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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. Change in y/ change in x rise/run






2. Add the exponents and keep the same base






3. 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)






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






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






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






7. Factor out the perfect squares






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






9. 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






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






12. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






15. 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






16. 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






17. 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






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






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






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. 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






22. 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






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






24. 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






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






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






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






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






29. The whole # left over after division






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






31. 2pr






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






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






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






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






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






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






38. 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






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






40. 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






41. 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






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






43. 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






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






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






46. Subtract the smallest from the largest and add 1






47. 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






48. 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






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






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