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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. 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






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. 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






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






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






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. 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






8. 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






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






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






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






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






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






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






16. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






17. 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






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






19. 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






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






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






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






23. 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






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






25. 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






26. Combine like terms






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






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






29. 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






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






31. 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






32. pr^2






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






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






35. 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






36. 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






37. 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






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






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






40. 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






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






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






43. 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






44. To solve a proportion - cross multiply






45. Factor out the perfect squares






46. Subtract the smallest from the largest and add 1






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






48. Probability= Favorable Outcomes/Total Possible Outcomes






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






50. 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