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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 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






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






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






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






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






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






8. 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






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






10. 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






11. 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






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






13. 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






14. Volume of a Cylinder = pr^2h






15. 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






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






17. Part = Percent x Whole






18. For all right triangles: a^2+b^2=c^2






19. 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






20. 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






21. To solve a proportion - cross multiply






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






23. 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)






24. 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.






25. 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






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






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






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






29. pr^2






30. 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






31. 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






32. 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






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






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






35. 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






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






37. 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






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






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






40. Subtract the smallest from the largest and add 1






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






42. Probability= Favorable Outcomes/Total Possible Outcomes






43. 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






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






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






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






47. 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






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






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






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