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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. 2pr






2. 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






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






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






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






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






7. pr^2






8. 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






9. 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






10. 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






11. 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






12. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






15. 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






16. 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






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






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






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






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






21. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






22. 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)






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






24. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






25. 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






26. 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






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






28. Factor out the perfect squares






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






30. 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






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






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






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






34. To solve a proportion - cross multiply






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






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






37. 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






38. 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






39. Part = Percent x Whole






40. 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






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






42. 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






43. 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






44. 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






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






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






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






48. 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)






49. 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






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