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






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 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






4. 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)






5. pr^2






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






7. 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






8. 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






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






10. 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






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






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






13. 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






14. Subtract the smallest from the largest and add 1






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






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






17. The whole # left over after division






18. Combine like terms






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






20. Volume of a Cylinder = pr^2h






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






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






23. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






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






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






26. 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






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






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






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






30. 2pr






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






32. 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






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






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






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






36. 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






37. 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)






38. 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






39. 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






40. 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






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






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






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






44. Add the exponents and keep the same base






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






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






47. To solve a proportion - cross multiply






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






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






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