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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. 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






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






3. 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






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






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






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






7. Multiply the exponents






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






9. Combine like terms






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






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






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






13. 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






14. 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






15. 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






16. To solve a proportion - cross multiply






17. pr^2






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






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






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






21. Factor out the perfect squares






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






23. 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






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






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






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






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. 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






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






30. 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






31. Part = Percent x Whole






32. 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






33. Volume of a Cylinder = pr^2h






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






35. Add the exponents and keep the same base






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






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






38. 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






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






40. 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






41. 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)






42. 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






43. 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






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






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






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






47. 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.






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






49. 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






50. 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