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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. 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






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






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






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






5. Subtract the smallest from the largest and add 1






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






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






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






9. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






10. 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






11. 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






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






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






14. 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






15. Factor out the perfect squares






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






17. Multiply the exponents






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






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






20. 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






21. 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






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






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






25. 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






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






27. 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






28. 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






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






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






31. 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






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






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






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. 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






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






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






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






40. 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






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






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






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






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






45. 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






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






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






48. Probability= Favorable Outcomes/Total Possible Outcomes






49. Part = Percent x Whole






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