Mathematics and Science PYQs

When observing children for the addition of algebraic expressions, a focus on understanding the underlying processes and strategies is typically more educationally valuable.

Key Points

• Ms. Anita to look for in the responses of the children would likely be strategies a child is applying and the child's progress towards higher level strategies.
• The development of higher-level thinking and problem-solving skills is key to understanding algebra.
• This approach allows Ms. Anita to gauge the children's understanding, identify misconceptions, and guide them towards more advanced methods, rather than merely assessing how quickly or neatly they are arriving at an answer.
• It aligns with a focus on conceptual understanding and problem-solving skills, which are central to mathematics education.

Hence, we can conclude that Ms. Anita looks for strategies a child is applying and the child's progress towards higher level strategies in the responses of the children.

Students constructing their knowledge refers to a process where learners actively build understanding through experience, exploration, inquiry, and reflection.

Key Points

• The lecture method typically involves a one-way flow of information from the teacher to the students.
• This can limit opportunities for active engagement, questioning, exploration, and reflection, all of which are important for students to construct their own knowledge.
• Activity-based, inductive-deductive, and problem-solving generally involve more interaction, exploration, and critical thinking, allowing students to engage with the material in a deeper and more personalized way.
• These methods encourage students to construct their knowledge by actively processing and applying information, rather than passively receiving it.

Hence, we can conclude that the Lecture method is the least appropriate strategy which will help students in constructing their knowledge.

Van Hieles' theory of geometrical thinking describes five levels of development in children's understanding of geometry.

Key Points

• Level 0: Intuitive thinking. Children at this level understand geometry through their senses and their physical experiences. They can recognize shapes and understand simple spatial relationships.
• Level 1: Visualization. Children at this level can visualize geometric objects and relationships. They can draw shapes and diagrams to help them solve problems.
• Level 2: Analysis. Children at this level can analyze geometric objects and relationships. They can identify properties of shapes and classify them. They can also use logic to solve problems.
• Level 3: Deduction. Children at this level can deduce general properties of geometric shapes and prove theorems. They can use formal logic to justify their conclusions.
• Level 4: Rigor. Children at this level understand the axioms and postulates of geometry. They can use these axioms and postulates to prove theorems and to justify their conclusions.

Hence, we can conclude that at Level 3 he/she is able to deduce general properties of geometrical shapes and is able to prove theorems.

Conservation in this context refers to the understanding that the length being measured remains the same regardless of the starting point on the ruler.

Key Points

• The child's statement, "Any point on my scale/ruler can be taken as the starting point," demonstrates an understanding that measurement is a relative concept and that the actual starting point on the ruler doesn't matter, as long as the same unit length is being used to measure the object.
• The child is able to understand that the length of a line segment does not depend on where you start measuring it.
• This is an important concept in measurement, and it is called conservation of length.
• This is a more advanced understanding of the concept of measurement and shows that the child has moved beyond a rigid attachment to the "0" mark on the ruler.

Hence, we can conclude that the child is able to conserve the idea of measurement.

Gender and caste are social constructs that do not have any bearing on a person's ability to understand or solve mathematical problems.

Key Points

The ability of mathematics involved:

• Practicing mathematical concepts helps to solidify understanding and improve problem-solving skills.
• Understanding mathematical concepts is essential for solving mathematical problems.
• Visualization of mathematical concepts can help to make problems more concrete and easier to understand.

Hence, we can conclude that the ability to solve mathematical questions is independent of Gender and caste.

The nature of mathematics refers to its essential characteristics and underlying principles. Mathematics is both a field of study and a tool used across disciplines. 

Key Points

• Mathematics deals with abstract concepts and structures that are not tied to physical objects, even though concrete examples often help us understand those concepts.
• Mathematical thinking is founded on logic. Deductive reasoning, in particular, is used to derive conclusions that necessarily follow from a set of premises or axioms.
• Mathematical knowledge builds on itself. Basic concepts and skills often form the foundation for understanding more complex ideas.
• Mathematics uses a specific and formal language, including symbols and notation, to express ideas precisely.

​Hence, we can conclude that primary-level mathematics is concrete and does not require abstraction is not correct with regard to the nature of mathematics.

Proportional thinking is the ability to see how two or more things are related to each other in terms of their size or quantity.

Key Points

• In this case, Raman was able to see that the interior angles of a triangle add up to 180° and that the three angles are in the ratio 2 ∶ 3 ∶ 4.
• He was then able to use this information to calculate the measurement of each angle.
• Counting ability is the ability to count objects or numbers. This is not the ability that Raman showed in his response.
• Ability of measurement is the ability to measure the size or quantity of something. This is not the ability that Raman showed in his response.
• Rote memorization is the ability to memorize something without understanding it. This is not the ability that Raman showed in his response.

