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






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






3. 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






4. Volume of a Cylinder = pr^2h






5. Multiply the exponents






6. 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






7. 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






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






9. pr^2






10. 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






11. 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






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






13. Add the exponents and keep the same base






14. 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






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






16. 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






17. 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)






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






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 find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






21. 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






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






23. To solve a proportion - cross multiply






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






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






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






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






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






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






31. 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






32. 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






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






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






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






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






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






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






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






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






41. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






42. 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






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






44. 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






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






46. 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






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






48. 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






49. Probability= Favorable Outcomes/Total Possible Outcomes






50. 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