| 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
| The value of r^x decreases as x increases. Hence r^2 x only when x>1 |
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