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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. Probability= Favorable Outcomes/Total Possible Outcomes






2. 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






3. 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.






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. 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






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






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






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






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






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






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






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






13. Part = Percent x Whole






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






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






16. 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






17. To solve a proportion - cross multiply






18. 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






19. 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






20. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






21. Volume of a Cylinder = pr^2h






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






23. 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






24. 2pr






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






26. Add the exponents and keep the same base






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






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






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






30. Multiply the exponents






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






32. 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






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






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






35. 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






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






37. 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)






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. 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






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






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






42. 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






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






44. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






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






46. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






48. Subtract the smallest from the largest and add 1






49. 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






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