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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 20 minutes. 2 minutes extra for reading the instructions.
  • 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. 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






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






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






4. 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






5. 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






6. 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






7. 2pr






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






9. Combine like terms






10. 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.






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






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






13. 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






14. 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






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






16. Probability= Favorable Outcomes/Total Possible Outcomes






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






18. 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






19. 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






20. pr^2






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






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






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






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. 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






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






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






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






29. Factor out the perfect squares






30. 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






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






32. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






33. 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






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






35. 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






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. 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






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






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






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






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






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






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






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






45. Multiply the exponents






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






47. Subtract the smallest from the largest and add 1






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






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






50. 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