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






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






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






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






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






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






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






8. 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






9. Factor out the perfect squares






10. 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






11. 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






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






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






14. 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.






15. Probability= Favorable Outcomes/Total Possible Outcomes






16. 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






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






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






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






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






22. Subtract the smallest from the largest and add 1






23. Part = Percent x Whole






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






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






26. 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)






27. 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






28. 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






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






30. 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






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






32. The whole # left over after division






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






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






35. Add the exponents and keep the same base






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






37. Multiply the exponents






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






39. pr^2






40. 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






41. Combine like terms






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






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






44. 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






45. 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






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






47. 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)






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






49. 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






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