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






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






5. 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






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






7. To solve a proportion - cross multiply






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






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






10. 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






11. Part = Percent x Whole






12. 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






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






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






15. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






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






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






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






19. 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






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






21. Volume of a Cylinder = pr^2h






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






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






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






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






27. The whole # left over after division






28. pr^2






29. 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






30. 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






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






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






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






34. 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






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






36. 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






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






38. 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






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






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






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






42. 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






43. Multiply the exponents






44. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






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






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






47. 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






48. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






49. Add the exponents and keep the same base






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