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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. 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






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






3. 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






4. 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






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






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






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






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






9. 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






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






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






12. 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






13. 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






14. To solve a proportion - cross multiply






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






16. 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






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






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






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






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






21. 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.






22. Part = Percent x Whole






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






24. pr^2






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






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






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






28. 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)






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






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






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






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






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






34. 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






35. 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






36. Subtract the smallest from the largest and add 1






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






38. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






39. 2pr






40. 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






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






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. The whole # left over after division






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






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






46. 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






47. 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






48. 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






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






50. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa