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






2. 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






3. 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.






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






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






6. 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






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






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






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






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






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






12. 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






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






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






15. 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






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






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






18. 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






19. Add the exponents and keep the same base






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. Change in y/ change in x rise/run






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






24. Part = Percent x Whole






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






26. To solve a proportion - cross multiply






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






28. 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






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






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






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






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






33. 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






34. The whole # left over after division






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






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






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






38. 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






39. 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






40. 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






41. 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)






42. 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






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






44. 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






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






46. 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






47. 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)






48. 2pr






49. 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






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