Mathematics and Science PYQs

According to National Curriculum Framework, 2005 learning mathematics should be an engaging, enjoyable and exploratory experience for children.

Key Points

• It suggests that children should not only learn important mathematical concepts but also develop the ability to form and solve meaningful mathematical problems.
• This approach promotes critical thinking, problem-solving skills, and creativity.
• By connecting mathematical learning to real-world experiences, children can better understand the relevance and applicability of the subject.
• Therefore, mathematics learning becomes more than rote memorization; it fosters curiosity, inquiry and active engagement with the subject matter.

Hence, it can be concluded that option 1 is the correct answer.

Empirical methods involve gathering data through observation or experimentation, which is commonly used in sciences but not in mathematics for establishing formal proofs or truths, as mathematical truths are universal and do not rely on specific observed instances.

Key Points

• The empirical method, often used in science, involves gaining knowledge through direct and indirect observation or experience.
• It includes conducting experiments, collecting data, and analyzing it to draw conclusions.
• In the context of scientific research, empirical evidence is often used to validate or refute theories.
• Mathematics is a deductive discipline that derives truths and theorems from general principles through logical reasoning.
• The proofs of mathematical theorems are not dependent on specific observed instances but on abstract, universally applicable principles and logical inference.

Hence, it can be concluded that Empirical approaches are NOT utilised to establish mathematical truths.

Rubrics as an assessment tool can be used in observation and peer assessment. 

Key Points

• Rubrics can serve as a structured tool during classroom observations.
• Teachers can use a rubric to observe and assess student behaviour, participation, or demonstration of a particular skill.
• It allows teachers to look for specific criteria and levels of competency or understanding, thus ensuring that the observations are focused and objective.
• In peer assessment, students evaluate their classmates' work.
• This practice can boost students' critical thinking and self-assessment skills.
• However, to make peer assessment effective, clear guidelines are necessary.
• A well-designed rubric provides students with clear expectations and criteria, allowing them to objectively assess the work of their peers.
• It ensures consistency in feedback and grading, reducing subjectivity.

Hence, it can be concluded that option 3 is the correct answer.

Using matchsticks to create patterns and represent numerical relationships can provide a hands-on and visual approach to help students understand basic algebraic concepts.

Key Points

It allows for concrete representation and manipulation, making the learning experience more engaging and tangible.

• Concrete Representation: Matchsticks provide a physical and concrete representation of numerical values and relationships. Students can manipulate the matchsticks to create different patterns, helping them grasp abstract algebraic ideas in a more tangible way.
• Visual Learning: Creating patterns with matchsticks allows students to visually observe the relationships between numbers and symbols. This visual representation aids in developing a conceptual understanding of algebraic expressions, making the learning process more accessible.
• Hands-On Exploration: Students can actively engage with the matchsticks, arranging them to form various patterns that represent mathematical expressions. This hands-on exploration promotes a kinesthetic learning experience, catering to different learning styles and enhancing comprehension.
• Connection to Symbols: By using matchsticks to represent numbers and symbols, students can bridge the gap between concrete objects and abstract algebraic expressions. This step is crucial in helping students transition from simple arithmetic to understanding the foundational principles of algebra.
• Pattern Recognition: Forming patterns with matchsticks encourages students to recognize and identify numerical relationships, paving the way for understanding variables, equations, and algebraic expressions. It lays the groundwork for more advanced algebraic concepts in later grades.

In summary, the use of matchsticks offers a dynamic and interactive approach to introducing algebra to class VI students, fostering a deeper understanding of abstract mathematical concepts through hands-on exploration and visual representation.

Using real life examples where ideas of ratio and proportion are used, such as in cooking, sewing clothes, and purchasing goods - encourages students to understand concepts through practical, real-world applications, facilitating an active learning process. 

Key Points

• Cooking: Recipes often involve ratios and proportions. For example, if a recipe calls for 2 cups of flour for every 1 cup of sugar, this is a ratio of 2:1 (flour to sugar). If a student wants to make a half or double batch, they would need to adjust the amounts of flour and sugar proportionally.
• Sewing clothes: When sewing clothes, different pieces need to be cut in specific proportions to each other to ensure a correct fit. For example, the length of a shirt sleeve might need to be a certain ratio to the circumference of the wrist opening.
• Purchasing goods: Suppose a student is buying fruits. If apples cost $2 per pound and oranges cost $3 per pound, students could explore questions like: "How many pounds of apples could you buy for the same price as 1 pound of oranges?" This involves understanding and applying ratios.

