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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 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






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






3. 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






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






5. 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






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






7. 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






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






9. Multiply the exponents






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






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






12. 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






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






14. pr^2






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






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






17. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






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






19. 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






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






21. 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






22. 2pr






23. Add the exponents and keep the same base






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






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






26. The whole # left over after division






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






28. 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






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






30. 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






31. 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.






32. Combine like terms






33. 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






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






35. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






36. Volume of a Cylinder = pr^2h






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






38. 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






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






40. 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






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






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






43. 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






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






45. 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






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






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






48. 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






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






50. 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