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






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






3. Probability= Favorable Outcomes/Total Possible Outcomes






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






5. 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






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






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






8. 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






9. 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






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






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






12. 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






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






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






15. Combine like terms






16. 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






17. 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






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






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






20. 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)






21. 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






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






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






24. The whole # left over after division






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






26. 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






27. Subtract the smallest from the largest and add 1






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






30. 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






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






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. 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






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






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. Volume of a Cylinder = pr^2h






37. Factor out the perfect squares






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






39. 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






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






41. 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






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






43. pr^2






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






45. 2pr






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






47. 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






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






49. 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






50. 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.