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






2. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






3. The whole # left over after division






4. 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






5. 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






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






7. Volume of a Cylinder = pr^2h






8. 2pr






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






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






11. 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






12. 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






13. 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






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






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






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






17. 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






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






19. Factor out the perfect squares






20. 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






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






22. 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






23. 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






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






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






26. 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






27. 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






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






29. Part = Percent x Whole






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






31. 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






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






33. 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






34. 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






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






36. 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)






37. 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)






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






39. Multiply the exponents






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






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






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






43. 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






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






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






46. Combine like terms






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






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






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






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