Class 9 Mathematics Chapter 13 Introduction to Graphs: 30 MCQs with Answers & Solutions

The rationalized CBSE Class 9 syllabus for 2024–25 emphasizes competency-based learning and objective assessment. MCQs are the preferred question type because they test conceptual understanding, quick recall, and analytical thinking simultaneously—three pillars of modern education. In Class 9 Mathematics, MCQs account for 30–35% of total marks (typically 8–10 questions out of 20 in a 1-hour paper). Introduction to Graphs is a high-frequency topic in MCQs because examiners can test: (1) coordinate identification and point plotting, (2) graph reading and interpretation, (3) real-world applications (temperature graphs, distance–time graphs, etc.), and (4) abstract reasoning about axes, quadrants, and transformations. Unlike short-answer questions, MCQs are 'negative-marking proof'—if you know the concept, you choose the right answer instantly. The new pattern also introduces assertion-reason MCQs (Type III) in which two statements are given, and you must judge their relationship. This demands deeper engagement with Chapter 13 than traditional rote learning. Regular MCQ practice reduces exam anxiety, builds speed, and trains your brain to think like an examiner.

**MCQ 1:** The coordinates of a point that lies on the x-axis are: (A) (0, y) where y ≠ 0 (B) (x, 0) where x ≠ 0 (C) (0, 0) (D) (x, y) where x = y **Answer:** (B) | **Reason:** On the x-axis, the y-coordinate is always 0; x can be any non-zero value. **MCQ 2:** Which quadrant contains the point (−3, 5)? (A) Quadrant I (B) Quadrant II (C) Quadrant III (D) Quadrant IV **Answer:** (B) | **Reason:** Quadrant II has negative x and positive y; (−3, 5) fits this. **MCQ 3:** The distance of the point (4, 3) from the y-axis is: (A) 3 units (B) 4 units (C) 5 units (D) 7 units **Answer:** (B) | **Reason:** Distance from the y-axis equals the absolute value of the x-coordinate, which is |4| = 4. **MCQ 4:** Plot the point (−2, −4). It lies in: (A) Quadrant I (B) Quadrant II (C) Quadrant III (D) Quadrant IV **Answer:** (C) | **Reason:** Both x and y are negative, so the point is in Quadrant III. **MCQ 5:** The origin is denoted by: (A) (1, 1) (B) (0, 0) (C) (−1, 1) (D) (1, −1) **Answer:** (B) | **Reason:** The origin is where the x-axis and y-axis intersect, at coordinates (0, 0). **MCQ 6:** A point (x, y) is reflected across the x-axis. Its new coordinates are: (A) (−x, y) (B) (x, −y) (C) (−x, −y) (D) (y, x) **Answer:** (B) | **Reason:** Reflection across the x-axis changes the sign of y while x remains the same. **MCQ 7:** Which point does NOT lie on the line y = 2x? (A) (1, 2) (B) (2, 4) (C) (3, 5) (D) (0, 0) **Answer:** (C) | **Reason:** If x = 3, then y = 2(3) = 6 ≠ 5, so (3, 5) does not satisfy y = 2x. **MCQ 8:** The perpendicular distance of (6, −2) from the x-axis is: (A) 6 units (B) 2 units (C) 8 units (D) 4 units **Answer:** (B) | **Reason:** Distance from the x-axis equals the absolute value of the y-coordinate: |−2| = 2. **MCQ 9:** In which quadrant do both x and y coordinates have the same sign (both positive or both negative)? (A) Quadrant I only (B) Quadrant III only (C) Quadrants I and III (D) All four quadrants **Answer:** (C) | **Reason:** Quadrant I has (+, +) and Quadrant III has (−, −); in II and IV, signs differ. **MCQ 10:** A point moves from (2, 3) to (2, 8). It moves: (A) Horizontally to the right (B) Horizontally to the left (C) Vertically upward (D) Vertically downward **Answer:** (C) | **Reason:** The x-coordinate stays at 2, but y increases from 3 to 8, so movement is vertical upward.

**MCQ 11:** A line graph shows distance (in km) vs. time (in hours). The graph is a straight line passing through (0, 0) and (2, 100). What is the speed? (A) 40 km/h (B) 50 km/h (C) 60 km/h (D) 100 km/h **Answer:** (B) | **Reason:** Speed = Distance ÷ Time = 100 ÷ 2 = 50 km/h. **MCQ 12:** The equation of a line passing through (0, 0) and (1, 3) is: (A) y = x (B) y = 2x (C) y = 3x (D) y = 4x **Answer:** (C) | **Reason:** When x = 1, y = 3, so the slope m = 3; since it passes through origin, y = 3x. **MCQ 13:** A temperature graph shows temperature (°C) on the y-axis and time (hours) on the x-axis. At 10 AM, temp = 20°C; at 2 PM (4 hours later), temp = 28°C. The average rate of temperature change is: (A) 1°C per hour (B) 2°C per hour (C) 4°C per hour (D) 8°C per hour **Answer:** (B) | **Reason:** Change = 28 − 20 = 8°C over 4 hours; Rate = 8 ÷ 4 = 2°C per hour. **MCQ 14:** On a line graph, if the line is parallel to the x-axis, what does this indicate? (A) x increases while y is constant (B) y increases while x is constant (C) Both x and y are increasing (D) Both x and y are decreasing **Answer:** (A) | **Reason:** A horizontal line means y does not change as x increases; y is constant. **MCQ 15:** The coordinates (−1, 2), (0, 4), and (1, 6) lie on which line? (A) y = x + 5 (B) y = 2x + 4 (C) y = 3x + 4 (D) y = 4x **Answer:** (B) | **Reason:** Check: y = 2(−1) + 4 = 2 ✓; y = 2(0) + 4 = 4 ✓; y = 2(1) + 4 = 6 ✓. **MCQ 16:** A bar graph shows the number of students in four classes. Class A has 40, Class B has 50, Class C has 35, and Class D has 45 students. The ratio of students in Class A to Class B is: (A) 4:5 (B) 5:4 (C) 8:10 (D) 2:3 **Answer:** (A) | **Reason:** Ratio = 40:50 = 4:5 (divide both by 10). **MCQ 17:** On a pie chart, if one sector has a central angle of 90°, it represents what percentage of the whole? (A) 20% (B) 25% (C) 30% (D) 45% **Answer:** (B) | **Reason:** Percentage = (90 ÷ 360) × 100 = 25%. **MCQ 18:** A scatter plot shows points: (1, 1), (2, 4), (3, 9), (4, 16). The relationship between x and y is: (A) Linear (y = x) (B) Linear (y = 2x) (C) Quadratic (y = x²) (D) Quadratic (y = 2x²) **Answer:** (C) | **Reason:** Each y-value is the square of the corresponding x-value: 1² = 1, 2² = 4, 3² = 9, 4² = 16. **MCQ 19:** A line graph has a negative slope (slanting downward from left to right). This indicates: (A) Both variables are increasing (B) Both variables are decreasing (C) One variable increases while the other decreases (D) The relationship is non-linear **Answer:** (C) | **Reason:** Negative slope means as x increases, y decreases; an inverse relationship. **MCQ 20:** A histogram shows the frequency distribution of heights (in cm) of students. The y-axis label should be: (A) Height (cm) (B) Number of students (frequency) (C) Cumulative frequency (D) Relative frequency **Answer:** (B) | **Reason:** In a frequency histogram, the y-axis always represents frequency (count or number of occurrences).

