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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. 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






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






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






4. 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






5. 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






6. Volume of a Cylinder = pr^2h






7. pr^2






8. Factor out the perfect squares






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






10. To solve a proportion - cross multiply






11. 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)






12. 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






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






14. 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






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






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






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






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






19. 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






20. 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






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






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






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






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






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






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






27. 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






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






29. 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






30. 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






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. Combine like terms






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






34. 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






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






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






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






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






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






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






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






42. 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






43. Subtract the smallest from the largest and add 1






44. Add the exponents and keep the same base






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






46. 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






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






48. 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






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






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