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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. The whole # left over after division






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






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






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






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






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






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






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






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






11. Part = Percent x Whole






12. 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






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






14. 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






15. 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






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






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






18. 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






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






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






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






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






23. 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






24. 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)






25. 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






26. 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






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. 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






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






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






31. 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






32. Combine like terms






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






34. 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






35. Subtract the smallest from the largest and add 1






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






37. 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






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






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






40. 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






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






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






43. To solve a proportion - cross multiply






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






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. 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






47. 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






48. 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






49. 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






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