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






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






3. 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






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






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






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






7. 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






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






9. 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






10. 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






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






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






13. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






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






16. 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






17. Multiply the exponents






18. 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






19. 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






20. 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






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






22. Factor out the perfect squares






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






24. 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






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






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






27. 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)






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






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






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






31. 2pr






32. 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






33. 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






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






35. 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






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






37. 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






38. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






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






40. 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






41. 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






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






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






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






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






46. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






47. Add the exponents and keep the same base






48. 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






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






50. 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