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






2. Multiply the exponents






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






4. 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






5. 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






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






7. 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






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






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






10. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






12. 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






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






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






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






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






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






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






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






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






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. 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






23. Factor out the perfect squares






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






25. Part = Percent x Whole






26. 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






27. 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






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






29. 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






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






31. 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






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






33. Combine like terms






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






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






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






37. 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






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






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






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






42. 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






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






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






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






46. 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






47. 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






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






49. The whole # left over after division






50. Subtract the smallest from the largest and add 1