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# PS-2

Question | Answer |
---|---|

When two quantities are in inverse proportion, what remains constant? | Their product remains constant.For example, speed and time are in inverse, hence S*T remains constant. So when you see a product of two numbers, they are in inverse proportion. |

When two quantities are in direct proportion, what remains constant? | Their ratio remains constant. For example, distance and time are in direct proportion, hence S/T remains constant. |

How to calculate the amount after certain percentage increase? | For 25% increase, we do 100+25=125. So original*1.25=Final. For 150% increase, 100+150=250. Thus we have to multiply by 2.5 |

How to calculate percentage decrease? | If percentage decrease is 20%, then 100-20=80. So Final=0.8*original. A natural number cannot decrease by more than 100%; at 100% it becomes 0. But if its real number, then it can. |

NCK = ? | NC(N-K) |

When is the multiplication principle applied? | In counting number of "ways". Remember example of ordering food from a menu with 5 entrees and 3 desserts. |

If R is the rate of compound interest paid annually, in how many years will the amount double? | In nearly 70/R years. |

When to use a Venn diagram and when to use a matrix? | When the same population is divided differently on 2 (or more) attributes, use a matrix. When there is only one attribute for segregation, use Venn diagram. |

What is the sum of the interior angles of a polygon? | (N-2)*180. Also remember that each interior angle is less than 180 |

What is the relation between the sum of any two sides of a triangle & the third side? | Sum of any two sides > Third side |

If two angles of a triangle are equal, what can you say about the opposite sides? | The sides opposite to the equal angles are also equal. It is infact, an isosceles triangle |

The sides of a 30-60-90 triangle are in what ratio? | 1:Root(3):2, where 1 is the side opposite to 30 and root(3) is side opposite to 60 |

What can be said of the altitude in an equilateral and isosceles triangle? | The altitude bisects the base |

Formula for distance between two points in the coordinate plane? | Root( (y2-y1)^2 + (x2-x1)^2 ). It is derived by forming a right angled triangle with the points and using Pythagorus theorem |

It is possible to form the equation of a line given two points on it? | Yes. Use the two points to get the slope using y2-y1/x2-x1. Then use formula y-y1=m(x-x1) to get the equation of the line |

What does the polarity of the slope of a line convey? | If the slope is negative, the line slants downwards from left to right. If it is positive, it slants upwards from left to right |

What is the slope of a line parallel to y axis and a line parallel to x axis? | Parallel to y axis = 0Parallel to x axis = undefinedJust use the slope formula! |

How do two linear equations with no common solution appear in coordinate plane? | They will be parallel to each other. 2x+3y=4 and 6x+9y=12 represent the same line and thus have infinite common points |

What does the graph of a quadratic equation look like? | It is a parabola. The x intercepts are the two solutions of the equation. The y intercept is the value of f(0) |

x^2+4=0 has real roots? | No |

What are the roots of quadratic equation ax^2+bx+c=0? | x= (-b + root(b^2-4ac)/2a and x= (-b - root(b^2-4ac)/2a |

How should you imagine x^r? | Imagine it as x*x*x*x...r times. For example, x^3 = x*x*x. If you think of it this way, all exponent rules will flow automatically |

Does multiplying or dividing both sides of an inequality by a positive number alter the inequality? | No. Only multiplying or dividing both sides of an inequality by a negative number reverses the inequality |

How do you solve |x+2|= 7? | +(x+2)=7 and -(x+2)=7. Now solve |

Of 25 students in a class, 20 study Math and 18 study History. How many study both? | 25-20=5 18-5=1313 is the answer |

If a cube ends in 9, its root ends in? | 9 |

The avg of 30 students is 65, and avg of 40 students is 85. What is the combined average? | 1) The ratio is 30:40=3:4. Inverse it i.e. 4:32) Divide the difference in the inverse ratio20 * 4/7 = 11.423) The average is 65+11.42 = 76.42 |

How to divide 5 chocolates between 3 children such that each gets at least 1? Theory of partitions | 1) Write 5 as 1 1 1 1 1. There are 4 gaps in between.2) x+y+z=5 There are 2 + signs in the equation3) Answer is 4C2=6 |

r+s is divisible by 3 if BOTH r & s are divisible by 3 | r & s could BOTH not be divisible by 3, but r+s could still be divisible. |

What should be your strategy when they ask you to count ways in a word problem? | Setup an equation, simplify it and then get your count from the equation instead of doing the counting manually or by logic. This reduces chances of error |

What can you say about r^x when 0<r<1? | The value of r^x decreases as x increases. Hence r^2<r<r^1/2. From this it can be inferred that x^2 > x only when x>1 |

Created by:
deepak.bhavi