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






2. 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






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






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






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






6. 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






7. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






8. 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






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






10. 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






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






12. 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)






13. 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






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






15. pr^2






16. 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






17. 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






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






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. The whole # left over after division






21. 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






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






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






24. Combine like terms






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






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






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






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






29. Factor out the perfect squares






30. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






31. 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






32. Add the exponents and keep the same base






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






34. To solve a proportion - cross multiply






35. Probability= Favorable Outcomes/Total Possible Outcomes






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






37. 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






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






39. 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






40. 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






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






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






43. 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






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






45. 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






46. 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)






47. 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






48. 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






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






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