Hence, it can be concluded that option 1 is the correct answer.

A mixed fraction consists of a whole number and a proper fraction (the numerator is less than the denominator).

Key Points

• For example, in 2 1/3, '2' is the whole number and '1/3' is the proper fraction.
• An improper fraction, however, has a numerator that is greater than or equal to its denominator, like 7/3.
• Therefore, the main distinction lies in the inclusion of a whole number in mixed fractions, while improper fractions only consist of a numerator that's equal to or exceeds the denominator.

Hence, it can be concluded that option 3 is the correct answer.

When students encounter algebraic concepts through real-world situations, it helps them understand the practical application of what they're learning.

Key Points

• This can make abstract concepts more concrete and easier to understand.
• For instance, a problem might ask students to figure out how much they would need to save each week from their allowance in order to buy a desired item.
• This problem involves variables (the unknown amount to save), and solving it would require understanding and applying algebraic concepts.
• Solving mathematical problems based on a daily life approach also helps students see the relevance of algebra, motivating them to learn.
• When they can see how algebra is used in everyday situations, it can feel less like an abstract concept and more like a useful tool. This can help reduce anxiety and increase engagement with the subject.

Hence, it can be concluded that option 3 is the correct answer.

Problem-solving skills involve the ability to analyze a given situation, identify the relevant information, and apply the appropriate techniques or knowledge to arrive at a solution.

Key Points

In this scenario, Mr. Chander's question is focused on assessing students' recall and reproduction skills. Let's break down the components:

• Recall Skill: Students are expected to remember the formula for calculating the perimeter of a rectangle. The formula for the perimeter (P) of a rectangle is given by�=2×(length+width)�=2×(length+width)�=2×(length+width)�=2×(length+width)�=2×(length+width)

   P=2×(length+width). This requires recalling the relevant mathematical concept.
  

• Reproduction Skill: Once the formula is recalled, students need to reproduce the correct calculation by plugging in the given dimensions. In this case, the length is 5 units, and the width is 7 units. Therefore, the students need to apply the formula: �=2×(5+7)�=2×(5+7)�=2×(5+7)�=2×(5+7)�=2×(5+7)

   P=2×(5+7) to reproduce the correct perimeter value.
  

This type of question assesses the fundamental ability of students to remember mathematical concepts (recall) and apply them correctly in specific situations (reproduction). It is more focused on testing foundational knowledge and basic problem-solving skills related to the given mathematical concept.

Providing similar questions for practice until the child solves them correctly, may seem like a reasonable approach to help a child overcome misconceptions in mathematics. 

Key Points

• Merely repeating similar questions without addressing the underlying misconceptions fails to promote conceptual understanding.
• It overlooks the fact that the child may continue to solve the questions incorrectly due to a flawed understanding of the underlying principles.
• Without intervention to address the specific misconceptions, the child may continue to make the same errors repeatedly.
• Effective strategies involve diagnosing misconceptions, providing targeted explanations, and offering a variety of examples in different contexts to deepen understanding and promote meaningful learning.

Hence, it can be concluded that option 2 is the correct answer.

Incorporating mathematics into everyday life helps children see the relevance and practical application of mathematical concepts outside the classroom.

Key Points

• By connecting mathematics to real-world situations, children can develop a deeper understanding of how math is used in various contexts.
• This approach enhances their perception of mathematics as a useful and meaningful subject, rather than something confined to the pages of a textbook.
• It allows children to explore and apply mathematical principles in authentic situations, fostering critical thinking, problem-solving skills, and mathematical reasoning.
• By integrating mathematics into everyday life, children can develop a stronger foundation and a more positive attitude towards the subject.

Hence, it can be concluded that option 3 is the correct answer.

The correct answer is acidic, basic, acidic.

Concept:

Acid:

• The substances which have a sour taste are called acids.
• They turn blue litmus red.
• They easily give away H+ ions.
• Examples - HCl, H2SO4.

Base:

• The substances which have a bitter taste are called bases.
• They turn red litmus blue.
• They easily give away 0H- ions.
• Examples - NH4OH, NaOH.

Explanation:

Acid-Base Indicators: The chemicals that are used to determine whether a given sample of element or compound is acidic, basic or neutral are called Acid-Base indicators.

• Solution A: Turmeric shows no change and Phenolphthalein is colourless, indicating an acidic solution.
• Solution B: Turmeric turns reddish-brown and Phenolphthalein turns pink, indicating a basic solution.
• Solution C: Turmeric turns yellow and Phenolphthalein is colourless, indicating an acidic solution.

