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






2. 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






3. 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






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






5. 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






6. Subtract the smallest from the largest and add 1






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






8. Probability= Favorable Outcomes/Total Possible Outcomes






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






10. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






11. 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






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






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






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






15. 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






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






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






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






19. 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






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






21. 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






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






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






24. 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






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






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






27. 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.






28. Multiply the exponents






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






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






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






32. Part = Percent x Whole






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






34. Factor out the perfect squares






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






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






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






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






39. 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






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






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






42. The whole # left over after division






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






44. To solve a proportion - cross multiply






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






46. pr^2






47. 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






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. 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






50. 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)