Hence, we can conclude that Raman showed Proportional thinking through his response.

Culture and context play an important role in constructing mathematical knowledge.

Key Points

• In some cultures, mathematics is seen as a very abstract and formal subject, while in other cultures, it is seen as a more concrete and practical subject.
• The context in which mathematics is learned can also play a role in how it is understood. For example, if students are learning about fractions in the context of cooking, they are more likely to understand the concepts involved.
• Mathematical knowledge can be created in primary classes through observation of patterns and generalizations.
• Mathematical learning is also a social process involving dialogue.
• A good mathematics teacher can enhance the interest of students in mathematics.

Hence, we can conclude that Culture and context have no role in constructing mathematical knowledge is incorrect regarding mathematics teaching-learning.

Standardized tests are typically designed to measure a student's knowledge of a particular subject, and they are often used to make decisions about a student's placement or progress.

Key Points

• However, standardized tests can be biased against certain groups of students, such as students with disabilities or students from minority groups.
• Additionally, standardized tests often do not measure the full range of mathematical skills that students need to be successful.
• ICT tools can be used to create interactive simulations, to provide visual representations of mathematical concepts, and to allow students to collaborate on mathematical projects.
• Tactile graphs and abacus can be used to help students visualize concepts such as fractions and decimals.
• The use of formative and summative tests can help teachers to assess student learning and to identify areas where students need additional support.

Hence, we can conclude that the use of standardized tests is the least effective pedagogical tool for an inclusive mathematics classroom.

Mathematics is a deductive science, which means that it is based on axioms and logical reasoning. 

Key Points

• Experimentation is a part of the scientific method, which is used to test hypotheses in the natural sciences.
• While experimentation can be used to test mathematical models, it is not a fundamental part of mathematics itself.
• Deductive reasoning is a type of reasoning that uses general principles to reach specific conclusions. This is a core part of mathematics, as it is used to prove theorems and to solve problems.
• Logical reasoning is a more general type of reasoning that uses logic to reach conclusions. This is also an important part of mathematics, as it is used to justify mathematical arguments.
• Axioms are statements that are assumed to be true without proof. They are the foundation of mathematics, as they provide the basis for all mathematical reasoning.

Hence, we can conclude that experimentation is least related to mathematics.

The correct answer is Both S1 and S2 are true and S2 is the correct explanation for S1.

Explanation:

S₁: All Combustion reactions are exothermic reactions.

• This statement is true.
• Combustion reactions are indeed exothermic reactions, meaning they release heat energy.
• This is because, in combustion reactions, a substance reacts with oxygen (usually from the air) to produce combustion products such as carbon dioxide (CO₂) and water (H₂O) while releasing energy in the form of heat and light.
• This release of energy is what characterizes an exothermic reaction.

S₂: Oxygen is added and heat is released in all these reactions.

• This statement is also true.
• In combustion reactions, oxygen is indeed required as one of the reactants.
• For most practical combustion reactions, the oxygen comes from the surrounding air.
• When the fuel combines with oxygen, chemical reactions occur, and heat is released as a byproduct.

Thus, Both S1 and S2 are true and S2 is the correct explanation for S1.

The correct answer is R1 - Double displacement reaction, R2 - Combination reaction.

Explanation:

(R1) Reaction 1: Barium chloride reacts with Sodium Sulphate.

• Barium chloride (BaCl₂) reacts with Sodium Sulphate (Na₂SO₄), resulting in the formation of Barium Sulphate (BaSO₄) and Sodium Chloride (NaCl).
• The exchange of ions between the two reactants indicates a double displacement reaction.
• The general representation of this reaction is:
• AB + CD → AD + CB

(R2) Reaction 2: Magnesium oxide reacts with carbon dioxide.

• Magnesium oxide (MgO) reacts with Carbon dioxide (CO₂), resulting in the formation of Magnesium carbonate (MgCO₃).
• Here, magnesium oxide combines with carbon dioxide to create a single product.
• This type of reaction is known as a combination reaction (a reaction in which two or more reactants combine to form a single product is known as a combination reaction).
• The general representation of this reaction is:
• A + B → AB

The correct answer is S₁ is false but S₂ is true.

Explanation:

Changes can be of two types, physical and chemical.

