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






2. 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






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






4. 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






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






6. 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






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






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






10. 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






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. Add the exponents and keep the same base






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






14. Subtract the smallest from the largest and add 1






15. Factor out the perfect squares






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






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






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






19. 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






20. Combine like terms






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






22. 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






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






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






25. pr^2






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






27. 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






28. 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






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






30. Volume of a Cylinder = pr^2h






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






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






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






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






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






36. 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






37. 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)






38. 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






39. 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






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






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






42. 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






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






44. 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






45. Multiply the exponents






46. 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






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






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






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






50. 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