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






2. 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.






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






4. 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






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






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






7. pr^2






8. 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






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






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






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






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






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






14. 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






15. 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






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






17. Multiply the exponents






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






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






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






21. Subtract the smallest from the largest and add 1






22. 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






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






24. 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






25. 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






26. 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






27. 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)






28. 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






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






30. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






31. 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






32. 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






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






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






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






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






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






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






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






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






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






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






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






44. Part = Percent x Whole






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






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






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






48. 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






49. 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






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