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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 30 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. 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






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






3. 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






4. 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






5. 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






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






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






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






9. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






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






11. 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.






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






13. Volume of a Cylinder = pr^2h






14. 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






15. To solve a proportion - cross multiply






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






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






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






19. 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)






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






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






22. 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






23. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






28. Combine like terms






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






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






31. Subtract the smallest from the largest and add 1






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






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






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






35. 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






36. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






37. Add the exponents and keep the same base






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






39. 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






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






41. 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






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






43. Part = Percent x Whole






44. 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






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






46. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






47. 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






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






49. 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






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