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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. 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






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






3. 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






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






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






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






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






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






9. 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






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






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






12. Add the exponents and keep the same base






13. 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)






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






15. To solve a proportion - cross multiply






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






17. The whole # left over after division






18. 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






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






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






21. 2pr






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






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






24. 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






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






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






27. 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






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






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






30. Probability= Favorable Outcomes/Total Possible Outcomes






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






32. pr^2






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






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






35. 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






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






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






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






39. 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






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






41. 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






42. 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






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






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






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






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






47. 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






48. 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






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






50. Factor out the perfect squares