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9th Class Mathematics 1st Quarter Book Paper

9th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

For three sets, the central region of a Venn diagram represents:
1. A ∪ B ∪ C
2. A ∩ B ∩ C
3. A − B
4. A′
If a.b = 1, what is be called?
1. multiplicative inverse of a
2. additive identiy
3. multiplicative identity
4. self-multiplicative inverse
log 125 can be written as:
1. log 5
2. 2 log 5
3. 3 log 5
4. 5 log 3
An ordered pair is written as:
1. {a, b}
2. (a, b)
3. [a, b]
4. a + b
Which of the following sets have the closure propetry w.r.t. multiplication?
1. { -1 , -2 }
2. { 0 , -1 }
3. { 0 , 1 }
4. ${ 1 , \sqrt{2} }$
5 log 2 - 2 log 5 is
1. $\frac{(\log 2)^5}{(\log 5)^2}$
2. $\frac{\log 2^5}{\log 5^2}$
3. $\frac{\log 2^2}{\log 5^5}$
4. $\frac{5}{2}log\frac{2}{5}$
The Venn diagram is used to represent:
1. Numbers only
2. Relations between sets
3. Equations only
4. Angles
A person walks 3.5 km/h for 12 hours. The total distance is:
1. 36 km
2. 40 km
3. 42 km
4. 45 km
Logarithmic methods are especially useful when numbers are:
1. Very small or very large
2. Equal to zero only
3. Negative only
4. Whole numbers only
If 52 people speak Arabic and 112 speak French, those who speak both are represented by:
1. A ∪ F
2. A ∩ F
3. A − F
4. F′
$\sqrt[m]{\sqrt[n]{a}} = \ldots\ldots$
1. $\sqrt[mn]{a}$
2. $\sqrt[m+n]{a}$
3. $\sqrt[m-n]{a}$
4. $\sqrt[n]{\sqrt[m]{a}}$
Scientific notation of 6.25 is:
1. 6.25 × 10⁰
2. 0.625 × 10¹
3. 62.5 × 10⁻¹
4. All represent same value, but standard form is A

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

Given that D = {a, e, i}, E = {a, c}, F = {b, c}. Find $D \times (E \cap F )$
If log b 2 = 0.3010 m log b 3 = 0.4771 log b 5 = 0.6990 , then evaluate $\log_b 0.0036$
Represent the following on a number line. x < 0
If A = Set of Natural numbers and $R = \{(x, y) \mid x \in A \land y \in A\} \text{ i.e. } R \subseteq A \times A.$ . Then find the domain and range of R.
Use laws of logarithms to evaluate the following. $\quad \log_3 65$
Write exponential expression as an equivalent radical expression and simplify if possible. $(29)^\frac{1}{2}$
Find all possible binary relations in the case mentioning the number of binary relation in case.C = {π , e}
Find the value of unknown by converting logarithmic form to exponential form. $\log_27 3 = y$
Represent number on the number line. $\frac{17}{3}$
Let E = {1, 3} and F = {4, 6, 8}. Express by graphically.E × E
Find value of $\log_2 3 \times \log_3 8$
Show the following numbers on a number line. $-\pi$

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

A cooking oil company produces four types of oils in packing of 1 litre & 10 litre. The inventory is shown in the table. After removal of 40% of an item, it is to be replenished. The daily removal of 1 litre cooking oil-II packing is 20% and for 10 litre cooking oil-IV packing, daily removal is 5%. Find (a) Number of daily removed 1 litre cooking oil-II packing. (b) After how many days, 1 litre cooking oil-II are to be replenished? (c) Number of daily removed 10 litre cooking oil-IV packing. (d) After how many days, 10 litre cooking oil-IV packing are to be replenished? $\begin{array}{|c|c|c|c|} \hline \text{Name / Packing size} & \text{1 litre} & \text{5 litre} & \text{10 litre} \\ \hline \text{Cooking oil-I} & 5000 & 2500 & 1000 \\ \hline \text{Cooking oil-II} & 5000 & 2500 & 1000 \\ \hline \text{Cooking olive-III} & 5000 & 2500 & 1000 \\ \hline \text{Cooking olive-IV} & 5000 & 2500 & 1000 \\ \hline \end{array}$
Prove by using Venn diagram when P = {0, 1, 2, 3} , Q = {2, 3, 4, 5, 6} and R = { 5, 6, 7, 8, 9} $(P \cup Q) \cup R = P \cup (Q \cup R)$
Evaluate applying laws of logarithms. $\frac{\sqrt[7]{129.4}}{\sqrt[3]{27.37}}$
Determine whether each statement is true or false. If false, give an example of a number that shows the statement is true. (a) Every rational number is an integer (b) Every real number is an irrational (c) Every irrational number is a real number (d) Every integer is a rational number (d) Every real number is either a rational number or an irrational number