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






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






3. 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






4. 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






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






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






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






9. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






10. 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






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






12. pr^2






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






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






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






16. 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






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






18. 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






19. Add the exponents and keep the same base






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






21. 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






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






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






24. 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






25. Probability= Favorable Outcomes/Total Possible Outcomes






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






27. 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






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






29. 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.






30. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






31. 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






32. 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






33. 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






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






35. Combine like terms






36. Multiply the exponents






37. The whole # left over after division






38. Factor out the perfect squares






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






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






41. 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






42. 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






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






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






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






46. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






47. Subtract the smallest from the largest and add 1






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






50. 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