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Thinka Jun 2024 (V2) Cambridge International A Level-Style Mock — Sciences - Co-ordinated (Double) (0654)

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An original Thinka practice paper modelled on the structure and difficulty of the Jun 2024 (V2) Cambridge International A Level Sciences - Co-ordinated (Double) (0654) paper. Not affiliated with or reproduced from Cambridge.

Section 1: Biology

Answer all questions in this section. Questions cover cell processes, transport, physiology, genetics, and ecology.
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PastPaper.question 1 · structured
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A student is studying different methods of reproduction in organisms. (a) Define the term asexual reproduction and state one advantage of this type of reproduction to a plant species. [3] (b) In human sexual reproduction, male gametes are produced in the testes. Describe the pathway of a sperm cell from where it is produced until it leaves the male body. [4] (c) Describe how the structure of a mature sperm cell is adapted to its function of reaching and fertilizing an egg cell. [3]
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(a) Asexual reproduction is a process resulting in the production of genetically identical offspring from one parent. An advantage is that it is rapid, allowing a species to colonise an area quickly without needing a partner. (b) Sperm are produced in the testes, then pass into the sperm duct (vas deferens). During ejaculation, they travel along the sperm duct, receive fluids from the prostate gland or seminal vesicle, and then enter the urethra, through which they leave the body. (c) Adaptations include: a flagellum (tail) for swimming towards the egg; many mitochondria in the midpiece to provide energy or ATP for movement; and an acrosome containing digestive enzymes in the head to penetrate the outer layer of the egg.

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(a) Definition: production of genetically identical offspring [1 mark] from one parent [1 mark]. Advantage: rapid reproduction / allows rapid colonisation / only requires one parent (no mate needed) / conserves energy [1 mark]. (b) Pathway: Testes to sperm duct (vas deferens) [1 mark]; glands (prostate/seminal vesicle) add fluid [1 mark]; urethra [1 mark]; penis [1 mark]. (c) Adaptations (any three): Flagellum/tail for swimming [1 mark]; Mitochondria to release energy/for respiration [1 mark]; Acrosome containing enzymes to digest egg membrane/jelly coat [1 mark]; Haploid nucleus containing half the genetic material [1 mark]. Max 3 marks.
PastPaper.question 2 · structured
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(a) Adrenaline is a hormone secreted in 'fight or flight' situations. Describe how adrenaline is transported around the body and state two of its physiological effects. [3] (b) Complete the comparison of nervous and endocrine control systems by describing: (i) the difference in their speed of transmission, (ii) the difference in the duration of their effects. [4] (c) Plants also respond to stimuli. Define gravitropism and explain why a positive gravitropic response is beneficial to a plant root. [3]
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(a) Adrenaline is secreted by the adrenal glands directly into the blood plasma, which transports it throughout the body. Its physiological effects include increased heart rate, increased breathing rate, and widened pupils. (b) (i) Nervous transmission is extremely rapid because electrical impulses travel along neurones, while endocrine transmission is slower because hormones are carried by the blood. (ii) Nervous response is short-lived, while hormone response is typically longer-lasting. (c) Gravitropism is a response in which parts of a plant grow towards or away from gravity. A positive gravitropic response in roots causes them to grow downwards into the soil, which is beneficial because it anchors the plant firmly and allows the roots to reach water and mineral ions.

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(a) Transport: dissolved in blood / blood plasma [1 mark]. Effects (any two): increased heart rate / increased breathing rate / increased blood glucose / pupil dilation [2 marks]. (b) (i) Speed: nervous transmission is fast/rapid [1 mark] whereas hormonal/endocrine transmission is slow [1 mark]. (ii) Duration: nervous effect is short-lived/instantaneous [1 mark] whereas hormonal/endocrine effect is long-lasting [1 mark]. (c) Gravitropism definition: a growth response to gravity / growing towards or away from gravity [1 mark]. Benefit (any two): anchors the plant firmly in the soil [1 mark]; grows downwards to find/absorb water [1 mark]; grows downwards to find/absorb mineral ions [1 mark]. Max 2 marks for benefits.
PastPaper.question 3 · Data Interpretation
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An investigation was carried out to study phototropism in oat coleoptiles. Five groups of coleoptiles were set up under unilateral light (light from one side only) for 24 hours. The treatments and results are shown below: Group A (Untreated control): Mean curvature = 25 degrees, Mean change in length = 6.2 mm. Group B (Tip removed): Mean curvature = 0 degrees, Mean change in length = 1.1 mm. Group C (Tip covered with an opaque cap): Mean curvature = 0 degrees, Mean change in length = 5.8 mm. Group D (Tip covered with a transparent cap): Mean curvature = 24 degrees, Mean change in length = 6.0 mm. Group E (Base covered with an opaque sleeve): Mean curvature = 26 degrees, Mean change in length = 6.1 mm. (a) State the response shown by the untreated control group (Group A) to unilateral light. [1] (b) (i) Describe and explain what can be concluded from the results of Groups A, B, and C about the site of light detection and the site of growth. [3] (ii) Explain the purpose of including Group D in this investigation. [2] (c) Auxin is a plant hormone. Explain the mechanism by which auxin causes the curvature observed in Group A. [4]
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Part (a): Positive phototropism (or phototropism). Part (b)(i): Group C (tip covered with an opaque cap) did not bend, showing that the tip is the site of light detection. Group B (tip removed) did not grow significantly, indicating the tip produces a growth-promoting substance. Group C grew well but did not bend, showing that growth occurs below the tip, but bending requires light detection by the tip. Part (b)(ii): Group D acts as a control for the physical presence of the cap, showing that the cap itself does not physically prevent bending as long as light can penetrate. Part (c): Auxin is synthesized in the tip of the shoot. Under unilateral light, auxin diffuses downwards and accumulates on the shaded side. A higher concentration of auxin on the shaded side stimulates greater cell elongation on that side, causing the shoot to bend towards the light.

