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






2. pr^2






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






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






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






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






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






8. 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






9. 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






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






11. 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)






12. Multiply the exponents






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






14. 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






15. 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






16. 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






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






18. To solve a proportion - cross multiply






19. 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






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






21. 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






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






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






26. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






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






29. 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






30. Combine like terms






31. 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






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






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






34. Add the exponents and keep the same base






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






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






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






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






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






40. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






41. 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






42. Volume of a Cylinder = pr^2h






43. 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






44. The whole # left over after division






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






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






48. 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






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






50. 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