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






2. 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






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






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






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






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






7. 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






8. Probability= Favorable Outcomes/Total Possible Outcomes






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






11. To solve a proportion - cross multiply






12. 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






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






14. 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)






15. 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)






16. 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






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






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. 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






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






21. 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






22. Combine like terms






23. 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






24. 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






25. 2pr






26. 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






27. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






28. Part = Percent x Whole






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






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






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






32. Factor out the perfect squares






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






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






35. 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






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






37. The whole # left over after division






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






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






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






41. 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






42. 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






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






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






45. 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






46. 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






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






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






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






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