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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. 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






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. Add the exponents and keep the same base






5. 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






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






7. 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






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






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






10. 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






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






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






13. 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






14. 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






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






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






17. 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






18. 2pr






19. 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.






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






21. 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






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






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






24. pr^2






25. 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






26. 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






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






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






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






30. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






31. 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






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






33. Part = Percent x Whole






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






35. 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






36. Factor out the perfect squares






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






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






39. 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






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






41. Volume of a Cylinder = pr^2h






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






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






44. 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






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






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






47. 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






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






49. Combine like terms






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