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






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






3. Multiply the exponents






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






5. 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






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






7. To solve a proportion - cross multiply






8. 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






9. pr^2






10. 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






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






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






14. 2pr






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






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






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






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






19. 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






20. 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






21. Subtract the smallest from the largest and add 1






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






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






24. Factor out the perfect squares






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






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






27. 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)






28. 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






29. Volume of a Cylinder = pr^2h






30. 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






31. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






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






33. 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






34. 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






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






36. 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






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






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. Combine like terms






40. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






41. Part = Percent x Whole






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






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






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






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






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






47. 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






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






49. 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






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