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






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






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






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






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. 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






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






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






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






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






11. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






16. 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






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






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






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






20. Volume of a Cylinder = pr^2h






21. Part = Percent x Whole






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






23. 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






24. 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






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






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






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






28. 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






29. 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






30. 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






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






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






33. To solve a proportion - cross multiply






34. 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






35. Factor out the perfect squares






36. 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






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






38. 2pr






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






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






41. 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






42. 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






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






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






47. Subtract the smallest from the largest and add 1






48. 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






49. 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






50. Multiply the exponents