9th Class Math Paper New Syllabus First Three Chapters
Total Marks 75
Total Time 2hours 30min
Section A
Q1:- Attempt all the MCQS (15×1=15)
i:-$$\mathrm\pi\;\mathrm{and}\;\mathrm e\;\mathrm{are}$$
(a) integer (b) rational number (c) irrational number (d) natural number
ii:-$$\sqrt3+\sqrt5\;is$$
(a) whole number (b) integer (c) rational number (d) irrational number
iii:-$$Let\;a,b,c\;\in\mathbb{R},\;then\\a>b\;and\;b>c$$
$$\Rightarrow\;a>c\;is\;called$$
(a) trichotomy property (b) transitive property (c) additive property (d) multiplicative property
iv:-$$Let\;a,b\;\in\mathbb{R},\;then\;a=b\\\;and\;b=a\;is\;called$$
(a) reflexive property (b) symmetric property (c) transitive property (d) additive property
v:- Scientific notation of 0.00034 is
$$(a)\;3.4\times10^3\;(b)\;3.4\times10^{-4}\\(c)\;3.4\times10^4\;(d)\;3.4\times10^{-3}$$
vi:- The base of common logarithm is
(a) 2 (b) 10 (c) 5 (d) e
vii:- $$Log_2\;2^3\;=\;$$
(a) 1 (b) 2 (c) 5 (d) 3
viii:- Log 100 =
(a) 2 (b) 3 (c) 10 (d) 1
ix:- Log (0) =
(a) Positive (b) Negative (c) Zero (d) Undefined
(x):- $$3^4\;=\;81\;in\;\log arithmic\;form\;is:$$
$$(a)\;Log_34\;=\;81\;\;(b)\;Log_43\;=81\\(c)\;Log_381\;=4\;\;(d)\;Log_481=\;3$$
xi:- If A = { }, then P(A) is
(a) { }
(b) { 1 }
(c) { { } }
$$(d)\;\phi$$
xii:- If A and B are overlapping sets, then n(A-B) is equal to
(a) n (A)
(b) n (B)
$$(c)\;A\cap B\;$$
$$(d)\;n(A)\;-\;n(A\cap B)$$
xiii:- If n(AUB) = 50, n(A) = 30 and n(B) = 35, then
$$n(A\cap B)\;=$$
(a) 23
(b) 15
(c) 9
(d) 40
xiv:- If A = { 1, 2, 3, 4 } and B = { x, y, z }, then cartesian product of A and B contains exactly _______ element.
(a) 13
(b) 12
(c) 10
(d) 6
xv:- If
$$f\mathit(x\mathit)\mathit\;\mathit=\mathit\;x^{\mathit2}\mathit-\mathit\;\mathit3x\mathit\;\mathit+\mathit\;\mathit2\mathit,\mathit\;then\mathit\;\\the\mathit\;value\mathit\;of\mathit\;\mathrm f(\;\mathrm a+1\;)\;\mathrm{is}\;\mathrm{equal}\;\mathrm{to}:$$
(a) a+1
$$(b)\;a^2+1\\(c)\;a^2+2a+1\\(d)\;a^2-a$$
Section B
Q2:- Attempt any six questions of the following (6×2=12)
(i):- Express the following as rational numbers p/q where p and q are integers and q is not equal to zero.
$$\;\;0\overline{.4}\\\\\\$$
(ii):- Insert two rational numbers between
1/3 and 1/4
(iii):- Sum of three consecutive integers if forty-two, find the three integers.
(iv):- Rationalize the denominator
$$\frac{13}{4+\sqrt3}\\\\\\$$
(v):-Find compound markup on Rs 375000 for one year at the rate of 14 % compounded annually.
(vi):-
$$x\;=\;3\;+\;\sqrt8\;\;\;\\\\Find\;the\;value\;of x-\frac1x\;\\\\$$
(vii):- Is 0 a rational number ? Explain.
(viii):- State trichotomy property of real numbers.
Q3:- Attempt any six questions of the following (6×2=12)
(i):- Express 2000000 in scientific notation
(ii):-
$$Express\;1.5\times10^{-2}\;in\\ordinary\;notation\\\\$$
(iii):-
$$Express\;1000=10^3\;in\\\log arithmic\;form\\\\$$
(iv):-
$$Express\;Log_{23}\;1=23\;in\\exponential\;form\\\\$$
(v):- Find the value of x
$$\;Log_2\;1024=x\\\\$$
(vi):- If Log 3.177 = 0.5019, then find Log 3177
(vii):- Find the value of x if Log x = 0.0065
(viii):- Without using calculator evaluate the following:
$$\underset2{Log\;18}\;-\;\underset2{Log\;9}$$
Q4:- Attempt any six questions of the following (6×2=12)
(i):- what is the difference between {a , b} and {(a , b)}?
(ii):- Write down the power set of each of A= { 0 }
(iii):- Write {6,12,18,….,120} in set builder notation
(iv):-
$$U=\{x:x\;is\;multiple\;of\;2\;and\;0<x\leq30\}$$
A= { x:x is a multiple of 6 } Find complement of A
(v):- A = { 1,2,3 } domain and range of AxA.
(vi):- If g(x)= 3x-1 Find g(1)
(vii):- Consider the following defined by f(x) = 5 x + 1 and f(x) = 31, find the value of x.
(viii):-If U={1,2,3,4,5} and A={1}. Draw the Venn diagram of complement of A
Section C
Note:- Attempt any three questions of the following (8×3=24)
Q5:-
(i):-Find two numbers whose sum is 68 and difference is 22
(ii):- Sum of ages of the father and son is 72 years. Six years ago, the father’s age was 2 times the age of the son. What was son’s age six years ago?
Q6:-
(i):- Simplify the following
$$\sqrt{\;\frac{\;{(216)}^\frac23\times{(25)}^\frac12}{{(0.04)}^{\displaystyle\frac{-3}2}}}\;\\\\$$
(ii):- Abdullah invested Rs 100,000 in a saving scheme and gains interest at the rate of 5 % per annum so that the total value of this investment after t years is Rs y. This is modelled by an equation y = 100,000 multiplied by 1.05 raised to power t, where t is greater than equal to 0. Find after how many years the investment will be double.
$$y\;=\;100,000\;{(1.05)}^t$$
Q7:-
(i):- U={a,b,c,d,e,f,g,h,i,j} A={a,b,c,d,g,h} B={c,d,e,f,j} Verify De Morgan’s Laws for these sets. Draw Venn diagram
(ii):- In year 2016, the population of a city was 22 millions and was growing at a rate of 2.5 % per year. The function P(t) = 22 multiplied by 1.025 raised to power t gives the population in millions, t years after 2016. Use the model to determine in which year the population will reach 35 millions. Round the answer nearest year
$$p\;(t)\;=\;22\;{(\;1.025\;)}^t$$
Q8:-
(i):- Find the value of the following with the help of Logarithm table:
$$\frac{\sqrt[3]{9.364}\;\times\;21.64}{3.21}$$
(ii):- Out of the 180 students who appeared in the annual examination, 120 passed the math test, 90 passed the science test, and 60 passed both the math and science test.
(a) How many passed either the math or science test ?
(b) How many did not pass either of the two tests ?
(c) How many passed the science test but not the math test ?
(d) How many failed the science test ?
