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






2. pr^2






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






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






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






6. 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






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






8. 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






9. 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






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






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






12. To solve a proportion - cross multiply






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






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






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






16. Combine like terms






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






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






19. 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






20. Subtract the smallest from the largest and add 1






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






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






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






24. 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






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






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






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






28. 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






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






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






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






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






33. 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






34. Multiply the exponents






35. 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






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






37. 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






38. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






39. 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






40. 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)






41. 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






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






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






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






45. 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






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






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






48. 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)






49. 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






50. 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