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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. 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






2. 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






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






4. 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






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






6. 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)






7. 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






8. Multiply the exponents






9. 2pr






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






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






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






13. Factor out the perfect squares






14. 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






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






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






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






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






19. The whole # left over after division






20. Probability= Favorable Outcomes/Total Possible Outcomes






21. 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






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






23. 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)






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






25. 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.






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






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






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






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






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






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






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






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






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






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






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






37. 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






38. 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






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






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






41. 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






42. Combine like terms






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






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. 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






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






48. 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






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






50. 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