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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. Subtract the smallest from the largest and add 1






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






3. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






4. 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






5. 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






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






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






8. 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






9. 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






10. To solve a proportion - cross multiply






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






12. 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.






13. 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






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






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






16. 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






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






18. 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)






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






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






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






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






23. 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






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






25. Factor out the perfect squares






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






27. Add the exponents and keep the same base






28. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






31. 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






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






33. 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






34. 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






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






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






37. 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






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






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






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






41. 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






42. 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






43. Part = Percent x Whole






44. 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






45. 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






46. 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






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






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






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






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