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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. 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






2. 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






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






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






5. 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






6. Multiply the exponents






7. pr^2






8. 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






9. 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)






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






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






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






13. Part = Percent x Whole






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






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






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






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






18. 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






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






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






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






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






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






24. Subtract the smallest from the largest and add 1






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






26. 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






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






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






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






30. Probability= Favorable Outcomes/Total Possible Outcomes






31. 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.






32. The whole # left over after division






33. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






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






35. 2pr






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






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






39. 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






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






41. 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)






42. Factor out the perfect squares






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






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






45. Change in y/ change in x rise/run






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






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






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






49. Combine like terms






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