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. 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






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






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






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






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






6. Probability= Favorable Outcomes/Total Possible Outcomes






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






8. 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






9. 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






10. 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






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






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






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






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






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






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






17. 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






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. 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






20. Subtract the smallest from the largest and add 1






21. 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






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






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






24. 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






25. 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






26. The whole # left over after division






27. Multiply the exponents






28. Factor out the perfect squares






29. 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






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






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






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






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






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






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






36. Add the exponents and keep the same base






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






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






39. 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)






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






41. 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






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






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






44. 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






45. 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






46. 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






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






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






49. pr^2






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