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






2. 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






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






4. 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






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






6. 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






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






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






9. Volume of a Cylinder = pr^2h






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






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






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






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






14. To solve a proportion - cross multiply






15. Factor out the perfect squares






16. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






17. 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






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






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






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






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






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






23. To find the reciprocal of a fraction switch the numerator and the denominator






24. Subtract the smallest from the largest and add 1






25. 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






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






27. 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






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






30. pr^2






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






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






33. Add the exponents and keep the same base






34. 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






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






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






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






38. 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






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






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






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






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






43. 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






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






45. 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






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






47. 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






48. 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






49. 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






50. 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