**MCQ 21:** **Assertion (A):** The point (a, b) reflected across the origin becomes (−a, −b). **Reason (R):** Reflection across the origin is equivalent to a 180° rotation about the origin. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation of A (C) A is true, but R is false (D) A is false, but R is true **Answer:** (A) | **Reason:** Both statements are correct and logically connected; reflection through the origin equals 180° rotation. **MCQ 22:** Three points (1, 1), (2, 2), and (3, 4) are plotted. Which statement is correct? (A) All three points lie on the same straight line (B) Points (1, 1) and (2, 2) are collinear, but (3, 4) is not on this line (C) The three points form an isosceles triangle (D) The three points are equidistant from the origin **Answer:** (B) | **Reason:** Line through (1, 1) and (2, 2) has equation y = x. Point (3, 4) gives 4 ≠ 3, so it does not lie on y = x. **MCQ 23:** **Assertion (A):** If a graph is symmetric about the y-axis, then f(x) = f(−x) for all x in the domain. **Reason (R):** Such a function is called an even function. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation of A (C) A is true, but R is false (D) A is false, but R is true **Answer:** (A) | **Reason:** Y-axis symmetry defines an even function; both statements are true and causally linked. **MCQ 24:** A graph shows y = |x| (absolute value function). Which quadrants does this graph occupy? (A) Quadrants I and II only (B) Quadrants I and III only (C) Quadrants I and IV only (D) All four quadrants **Answer:** (A) | **Reason:** |x| is always non-negative, so y ≥ 0. The graph lies above or on the x-axis, in Quadrants I and II. **MCQ 25:** Two lines y = 2x + 1 and y = 2x − 3 are plotted. These lines are: (A) Perpendicular (B) Parallel (C) Intersecting at one point (D) Identical **Answer:** (B) | **Reason:** Both lines have slope m = 2, so they are parallel; they never intersect. **MCQ 26:** A student plots the equation y = −x² on a graph. The student claims the graph is symmetric about the y-axis and passes through (0, 0). Which is correct? (A) Both claims are true (B) First claim is true, second is false (C) First claim is false, second is true (D) Both claims are false **Answer:** (A) | **Reason:** y = −x² is symmetric about the y-axis (even function: f(−x) = f(x) = −x²) and passes through (0, 0). **MCQ 27:** A line passes through (−2, −3) and (4, 6). Its slope is: (A) 1/2 (B) 3/2 (C) 2 (D) 3 **Answer:** (B) | **Reason:** Slope = (6 − (−3)) ÷ (4 − (−2)) = 9 ÷ 6 = 3/2. **MCQ 28:** **Assertion (A):** A line perpendicular to y = 3x + 5 has slope −1/3. **Reason (R):** The product of slopes of two perpendicular lines is −1. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation of A (C) A is true, but R is false (D) A is false, but R is true **Answer:** (A) | **Reason:** If m₁ = 3 and m₁ × m₂ = −1, then m₂ = −1/3. Both statements are true and logically connected. **MCQ 29:** A quadrilateral has vertices at (0, 0), (4, 0), (4, 3), and (0, 3). Its perimeter is: (A) 7 units (B) 12 units (C) 14 units (D) 24 units **Answer:** (C) | **Reason:** Sides are 4, 3, 4, and 3 units; Perimeter = 4 + 3 + 4 + 3 = 14 units (it's a rectangle). **MCQ 30:** A data visualization expert says, 'A line graph is best for showing trends over time, while a pie chart is best for showing parts of a whole.' Which component is incorrect? (A) First statement only (B) Second statement only (C) Both statements are incorrect (D) Both statements are correct **Answer:** (D) | **Reason:** Both statements accurately describe standard uses of these graph types in data representation and interpretation.

Graph MCQs are designed to test both conceptual understanding and attention to detail. Examiners intentionally craft wrong options (distractors) that lure students into careless mistakes. Understanding these traps is half the battle. **Trap 1: Confusing x and y axes.** A classic error occurs when reading coordinates. For example, "The point is 5 units from the y-axis" is often misread as 5 units from the x-axis. Remember: distance from the y-axis = |x-coordinate|; distance from the x-axis = |y-coordinate|. Always reread the question after identifying the axis. **Trap 2: Forgetting the sign of coordinates.** In a question like 'Which quadrant contains (−3, 5)?', a student may mistakenly think −3 and 5 both refer to distances (always positive) rather than signed coordinates. Quadrants are defined by the signs of x and y: I (+, +), II (−, +), III (−, −), IV (+, −). Never drop the negative sign. **Trap 3: Confusing slope and y-intercept.** For y = 2x + 3, the slope is 2 and the y-intercept is 3. A distractor option might swap these: 'slope = 3, intercept = 2.' Always use the form y = mx + b, where m is slope and b is the intercept. **Trap 4: Reflection vs. rotation confusion.** Reflecting (a, b) across the x-axis gives (a, −b); across the y-axis gives (−a, b); across the origin gives (−a, −b). A 180° rotation about the origin gives (−a, −b). Many students mix these up. Create a mental grid and practice these transformations. **Trap 5: Reading graphs inaccurately.** When a line graph shows two intersecting lines, always verify the exact intersection point by tracing carefully. An option may list a nearby but incorrect point (e.g., (2, 4) instead of (2, 5)). Use a ruler or straight edge to align points precisely. **Trap 6: Assuming collinearity without checking.** Three points may appear to lie on a straight line visually, but they may not. Always verify by checking if they satisfy the same linear equation. Trap options often include 'all three points are collinear' when only two are. **Trap 7: Confusing 'average rate' with 'instantaneous rate.'** If a graph shows distance vs. time, the slope at a point represents instantaneous speed, but the average slope over a segment represents average speed. A distractor may give the instantaneous rate when the question asks for average, or vice versa. **Trap 8: Misreading bar and pie charts.** A bar showing 'class A = 40 students' is not the same as a pie sector with 40° central angle. Always check the axis labels and legend. Examiners deliberately mix these units in distractor options. Examination tip: Before selecting an answer, re-read the question once more and cross-check your option against what was asked, not what you think was asked.

