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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. Change in y/ change in x rise/run






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






3. 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






4. 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






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






6. 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)






7. 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






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






9. 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






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






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






12. 2pr






13. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






14. 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






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






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






17. Volume of a Cylinder = pr^2h






18. 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






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. To solve a proportion - cross multiply






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






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






23. 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






24. 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






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






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






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






28. 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






29. 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






30. Combine like terms






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






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






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






34. 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






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






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






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






38. 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






39. 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






40. 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






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






42. 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






43. 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.






44. 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)






45. Add the exponents and keep the same base






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






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






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






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






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