/* */

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






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






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






4. 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






5. Probability= Favorable Outcomes/Total Possible Outcomes






6. 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






7. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






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






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






10. 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






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






12. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






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






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






15. Combine like terms






16. 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






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






18. 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






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






20. 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.






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






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






23. The whole # left over after division






24. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






25. Part = Percent x Whole






26. 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






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






28. 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






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






30. 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






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






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






33. 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






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






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






37. 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






38. 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






39. 2pr






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






41. 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






42. Multiply the exponents






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






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






45. pr^2






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






47. Factor out the perfect squares






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






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






50. 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






//