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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. 2pr






2. 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






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






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






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






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






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






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






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






10. Combine like terms






11. 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






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






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






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






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






16. 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






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






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






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






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. 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






23. 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






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






25. 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)






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






27. 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






28. Probability= Favorable Outcomes/Total Possible Outcomes






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






30. Factor out the perfect squares






31. Volume of a Cylinder = pr^2h






32. 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






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






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






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






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






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






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






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






41. 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






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






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






44. 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






45. 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






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






47. 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






48. 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






49. 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






50. The whole # left over after division