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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. 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. 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






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






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






5. The whole # left over after division






6. 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






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






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






9. 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






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






11. pr^2






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






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






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






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






16. Combine like terms






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






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






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






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






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






22. 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






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






24. 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






25. Volume of a Cylinder = pr^2h






26. 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






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. 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






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






30. 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.






31. 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






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






33. 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






34. 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






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






36. 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






37. 2pr






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






39. 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






40. 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






41. Factor out the perfect squares






42. 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






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






44. 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






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






46. 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






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






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






49. 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






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