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






2. 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






3. pr^2






4. Multiply the exponents






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






6. Add the exponents and keep the same base






7. Factor out the perfect squares






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






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






10. 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






11. 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






12. 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






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






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






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






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






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






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






20. 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






21. Volume of a Cylinder = pr^2h






22. 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






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






24. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






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






27. 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






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






29. 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






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






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






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






33. 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






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






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






36. 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






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






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






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






40. To solve a proportion - cross multiply






41. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






45. 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.






46. 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






47. Subtract the smallest from the largest and add 1






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






49. Part = Percent x Whole






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