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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. 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






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






4. 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






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






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






7. Volume of a Cylinder = pr^2h






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






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






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






11. 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






12. pr^2






13. 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






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






15. 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






16. 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






17. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






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






19. 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






20. 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






21. 2pr






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






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






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






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






26. To solve a proportion - cross multiply






27. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






30. 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






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






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






33. 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






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






35. 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






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






37. 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.






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






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. Subtract the smallest from the largest and add 1






41. Part = Percent x Whole






42. 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






43. 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






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






45. 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






46. 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)






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






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






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






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