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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 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






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






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






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






5. 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






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






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






9. Add the exponents and keep the same base






10. Volume of a Cylinder = pr^2h






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






12. 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






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






14. 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






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






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






17. Combine like terms






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






19. The whole # left over after division






20. 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






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






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






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






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






25. 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






26. Subtract the smallest from the largest and add 1






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






28. 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






29. 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)






30. 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






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






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






33. 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






34. 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






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






36. 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






37. To solve a proportion - cross multiply






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






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






40. 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






41. 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






42. 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






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






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






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. 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






47. 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






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






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






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