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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. 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






2. Add the exponents and keep the same base






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. 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






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






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






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






8. 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






9. Subtract the smallest from the largest and add 1






10. 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






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






12. Part = Percent x Whole






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






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






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






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






17. 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






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






19. 2pr






20. To solve a proportion - cross multiply






21. 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






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






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






24. 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






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






26. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






27. 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






28. 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






29. The whole # left over after division






30. 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






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






32. 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






33. Factor out the perfect squares






34. 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






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






36. 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






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






38. Probability= Favorable Outcomes/Total Possible Outcomes






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






40. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






42. 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






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






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






46. 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






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






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






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






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