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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 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)






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






3. 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






4. 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






5. Subtract the smallest from the largest and add 1






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






7. 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






8. 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






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






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






11. 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






12. The whole # left over after division






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






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






15. 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






16. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






21. 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






22. 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






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






24. 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)






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






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






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






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






29. 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






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






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






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






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






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






35. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






36. 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






37. 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






38. 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






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






40. To solve a proportion - cross multiply






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






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. 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






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






45. Multiply the exponents






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






47. 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






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






49. 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






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







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