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






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






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






4. 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)






5. 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)






6. 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






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






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






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






10. 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






11. 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






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






13. 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






14. 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.






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






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






17. Volume of a Cylinder = pr^2h






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






19. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






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






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






22. 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






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






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






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






26. 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






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






28. To solve a proportion - cross multiply






29. Part = Percent x Whole






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






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






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






33. 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






34. 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






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






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






37. 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






38. Subtract the smallest from the largest and add 1






39. Multiply the exponents






40. 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






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






42. 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






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






44. Add the exponents and keep the same base






45. 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






46. Factor out the perfect squares






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






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






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






50. 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