Test your basic knowledge |

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






2. Volume of a Cylinder = pr^2h






3. Add the exponents and keep the same base






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






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






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






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






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






9. 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






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






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






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






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






14. Part = Percent x Whole






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






16. 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






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. 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






19. To solve a proportion - cross multiply






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






21. 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






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






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






24. 2pr






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






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






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






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






29. pr^2






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






31. The whole # left over after division






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






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






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






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






36. 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






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






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






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






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






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






42. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






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






44. 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






45. 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






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






47. 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






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






49. 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






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