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






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. 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






4. 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






5. 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






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






7. Combine like terms






8. 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






9. 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






10. To solve a proportion - cross multiply






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






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






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






14. 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






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






16. 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)






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






18. 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






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






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






21. 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






22. Subtract the smallest from the largest and add 1






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






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






25. 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






26. 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






27. 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






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






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






30. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






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






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






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






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






35. Volume of a Cylinder = pr^2h






36. The whole # left over after division






37. 2pr






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






39. Add the exponents and keep the same base






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






41. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






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






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






44. 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






45. 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






46. 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






47. 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






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






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






50. 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)