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






2. Factor out the perfect squares






3. 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






4. Part = Percent x Whole






5. 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)






6. 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






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






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






9. Add the exponents and keep the same base






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






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






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






13. 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






14. 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






15. 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






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






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






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






19. Combine like terms






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






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






22. 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






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






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






25. Volume of a Cylinder = pr^2h






26. 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






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






28. 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






29. To solve a proportion - cross multiply






30. 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






31. Subtract the smallest from the largest and add 1






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






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






34. 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






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






36. 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






37. 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)






38. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






41. 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






42. 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






43. pr^2






44. 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






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






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






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






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






49. 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






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