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






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






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






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






5. Multiply the exponents






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






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. 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)






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






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. pr^2






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






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






14. 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






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






16. 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






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






18. 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






19. 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.






20. To solve a proportion - cross multiply






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






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






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






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






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






26. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






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






28. 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






29. 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






30. 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






31. 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






32. 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






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






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






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






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






37. The whole # left over after division






38. 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)






39. 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






40. 2pr






41. 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






42. 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






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






44. 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






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






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






47. Subtract the smallest from the largest and add 1






48. Probability= Favorable Outcomes/Total Possible Outcomes






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






50. Factor out the perfect squares