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






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






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






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






5. 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






6. 2pr






7. 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






8. 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






9. 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






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






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






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






14. Add the exponents and keep the same base






15. 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






16. 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






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






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






19. Multiply the exponents






20. The whole # left over after division






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






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






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






24. 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






25. 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






26. pr^2






27. 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






28. 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






29. 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






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






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






32. 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






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






34. Subtract the smallest from the largest and add 1






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






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






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






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






39. Part = Percent x Whole






40. Volume of a Cylinder = pr^2h






41. 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






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






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






44. 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






45. 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






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






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






48. 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)






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






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






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