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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. 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






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






3. 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






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






5. 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






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






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






8. Add the exponents and keep the same base






9. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






10. 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






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






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






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






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






15. 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






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






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






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






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






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






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






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






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






24. 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






25. 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






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






27. To solve a proportion - cross multiply






28. 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






29. 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






30. 2pr






31. 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






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






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






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






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






36. 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






37. 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






38. Part = Percent x Whole






39. pr^2






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






41. 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






42. 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)






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






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






45. 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






46. 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






47. 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






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






49. 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






50. Combine like terms






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