






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






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






22. 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.






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






24. 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






25. To solve a proportion - cross multiply






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






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






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






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






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






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






32. 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






33. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






38. 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






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






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






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






43. Subtract the smallest from the largest and add 1






44. The whole # left over after division






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






46. pr^2






47. 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






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






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






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