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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 whole # left over after division






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






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






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






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






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






7. 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






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






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






10. Volume of a Cylinder = pr^2h






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






12. 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






13. Add the exponents and keep the same base






14. 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






15. 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






16. 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






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






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






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






20. Factor out the perfect squares






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






22. 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






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






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






25. 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






26. pr^2






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






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






29. 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)






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. To divide fractions - invert the second one and multiply






32. 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






33. 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






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






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. 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






37. 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






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






39. 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






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






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






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






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






46. 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






47. 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






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. 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






50. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3