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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. pr^2






2. To solve a proportion - cross multiply






3. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






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






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






6. Add the exponents and keep the same base






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






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






9. Multiply the exponents






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






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






12. Part = Percent x Whole






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






14. 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






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






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






17. 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






18. 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






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






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






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. 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






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






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






25. Factor out the perfect squares






26. 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






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






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






30. 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






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






32. 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






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






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






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






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






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






39. 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






40. 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)






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






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






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






44. 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






45. 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)






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






47. 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






48. 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






49. Volume of a Cylinder = pr^2h






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