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






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






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






4. 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.






5. The whole # left over after division






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






7. 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






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






9. 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






10. 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






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






12. To solve a proportion - cross multiply






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






14. 2pr






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






16. 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






17. pr^2






18. 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






19. 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)






20. 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






21. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






22. 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






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






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






25. 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






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






27. 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






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






29. Subtract the smallest from the largest and add 1






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






31. 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






32. 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






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






34. Volume of a Cylinder = pr^2h






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






36. 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






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






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






39. Add the exponents and keep the same base






40. 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






41. 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






42. 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






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






45. 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






46. 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






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






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






49. 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






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