Additional Information Some natural indicators are -

The correct answer is (B) and (C).

Concept:

Extinguishing fire :

• When there is any fire breakout water is poured on the fire.
• Water cools the combustible material so that its temperature is brought below its ignition temperature.
• This prevents the fire from spreading.
• Water vapors also surround the combustible material, helping in cutting off the supply of air
• Hence the fire is extinguished.

Explanation :

• The most common fire extinguisher is water.
• But water works only when things like wood and paper are on fire.
• If electrical equipment is on fire, water may conduct electricity and harm those trying to douse the fire.
• Water is also not suitable for fires involving oil and petrol.
• As water, sinks below the oil, it keeps burning on the top.
• For fires involving electrical equipment and inflammable materials like petrol, carbon dioxide (CO2 ) is the best extinguisher.
• CO2, being heavier than oxygen, covers the fire like a blanket.
• Since the contact between the fuel and oxygen is cut off, the fire is controlled.

The correct answer is Increase in area of contact reduces pressure exerted.

Concept:

Pressure:

• Pressure refers to the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
• The SI unit is the Pascal (pa).
• The formula for pressure is:
• P = F / A
• The pressure is dependent on the area over which the force is acting.
• The pressure can be decreased or increased without any change in the force.
• The force applied is constant if the surface becomes smaller, the pressure increases, and vice versa.

Explanation:

• The weight of a bag is the force with which it is pulled towards the earth.
• The shoulder carries a bag that exerts a force that is equal to its weight.
• So, using a large and wide strap of bags ensures that the same weight (Force) is transferred to the shoulder through the large area of the strap.
• For the same force, pressure ∝ 1 / area. Hence, as the area increases the pressure produced is less.

The correct answer is A > D > C > B.

Concept:

Refraction of Light:

• When a ray of light propagating in a medium enters the other medium, it deviates from its path.
• This phenomenon of change in the direction of propagation of light at the boundary, when it passes from one medium to another medium, is called the refraction of light.
• When a ray of light enters from a rarer medium to a denser medium (air to water) it deviates towards the normal drawn on the boundary of two media at the incident point.
• The entity that doesn't change is the frequency.
• The entity that changes are wavelength and velocity.
• The refractive index is also equal to the velocity of light c of a given and the wavelength in empty space divided by its velocity v in a substance.
• Thus, Velocity, Wavelength & Refractive index change when light travels from one medium to another but Frequency remains unchanged.
• Similarly, in passing from denser to rarer medium, a ray deviates away from the normal.
• If the light is incident normally on the boundary, i.e. parallel to normal, it enters the second medium undefeated.

Explanation:

• The optical density of a medium is inversely proportional to the speed of light in that medium.
• If the speed of light increases as light travels from medium A to medium B, then medium B must be less optically dense than medium A. Similarly, if the speed of light decreases as light travels from medium B to medium C, then medium C must be more optically dense than medium B.
• A (most optically dense)
• D
• C
• B (least optically dense)

The Correct answer is Both (A) and (R) are true but (R) is not correct explanation of (A).

Explanation:

• Venus is indeed hotter than Mercury, despite being farther from the Sun. The reason for this lies in the atmospheric conditions on Venus.
• Venus has a thick atmosphere composed mainly of carbon dioxide (around 96%), which creates a greenhouse effect.
• The greenhouse effect traps heat in the atmosphere, causing Venus to have an extremely high surface temperature.
• Venus rotates from east to west, which is known as retrograde rotation. This means that if you were observing Venus from above the Sun's North Pole, you would see Venus rotating in the opposite direction of most other planets in our solar system. Most planets, including Earth, have a prograde rotation, which is from west to east.

The Correct answer is A - Lemon, B - Lactic acid, C - Formic acid, D - Toilet cleaner

Explanation:

• Naturally occurring acids occur naturally in foods.
• Food acids are the important acids found in natural food products that give them a distinct flavor or a tinge.
• The human body tends to react differently to different types of food acids.
• There are different types of food acids like citric acid, malic acid, and tartaric acid that are naturally occurring food acids.
• Citric acid is commonly found in citrus fruits such as oranges, lemons, and tomatoes.
• Lactic acid is commonly produced during the fermentation process in curd
• Ant's sting injects formic acid,
• hydrochloric acid (HCl) is acids found in toilet cleaners

The correct answer is Sand, tap water, blood, air.

Concept:

A mixture contains more than one substance or element or compound mixed in any proportion.

