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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. 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






3. 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)






4. 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






5. 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






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






7. Factor out the perfect squares






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






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






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






11. 2pr






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






13. 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






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






15. 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






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






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






18. 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






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






20. To solve a proportion - cross multiply






21. pr^2






22. 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






23. 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






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






25. To find the reciprocal of a fraction switch the numerator and the denominator






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






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






28. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






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. 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






31. 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






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






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






34. 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)






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






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






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






38. 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






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






40. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






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






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






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






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






45. Add the exponents and keep the same base






46. Combine like terms






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






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






49. Volume of a Cylinder = pr^2h






50. 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