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






2. 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)






3. pr^2






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






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






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






7. 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






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






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






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






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






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






15. 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






16. Combine like terms






17. Part = Percent x Whole






18. 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






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






20. 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






21. Factor out the perfect squares






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






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






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






25. 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






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






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






28. 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






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






30. Probability= Favorable Outcomes/Total Possible Outcomes






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






32. 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






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






34. 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






35. Multiply the exponents






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






37. 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)






38. 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






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






40. 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






41. To solve a proportion - cross multiply






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






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






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






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






46. 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






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






48. 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






49. Subtract the smallest from the largest and add 1






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