• There are 2 types of mixtures-
• Homogenous mixture
• Heterogenous mixture
• A homogenous mixture has the same proportions of its compound in a sample.
• A heterogeneous mixture has different proportions of its compound in a sample.

Explanation:

Homogenous Mixtures:

• Those mixtures in which the substances are completely mixed together and are indistinguishable from one another are called homogeneous mixtures.
• A homogeneous mixture is a mixture in which the composition is uniform throughout the mixture.
• Many homogeneous mixtures are commonly referred to as solutions.
• Some examples of homogeneous mixtures (or solutions) are Sugar solution, Salt solution, Copper sulfate solution, Seawater, Alcohol and water mixture, Petrol and oil mixture, Soda water, etc.

Heterogeneous mixture:

• A heterogeneous mixture is a mixture with a non-uniform composition that contains components in different phases.
• The composition varies from one region to another with at least two phases that remain separate from each other, with clearly identifiable properties.
• Heterogeneous mixtures contain particles that retain their chemical properties when they are mixed and can be distinguished after they are mixed.
• The components of heterogeneous mixtures can be separated by the filtration of chemical procedures.
• The two types of heterogeneous mixtures are suspensions and colloids.
• Sugar and sand form a heterogeneous mixture. If you look closely, you can identify tiny sugar crystals and particles of sand.
• Sand is a solid substance. Tap water is a liquid substance.
• Blood is a complex mixture of cells, proteins, and other components found in animals. Air is a gaseous mixture primarily composed of nitrogen, oxygen, carbon dioxide, and other gases.

The correct answer is they are more ductile than metals.

Concept:

• Alloys: An alloy is a combination of a metal with at least one other metal or nonmetal.
• The combination must be part of a solid solution, a compound, or a mixture with another metal or nonmetal in order for it to be considered an alloy.
• The most common way to combine metals into an alloy is by melting them, mixing them together, and then allowing them to solidify and cool back to room temperature.

Explanation:

• Alloys do not necessarily have higher melting points than their constituent metals. An alloy is a mixture of two or more elements, where at least one is a metal. When metals combine to form an alloy, the final product’s characteristics—including its melting point—depend on the properties and ratios of the combined elements.
• ​ Some alloys, such as solder (an alloy of lead and tin), have lower melting points compared to their constituent metals to serve their specific purpose (in this case, to melt and flow into joints between metal workpieces).
• However, it's important to note that some alloys can have higher melting points, but it's not a blanket rule for all alloys.
• Hence the correct option is 3.

The Correct answer is (A) - (iii), (B) - (ii), (C) - (iv), (D) - (i)

Concept:

• The organisms which cannot be seen through the naked eye are called microorganisms.
• Microorganisms are classified into four major groups. These groups are bacteria, fungi, protozoa, and some algae.
• Viruses are also microscopic.
• Microorganisms are both beneficial as well as harmful.

Explanation:

• Microorganisms are harmful in many ways.

Some microorganisms cause diseases in human beings, plants, and animals.

• Such disease-causing microorganisms are called pathogens.
• On the basis of these pathogens, diseases can be categorized as - Viral diseases, Bacterial diseases, Nematode diseases, etc.
• Some of the viral diseases include - Measles, Chickenpox, Polio, Common cold, AIDS, etc.
• Hepatitis A is an inflammation of the liver caused by the hepatitis A virus (HAV). The virus is primarily spread when an uninfected (and unvaccinated) person ingests food or water that is contaminated with the faces of an infected person

Common Human Diseases are caused by Microorganisms.

The Correct answer is Pancreas, insulin, diabetes, sugar, digestion.

Explanation:

• Pancreas: The pancreas is both an exocrine and endocrine gland in human beings. It has specialized cells called Islets of Langerhans that produce hormones.
• Insulin: The pancreas produces insulin hormone. Insulin plays a crucial role in regulating blood sugar levels by allowing cells to take in glucose from the bloodstream.
• Diabetes: Insufficient production or ineffective utilization of insulin by the body leads to a condition called diabetes. In diabetes, the person may have high blood sugar levels, and the body may not be able to properly regulate glucose.
• Sugar (glucose): In diabetes, when blood sugar levels are high, the kidneys may not be able to reabsorb all the glucose and it may be excreted in the urine. This can result in the person excreting sugar (glucose) in their urine.
• Digestion: The exocrine function of the pancreas is to aid in the process of digestion. It produces and releases digestive enzymes into the small intestine, which help break down carbohydrates, proteins, and fats.