In a 1-hour CBSE Class 9 Mathematics exam with 20 questions (16 MCQs + 4 short-answer), you have roughly 3 minutes per MCQ. For graph-related questions, this timing is tight. Here's a battle-tested strategy: **Phase 1: Scan and sort (1 minute per 5 questions).** Read all graph MCQs first without solving. Mentally sort them into three buckets: (1) I can solve in under 1.5 minutes, (2) I need 2–2.5 minutes, (3) I'll come back if time permits. This prevents you from spending 4 minutes on a 1-minute question. **Phase 2: Easy win (under 1.5 minutes).** Start with bucket (1): straightforward coordinate identification, quadrant location, or basic graph reading. These are your confidence boosters. Avoid second-guessing; if you know the answer, move on. **Phase 3: Medium challenges (2–2.5 minutes).** Next, tackle bucket (2). For graph interpretation or slope calculations, use shorthand: write the formula, plug in numbers, solve once, and move. Do NOT verify your answer unless you're unsure; verification eats time. **Phase 4: Strategic skipping.** If a graph MCQ requires drawing, plotting multiple points, or involves assertion-reason logic (especially if the first statement itself is complex), skip it initially. Return with fresh eyes if time remains. Skipping strategically is not defeat; it's smart allocation of cognitive bandwidth. **Specific techniques for graph MCQs:** **For coordinate-based questions:** Use the grid and your pencil. Mark the point lightly; read the value directly from the axis. Never calculate unless the question explicitly demands a formula (e.g., 'distance from origin'). **For line graph interpretation:** Trace your finger along the line. Identify the start and end points, then calculate slope as (Δy ÷ Δx). Write this calculation in the margin for reference. **For assertion-reason questions:** Read the assertion first. If you immediately spot it as false, eliminate all options with 'A is true.' Then read the reason. This filters options fast. **For transformation questions (reflection, rotation):** Use a mental or actual grid. Practice the transformation rule once in the margin (e.g., 'reflection across x-axis: (a, b) → (a, −b)'), then apply to the given point. No guessing. **Final 2 minutes:** If time allows, skim skipped questions. For those you couldn't solve, look for patterns in your other answers (e.g., if too many are option C, reconsider). Avoid random selection; even a blank answer is safer than a wild guess in some marking schemes. **Memory jogger:** "E-M-H-S" = Easy, Medium, Hard, Skip-strategically. This mental anchor keeps you calm and organized under exam pressure. Start your MCQ section with this mantra, and you'll maximize both speed and accuracy. For personalized practice and timed MCQ drills aligned with the 2024–25 CBSE syllabus, start a 3-day free trial at cbsetutor.ai.

The Introduction to Graphs chapter (Chapter 13) is not just about plotting points or reading graphs—it's about developing spatial reasoning and data literacy, both critical for Board exams and real-world problem-solving. The 30 MCQs in this guide span the full spectrum of difficulty and question types you'll encounter in CBSE Class 9 assessments. By working through Easy, Medium, Hard, and Assertion-Reason MCQs, you've trained your brain to recognize patterns, avoid trap options, and solve under time pressure. The key to mastery is repetition: solve each MCQ twice—once for understanding, once for speed. Review your errors ruthlessly; every wrong answer is a lesson in disguise. Don't just memorize formulas; understand why reflection changes a sign, why parallel lines have equal slopes, or why a horizontal graph means a variable is constant. These conceptual anchors will serve you across geometry, coordinate geometry, and even physics (in later classes). As you prepare further, combine this MCQ practice with NCERT textbook examples and real-world graph interpretation tasks (reading temperature graphs, stock prices, or distance-time data). If you need adaptive, AI-powered practice aligned to your learning pace and the exact CBSE pattern, explore personalized quizzes and instant feedback at cbsetutor.ai. Your consistent effort now will directly translate into confident, accurate MCQ performance in your quarterly, pre-board, and Board exams. Keep practicing, stay curious, and master graphs!