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






2. 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.






3. pr^2






4. Part = Percent x Whole






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






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






7. Combine like terms






8. 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






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






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






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






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






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






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






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






16. 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






17. 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)






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






19. 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






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






21. 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






22. 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






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






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






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






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






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






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






29. 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






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






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






32. 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






33. Add the exponents and keep the same base






34. The whole # left over after division






35. 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






36. 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






37. Factor out the perfect squares






38. 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






39. 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






40. 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






41. 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






42. 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






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






44. 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






45. Change in y/ change in x rise/run






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






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. 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






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






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