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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. 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)






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






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






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






5. 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






6. 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






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






8. 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






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






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






11. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






12. 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






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






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






15. 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






16. pr^2






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






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






19. 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






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






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






22. 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






23. 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






24. Multiply the exponents






25. 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






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






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






28. 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






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. 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






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






32. 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






33. The whole # left over after division






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






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






36. 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






37. 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






38. Volume of a Cylinder = pr^2h






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






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






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






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






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






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






45. 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






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






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






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






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






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