Physical change:

• A change in which a substance's physical properties change is referred to as a physical change.
• In most cases, a physical change can be reversed. Thus, physical changes are not always reversible.
• No new products are formed in physical changes.
• The conversion of steam to water droplets is a physical change because it is reversible.

Chemical change:

• When one chemical substance is transformed into one or more different substances, this is referred to as a chemical change.
• A chemical reaction is another term for a chemical change.
• In most cases, a chemical change is irreversible.
• Rotting of bananas, Metabolism of food in the body, and Cooking an egg are all examples of chemical changes that are irreversible.

The correct answer is a - iii, b - ii, c - i.

Explanation:

A candle flame consists of three different zones.

Outermost zone

• The outermost zone is also known as the non-luminous zone.
• It is the hottest of the zones, with a temperature of around 1400°C.
• The colour of the outermost zone is blue due to the complete combustion of wax as there is a sufficient supply of air around it.

Middle zone

• The middle zone is also known as the luminous zone.
• It is a moderately hot zone of candle flame and has a temperature of around 1200°C.
• The colour of the middle zone is yellow due to the partial combustion of wax as there is an insufficient supply of air in this zone.

Innermost zone

• The innermost zone is also known as the dark zone.
• It is the least hot zone, with a temperature of approximately 600°C.
• The innermost zone is black in colour and contains unburnt wax vapours.

 

The correct answer is Copper.

Explanation:

• The metal reactivity series governs metal reactivity.
• Metals placed above hydrogen react with dilute acids to form salt, whereas metals placed below hydrogen do not react with dilute acids because they are less reactive than hydrogen and thus cannot displace hydrogen from dilute acids.
• Copper metal does not react with dilute Hydrochloric acid because it is placed below hydrogen in the metal reactivity series, and thus it cannot displace hydrogen from dilute hydrochloric acid.

Additional InformationIron

• Iron metals do indeed react with dilute hydrochloric acid.
• The reaction between iron and hydrochloric acid is a classic example of a metal-acid reaction.

Fe (s) + 2HCl (aq) → FeCl₂ (aq) + H₂ (g)

Magnesium

• When magnesium is treated with dilute hydrochloric acid, it forms magnesium chloride and emits hydrogen gas.

Mg (s) + 2HCl (aq) →  MgCl2 (aq) + H2(g)

Aluminum

• At room temperature, aluminum reacts with diluted hydrochloric acid.
• Aluminum chloride and colourless hydrogen gas are produced when the metal aluminum dissolves in hydrochloric acid.
• The reaction between aluminum and hydrochloric acid is irreversible.

2Al + 6HCl → 2AlCl3 + 3H2

Concept:

• Soil is arranged in distinct layers and each layer is different from subsequent ones in terms of physical properties, colour, and texture.
• There are five horizons in soil, such as O, A, B, C, and R.
• O horizon starts with the top layer of soil and while the other horizons are below it.
• R horizon is the deepest horizon, representing the bedrock at the bottom of the soil.

Explanation:

Statement 1: Growth and branching of roots in A and B horizons are advantageous for the absorption of water and minerals.

• A horizon is made up of organic matter, such as leaf litter and decaying animal remains.
• A horizon is rich in humus.
• B horizon contains clay and has rich deposits of minerals.
• That is why the growth and branching of roots in A and B horizons are advantageous for the absorption of water and minerals.
• Thus, this statement is true.

Statement 2: A and B horizons are rich in water, minerals & humus. 

• A and B horizons are rich in water, minerals, and humus.
• Humus enhances soil texture, promotes soil aeration and water-holding capacity, and delivers nutrients to growing plants.
• This soil layer also contains minerals. Humus and minerals enrich the soil and favour plant growth.
• Thus, this statement is true.

Hence, the correct option is (1).

The correct answer is Only (B).

Explanation:

• Inorganic impurities are substances that do not contain carbon-hydrogen (C-H) bonds and are not derived from living organisms.
• Inorganic impurities include phosphates, nitrates, and metals.
• Phosphate is considered an inorganic impurity in sewage.
• These impurities are removed by using bacteria.

Additional InformationUrea

• Urea is an organic compound containing carbon-hydrogen (C-H) bonds.
• Urea is an example of nitrogenous fertilizer.

Pesticides

• Pesticides are organic compounds used to control pests in the field.
• Only organic pesticides are found in sewage.

Vegetable wastes

• Vegetable waste is totally organic material found in sewage.
• Therefore it is not considered inorganic impurities.

