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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. 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






2. 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






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






4. 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






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






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






7. 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






8. 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)






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






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






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






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






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






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






15. 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






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






17. Part = Percent x Whole






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






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






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






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






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






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






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






25. To solve a proportion - cross multiply






26. Subtract the smallest from the largest and add 1






27. Add the exponents and keep the same base






28. 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






29. 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






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






31. 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






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






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






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






35. pr^2






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






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






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






39. 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






40. Volume of a Cylinder = pr^2h






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






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






44. 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






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






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






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






49. 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






50. 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