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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. 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






2. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






4. 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






5. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






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






7. Multiply the exponents






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






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






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






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






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






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






14. 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






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






16. 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.






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






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. To divide fractions - invert the second one and multiply






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






21. 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






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






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






24. Combine like terms






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






26. 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






27. Part = Percent x Whole






28. 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






29. 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






30. 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






31. 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






32. Probability= Favorable Outcomes/Total Possible Outcomes






33. 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






34. 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






35. 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






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






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






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






39. 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






40. 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






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






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






43. 2pr






44. 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






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






46. 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






47. Volume of a Cylinder = pr^2h






48. 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






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






50. The whole # left over after division