Concept:

• Sexual reproduction involves a male gamete and female gametes fertilized to form a zygote.
• Sexual reproduction brings variation among offspring and offspring are different from parents, genetically and physically.
• Plants reproduce sexually and asexually as well, but the majority of flowering plants reproduce sexually.
• Sexual reproduction in plants takes place in flowers.
• Flower is the reproductive whorl that contains male and female reproductive parts.

Important Points

Statement (A) Two plants are essential for sexual reproduction.

• Two plants are not essential for sexual reproduction.
• Because plants can be both unisexual and bisexual.
• The flowers have only male or female reproductive parts, i.e., either stamens or carpels present, are known as unisexual flowers. E.g., Cucumber, Maize, Papaya, etc.
• ​The flowers contain both the male and female reproductive parts that is stamens and carpels, and are known as bisexual flowers. E.g., Mustard, Pea, Rose, etc.
• Thus, this statement is false.

Statement (B) Only insects are agents of pollination.

• Pollination is a process in which pollen grains are picked from an anther part of a flower and transferred to the stigma of the flower.
• There are two types of pollination self-pollination and cross-pollination.
• The self-pollinating plants do not need a pollinator for pollination.
• Self-pollination happens when pollen grains fall straight from the anther into the stigma of the flower.
• In cross-pollination, the transfer of pollen grains from the anther of the flower into the stigma of another flower.
• This requires different types of biotic and abiotic pollinators like animals, birds, wind, insects, water, etc.
• Thus, this statement is false.

Statement (C) Fertilization occurs only after pollination.

• Fertilization is the process of fusion of nuclei of the male gamete- sperm and the female gamete- ovary to form a zygote.
• During pollination, pollen grains are transferred from an anther to the stigma of the flower.
• Pollination starts when pollen grains from the respective flowers settle on the stigma and form a pollen tube the length of the style.
• When the pollen tube formation is completed, the pollen grain begins to convey sperm cells from the pollen grain to the ovary.
• After that fertilization starts and fusion of gametes occurs.
• Thus, this statement is true.

Statement (D) Plants are obtained from seeds.

• Seeds are developed from the ovules and plants are obtained from them.
• Seeds are germinated to produce whole plants.
• Seeds are enclosed by fruits, that are ripened ovary.
• Thus, this statement is true.

Hence, the correct option is 4.

Key Points

• The respiratory system involves gaseous exchange through inhalation and exhalation.
• The primary function of the system is to take O₂ into the body and expel CO₂ from the body.
• Different organisms have different respiratory organs, mammals and birds have lungs, fish respires through gills, amphibians respire through the skin, gills, and lungs, and reptiles by skin and lungs.
• Invertebrates also have different types of respiratory organs, viz. body surface, spiracles, Malpighian tubules, tracheal system, gills, etc.

Explanation:

• On the basis of the respiratory organ, snail differs from grasshopper, cockroach, and ant.
• In snails, feather-like gills are present inside the mantle cavity.
• Snails breathe in and out through the pneumostome or the breathing pore.
• The mantle cavity is the space between the visceral hump and the mantle of the snail.
• Snail belongs to the class Gastropoda of the phylum Mollusca.

Additional Information

• Grasshoppers, cockroaches, and ants belong to the class Insecta of the phylum Arthropoda.
• They have a tracheal system to respire that allows the transport of oxygen directly to each cell in the body.

Hence, the correct option is (3) Snail.

Key Points

• The kidney is the primary excretory organ.
• It is a bean-shaped organ that is located below the rib cage on each side of the spinal cord.
• The kidney aids in the filtration of blood before the formation of urine.
• Nephron is the structural and functional unit of the kidney.
• Nephrons comprise the renal corpuscle and renal tubules such as proximal convoluted tubules, distal convoluted tubules, the loop of Henle, and collecting ducts.
• The renal corpuscle consists of a glomerulus.
• The fundamental function of the nephron is to remove all waste products from the blood, including solid wastes and excess water.

Explanation:

• The kidney plays an important role in the filtration and purification of blood.
• The urine formation involves three processes namely, glomerular filtration, reabsorption, and secretion, that take place in different parts of the nephron.
• The correct sequence of the process is 
• (D) Blood containing useful & harmful substances reaches the kidney for filtration.
• (C) Useful Substances are absorbed back into the blood.
• (E) Wastes dissolved in water are filtered out as urine in the kidneys.
• (B) Ureters carry urine to the urinary bladder.
• (A) Urine stored in the urinary bladder is passed out through the urinary opening at the end of the urethra.

Hence, the correct option is (3) (D) → (C) → (E) → (B) → (A)