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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 Cylinder = pr^2h






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






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






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






5. Subtract the smallest from the largest and add 1






6. 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






7. 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)






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






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






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






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






12. 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






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






14. Part = Percent x Whole






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






16. 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






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






19. Add the exponents and keep the same base






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






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






22. 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






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






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






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






26. 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






27. pr^2






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






29. 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






30. 2pr






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






32. 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)






33. 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






34. 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






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






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






37. To solve a proportion - cross multiply






38. Multiply the exponents






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






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






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






42. Probability= Favorable Outcomes/Total Possible Outcomes






43. 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






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






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






46. 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






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






48. 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.






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






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