Optional Mathematics Grade 9

Cheatsheet Content

Group A: Objective Questions 1. Multiple Choice Questions (Set 1) A. If $(a, b) = (3, 4)$, then what are the values of $a$ and $b$? Correct Option: d. $a = 3, b = 4$ B. What is the solution to the inequality $-3x \le 9$? Correct Option: b. $x \ge -3$ C. What is the rationalizing factor of $3 - \sqrt{2}$? Correct Option: b. $3 + \sqrt{2}$ D. Simplify: $\tan \alpha \cdot \cos \alpha$. Correct Option: a. $\sin \alpha$ E. $90^\circ$ are equal to how many right angles? Correct Option: a. 1 F. Find the slope of a straight line making an angle of $150^\circ$ with the x-axis. Correct Option: d. $-1/\sqrt{3}$ G. Which is the correct formula for a point that divides a line segment internally in the ratio $m_1:m_2$? Correct Option: b. $\left(\frac{m_1x_2+m_2x_1}{m_1+m_2}, \frac{m_1y_2+m_2y_1}{m_1+m_2}\right)$ H. The formula $P(x, y) \to P'(y, x)$ represents reflection on which line? Correct Option: c. $y=x$ I. Find the magnitude of vector $\vec{p} = 6\mathbf{i} + 8\mathbf{j}$. Correct Option: c. 10 J. What is the position vector of the point $P(3, -4)$? Correct Option: c. $\begin{pmatrix} 3 \\ -4 \end{pmatrix}$ K. If the $Q_1=10$ and $Q_3=30$, what is the coefficient of Q.D.? Correct Option: b. 0.5 2. Multiple Choice Questions (Set 2) A. Which test is used to determine if a relation is a function from its graph? Correct Option: b) Vertical Line Test (ठाडो रेखा परीक्षण) B. In Synthetic Division, which value is used for dividing by the divisor $(x-a)$? Correct Option: b) a C. What is the result of simplifying $(1+\tan A)^2 - 2\tan A$? Correct Option: a) $\sec^2 A$ D. $\cos(0-90^\circ)$ as $\cos[-(90^\circ-0)]$ what is its value? Correct Option: c) $\sin \theta$ E. What are the expression $\operatorname{cosec}\theta - \cot\theta$ and $\operatorname{cosec}\theta + \cot\theta$ called in relation to each other? Correct Option: d) Conjugates (संयुग्मी) F. Which of the following is an identity matrix? Correct Option: d) $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ G. What is the path traced by a moving point satisfying a given geometric condition called? Correct Option: a) A locus (विन्दुपथ) H. What is the product of the intercepts of the line $2x+3y=6$? Correct Option: c) 6 I. Find the value of $f(0)$ from the adjoining graph of $y=f(x)$. Correct Option: b) 1 K. If the first quartile ($Q_1$) of employee salaries in a company is Rs. 20,000. What does this signify? Correct Option: c) 25% of employees earn Rs. 20,000 or less L. Based on the whisker box plot below, what is the interquartile range (IQR) of the data? From the box plot: $Q_1 = 10$, Median $= 20$, $Q_3 = 30$. Correct Option: d) 10 3. Multiple Choice Questions (Set 3) 1. How is $(x^2)^{1/3}$ written in radical form? Correct Option: c) $\sqrt[3]{x^2}$ 2. If $A = \{1,2,3\}$ and $B = \{a,b\}$, then what is the value of $n(A \times B)$? Correct Option: d) 6 3. If a polynomial $P(x) = x^3 + 3x^2 + 4x + 2$ is divided by $x+2$, what is the remainder? Correct Option: d) -2 4. What element in the domain has its image 2 under the function $f(x) = \frac{x-1}{3}$? Correct Option: c) 7 5. Which of the following is the correct method to convert $60^\circ$ into radians? Correct Option: a) $60 \times \frac{\pi}{180}$ 6. If a polynomial $P(X)$ has a root $-2$, at which point does its graph intersect the X-axis? Correct Option: b) $(-2,0)$ 7. In a right-angled triangle, if $\sin A = \frac{\sqrt{3}}{2}$, what is the value of $\cos A$? Correct Option: $1/2$