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






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






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






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






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






7. Probability= Favorable Outcomes/Total Possible Outcomes






8. 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.






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






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






11. 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






12. Volume of a Cylinder = pr^2h






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






14. 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






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






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






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






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






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






20. 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






21. Factor out the perfect squares






22. 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






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






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






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






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






27. To solve a proportion - cross multiply






28. 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






29. 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






30. Combine like terms






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






32. Add the exponents and keep the same base






33. 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






34. 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






35. Part = Percent x Whole






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






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






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






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






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






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. 2pr






44. 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






45. 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






46. pr^2






47. Multiply the exponents






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






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






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