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






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






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






5. 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






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






7. Factor out the perfect squares






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






12. 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






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






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






15. 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






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






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






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






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






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






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






22. 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






23. 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






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






25. 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






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






27. To solve a proportion - cross multiply






28. 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






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






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






31. 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






32. Probability= Favorable Outcomes/Total Possible Outcomes






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






34. 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






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






36. Volume of a Cylinder = pr^2h






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






38. 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






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






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






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






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






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






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






45. 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






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






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






50. 2pr