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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. 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






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






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






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






5. 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






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






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






8. 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.






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






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






11. 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






12. pr^2






13. To solve a proportion - cross multiply






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






15. 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






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






17. 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






18. 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






19. 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






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






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






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






25. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






30. 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






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






32. 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






33. 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






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






35. 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






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






37. 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






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






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






40. 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






41. 2pr






42. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






43. 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






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






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






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






47. The whole # left over after division






48. 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






49. Part = Percent x Whole






50. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






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