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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. 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)






2. Combine like terms






3. 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






4. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






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






6. 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






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






8. Multiply the exponents






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






10. Subtract the smallest from the largest and add 1






11. To solve a proportion - cross multiply






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






13. 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






14. 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






15. 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






16. Probability= Favorable Outcomes/Total Possible Outcomes






17. 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






18. 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






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






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






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






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






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






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






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






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






27. 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






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






29. 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






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






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






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. 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






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






35. Factor out the perfect squares






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






37. 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






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






39. 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






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






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






42. 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






43. pr^2






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






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






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






47. 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






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






49. 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






50. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height