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






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






3. The whole # left over after division






4. 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






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. To divide fractions - invert the second one and multiply






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






8. 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






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






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






11. 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






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






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






14. 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






15. 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






16. 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.






17. To solve a proportion - cross multiply






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






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. 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






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






22. 2pr






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






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






25. 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






26. 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






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






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






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






30. Combine like terms






31. pr^2






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






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






34. 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






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






36. 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






37. 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






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






39. 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)






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






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. 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






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






44. 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






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






46. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






47. 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






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






49. Factor out the perfect squares






50. Probability= Favorable Outcomes/Total Possible Outcomes