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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. 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






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






3. 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






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






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






6. 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






7. 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






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






9. 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)






10. Add the exponents and keep the same base






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






12. 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






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






14. To solve a proportion - cross multiply






15. Part = Percent x Whole






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






17. 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






18. 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






19. Subtract the smallest from the largest and add 1






20. 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.






21. 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






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






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






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






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






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






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






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






29. 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






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






31. 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






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






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






34. 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






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






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






38. 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






39. 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






40. 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






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






42. Factor out the perfect squares






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






44. Multiply the exponents






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






46. 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






47. Probability= Favorable Outcomes/Total Possible Outcomes






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






49. The whole # left over after division






50. 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