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






3. Combine like terms






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






5. 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






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






7. Multiply the exponents






8. 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






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






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






11. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






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






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






14. 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)






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






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






17. 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






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






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






20. 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






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. 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






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






24. To solve a proportion - cross multiply






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






26. Part = Percent x Whole






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






28. 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






29. 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






30. 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)






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






32. 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






33. 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






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






35. To find the reciprocal of a fraction switch the numerator and the denominator






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






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






38. Subtract the smallest from the largest and add 1






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






40. Factor out the perfect squares






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






42. 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






43. The whole # left over after division






44. Probability= Favorable Outcomes/Total Possible Outcomes






45. 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






46. 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






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






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






49. 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






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






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