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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. 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)






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






3. 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






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






5. 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






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






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






8. 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






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






10. 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






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






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






13. To solve a proportion - cross multiply






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






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






16. 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






17. 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)






18. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






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






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






25. 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






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






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






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






29. 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.






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






31. 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






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






33. 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






34. Volume of a Cylinder = pr^2h






35. 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






36. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






37. 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






38. 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






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






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






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. 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






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






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






45. 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






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






47. 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






48. 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






49. 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






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