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






2. 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






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






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






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






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






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






8. pr^2






9. 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






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






11. Multiply the exponents






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. 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






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






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






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






17. Subtract the smallest from the largest and add 1






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. 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






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






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






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






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






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






25. 2pr






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






27. Add the exponents and keep the same base






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






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






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. 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






32. 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






33. Volume of a Cylinder = pr^2h






34. 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






35. 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






36. 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






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






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






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






40. 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






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






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






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






44. 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






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






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






47. Combine like terms






48. 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






49. 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






50. Factor out the perfect squares