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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. 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






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






3. 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






4. 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






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






6. 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






7. Probability= Favorable Outcomes/Total Possible Outcomes






8. Subtract the smallest from the largest and add 1






9. 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






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






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






12. Multiply the exponents






13. 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.






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






15. 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






16. 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






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






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






19. 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)






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






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






22. 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






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






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






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






27. 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






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






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






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






31. 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






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






33. 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






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






35. 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






36. 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






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






38. 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






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






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






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






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






44. 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






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






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






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






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






49. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






50. Part = Percent x Whole