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






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






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






4. 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






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. 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






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






8. 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






9. 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






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






11. 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






12. Add the exponents and keep the same base






13. 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






14. 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






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






16. 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






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






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






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






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






21. 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






22. 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






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






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






25. Part = Percent x Whole






26. 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






27. 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






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






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






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






31. Probability= Favorable Outcomes/Total Possible Outcomes






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






33. pr^2






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






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






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






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






38. 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






39. 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.






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






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






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. Volume of a Cylinder = pr^2h






45. 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)






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






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






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






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






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