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






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






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






4. 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






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






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






7. Add the exponents and keep the same base






8. Multiply the exponents






9. Probability= Favorable Outcomes/Total Possible Outcomes






10. 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






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






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






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






14. 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






15. 2pr






16. Factor out the perfect squares






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






18. 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






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






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






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






22. To solve a proportion - cross multiply






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






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






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






26. 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






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






28. 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






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






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






31. 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






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. 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






35. 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






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






37. Combine like terms






38. 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






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






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






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






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






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






45. 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






46. 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






47. 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






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






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






50. 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