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






2. 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






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






4. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






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






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






7. 2pr






8. 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






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






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






11. 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






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






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






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






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






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






17. 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






18. 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






19. 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






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






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






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






23. 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






24. pr^2






25. 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






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






27. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






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






29. Volume of a Cylinder = pr^2h






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






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






33. 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






34. 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






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






36. Combine like terms






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






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






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






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






41. 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






42. 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






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






44. 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






45. The whole # left over after division






46. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






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






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. 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






50. To solve a proportion - cross multiply