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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. 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






2. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






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






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






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






6. Add the exponents and keep the same base






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






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






9. 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






10. 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






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






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






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






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






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






16. 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






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






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






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






20. 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






21. 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






22. 2pr






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






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






26. 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






27. 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






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






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






30. 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






31. 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






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






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






34. Subtract the smallest from the largest and add 1






35. pr^2






36. 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






37. 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






38. Volume of a Cylinder = pr^2h






39. 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.






40. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






41. 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






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






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






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






45. 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






46. 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






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






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