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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. 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






2. 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






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






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. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






8. Volume of a Cylinder = pr^2h






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






11. 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






12. 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






13. 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






14. pr^2






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






16. Combine like terms






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






18. 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






19. The whole # left over after division






20. 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.






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






22. 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






23. Subtract the smallest from the largest and add 1






24. Part = Percent x Whole






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






26. 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






27. Factor out the perfect squares






28. 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






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






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






31. Add the exponents and keep the same base






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






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






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. 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






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






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






38. 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






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






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






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






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






43. 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






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






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






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






47. 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






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






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






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