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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 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






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






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. 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






5. 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






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






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






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






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






10. 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






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






12. 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






13. Factor out the perfect squares






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






15. The whole # left over after division






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






17. Part = Percent x Whole






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






19. 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






20. 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






21. Probability= Favorable Outcomes/Total Possible Outcomes






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






23. 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






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






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






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






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






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






29. To solve a proportion - cross multiply






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






31. 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






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






33. Combine like terms






34. 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






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






36. 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






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






38. 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






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






41. Multiply the exponents






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






44. 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






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






46. 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






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






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






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






50. Subtract the smallest from the largest and add 1