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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. 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






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






4. 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






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






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






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






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






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






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






12. Subtract the smallest from the largest and add 1






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






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






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






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






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






18. 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






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






20. 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






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






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






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






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






25. 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






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






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






28. 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






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






30. 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






31. 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






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






33. 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






34. 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.






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






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






37. 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






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






39. The whole # left over after division






40. 2pr






41. Multiply the exponents






42. 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






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






44. Volume of a Cylinder = pr^2h






45. pr^2






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






47. 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






48. 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






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






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