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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 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






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






3. To solve a proportion - cross multiply






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






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






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






7. 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






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






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






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






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






12. 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






13. 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






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






15. Multiply the exponents






16. 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






17. Add the exponents and keep the same base






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






19. 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






20. 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






21. 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






22. Factor out the perfect squares






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






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






25. 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






26. 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






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






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






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






30. Volume of a Cylinder = pr^2h






31. 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






32. 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.






33. 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






34. 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)






35. 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






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






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






38. 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






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






40. Part = Percent x Whole






41. The whole # left over after division






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






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






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






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






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






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






48. 2pr






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






50. 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