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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. 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






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






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






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






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






6. 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






7. 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






8. Multiply the exponents






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






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






11. 2pr






12. Factor out the perfect squares






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






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






15. 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






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






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






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






20. 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






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






22. pr^2






23. Part = Percent x Whole






24. The whole # left over after division






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






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






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






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






30. 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






31. 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






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






33. 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






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






35. 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






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






37. 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






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. 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






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






41. Add the exponents and keep the same base






42. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






43. 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






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






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






46. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






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. 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






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






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