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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 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






2. 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






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






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






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






6. 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






7. 2pr






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






9. Factor out the perfect squares






10. 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






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






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






13. 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






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






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






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






17. 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






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






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






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






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






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






23. Multiply the exponents






24. The whole # left over after division






25. 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






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






27. 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






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






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






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






31. 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






32. Add the exponents and keep the same base






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






34. 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






35. 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






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






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






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






40. Volume of a Cylinder = pr^2h






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






42. 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)






43. To solve a proportion - cross multiply






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






45. 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






46. 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






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






48. Combine like terms






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






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