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






2. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






3. Multiply the exponents






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






5. 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






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






7. 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






8. 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






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






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






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






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






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






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






17. To solve a proportion - cross multiply






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






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






20. 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






21. 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






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






23. 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






24. 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






25. 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






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






27. 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






28. 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






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






30. 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






31. 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






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






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






34. 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)






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






36. 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)






37. 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






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






39. Part = Percent x Whole






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






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






42. 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






43. 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






44. Factor out the perfect squares






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






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






47. pr^2






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






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






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