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






2. 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






3. 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)






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






5. 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






6. 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






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






8. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






9. Multiply the exponents






10. Combine like terms






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






12. 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






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






14. 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






15. 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






16. 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






17. 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






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






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






20. To solve a proportion - cross multiply






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






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






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






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






26. pr^2






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






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






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






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






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






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






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






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






35. 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.






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






37. The whole # left over after division






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. 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






40. 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






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






42. 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






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






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






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






46. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






50. Factor out the perfect squares