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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. 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






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






4. 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






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






6. 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






7. The whole # left over after division






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






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






10. 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






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






12. 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)






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






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






15. 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






16. 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






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






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






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






20. 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






21. Add the exponents and keep the same base






22. 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






23. 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






24. To solve a proportion - cross multiply






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






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






27. Multiply the exponents






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






29. Volume of a Cylinder = pr^2h






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






31. 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






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






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






34. 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






35. 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






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






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






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






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






40. 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






41. 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






42. 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






43. 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






44. 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






45. 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






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. 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






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






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






50. To multiply fractions - multiply the numerators and multiply the denominators