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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 of the x coordinates - average of the y coordinates)






2. 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






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






4. 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






5. The whole # left over after division






6. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






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






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. 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






10. 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






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






12. Volume of a Cylinder = pr^2h






13. 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






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






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






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






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






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






19. 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






20. 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)






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






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






23. pr^2






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






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. Subtract the smallest from the largest and add 1






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






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






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






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






32. Part = Percent x Whole






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






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






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






36. 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.






37. 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)






38. To solve a proportion - cross multiply






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






40. Combine like terms






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






42. Probability= Favorable Outcomes/Total Possible Outcomes






43. 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






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






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






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






47. 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






48. 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






49. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






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