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






2. 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






3. 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






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






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






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






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






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






9. 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






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






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






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






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






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






15. Volume of a Cylinder = pr^2h






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






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






18. 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






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






20. 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






21. 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






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






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






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






26. 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






27. 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






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






29. Multiply the exponents






30. 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






31. 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






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






33. 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






34. pr^2






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






36. Factor out the perfect squares






37. Add the exponents and keep the same base






38. 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






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






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






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






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






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






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






46. 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






47. 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






48. 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)






49. 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






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







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