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Part (a): Positive phototropism [1 mark] (do not accept gravitropism). Part (b)(i): The tip detects light because Group C (opaque cap) shows 0 curvature [1 mark]; growth occurs below the tip because Group C grows (5.8 mm) [1 mark]; the tip produces growth hormone because Group B (no tip) shows almost no growth [1 mark]. Part (b)(ii): To act as a control for the cap's presence [1 mark]; to show the cap does not mechanically prevent bending [1 mark]. Part (c): Auxin produced in tip [1 mark]; diffuses down shoot [1 mark]; accumulates on shaded side [1 mark]; causes cell elongation [1 mark] leading to bending towards light [1 mark] (max 4 marks).
PastPaper.question 4 · Data Interpretation
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An investigation was conducted to study the effects of temperature and water availability on the germination of wild mustard (Sinapis arvensis) seeds. Five batches of 100 seeds were incubated at different temperatures for 7 days under two treatments: Treatment 1 (seeds kept in moist conditions) and Treatment 2 (seeds kept in dry conditions). The results are shown below: At 5 degrees C, Treatment 1 germination = 5 percent, Treatment 2 = 0 percent. At 15 degrees C, Treatment 1 germination = 45 percent, Treatment 2 = 0 percent. At 25 degrees C, Treatment 1 germination = 85 percent, Treatment 2 = 0 percent. At 35 degrees C, Treatment 1 germination = 92 percent, Treatment 2 = 0 percent. At 45 degrees C, Treatment 1 germination = 12 percent, Treatment 2 = 0 percent. (a) Identify the independent variable and the dependent variable in this investigation. [2] (b) Using the data for Treatment 1, describe the effect of temperature on the germination of the seeds. [3] (c) State three environmental conditions required for seed germination. Explain how the data supports the requirement of one of these conditions. [3] (d) Explain, in terms of enzymes, why the germination percentage in Treatment 1 decreased significantly when the temperature was increased from 35 degrees C to 45 degrees C. [2]
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Part (a): Independent variable is temperature (or water availability). Dependent variable is germination percentage. Part (b): As temperature increases from 5 to 35 degrees C, germination increases from 5 percent to 92 percent. The optimum temperature is 35 degrees C. Above 35 degrees C, germination decreases to 12 percent at 45 degrees C. Part (c): The three conditions are water, oxygen, and suitable temperature. The data supports the requirement of water because in Treatment 2 (dry), no seeds germinated (0 percent) at any temperature, while in Treatment 1 (moist) germination occurred. Part (d): High temperature (45 degrees C) denatures enzymes needed for germination, changing the shape of their active sites so they can no longer function.

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Part (a): Independent variable: temperature / moisture treatment [1 mark]. Dependent variable: germination percentage [1 mark]. Part (b): Germination increases from 5 to 35 degrees C [1 mark]; optimum germination is at 35 degrees C [1 mark]; germination decreases above 35 degrees C [1 mark]. Part (c): Water, oxygen, suitable temperature [1 mark for all three]; Treatment 2 had 0 percent germination [1 mark]; showing water is essential [1 mark]. Part (d): Enzymes denatured at 45 degrees C [1 mark]; active site changes shape / substrate cannot fit [1 mark].

Section 2: Chemistry

Answer all questions in this section. Questions cover physical, analytical, and organic chemistry, including calculations.
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PastPaper.question 1 · structured
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A student investigates the reaction between magnesium ribbon and dilute sulfuric acid.

(a) Write the balanced chemical equation, including state symbols, for this reaction. [3]

(b) Calculate the mass of magnesium required to produce \(240\text{ cm}^3\) of hydrogen gas, measured at room temperature and pressure (r.t.p.).
[Molar volume of a gas at r.t.p. is \(24.0\text{ dm}^3/\text{mol}\); \(A_r(\text{Mg}) = 24\)] [3]

(c) Calculate the volume, in \(\text{cm}^3\), of \(0.50\text{ mol/dm}^3\) sulfuric acid needed to react completely with the mass of magnesium calculated in (b). [3]

(d) State one visible change that can be observed during this reaction. [1]
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**(a)**
Reactants: \(\text{Mg}\) and \(\text{H}_2\text{SO}_4\)
Products: \(\text{MgSO}_4\) and \(\text{H}_2\)
State symbols: \(\text{Mg(s)}\), \(\text{H}_2\text{SO}_4\text{(aq)}\), \(\text{MgSO}_4\text{(aq)}\), \(\text{H}_2\text{(g)}\)
Full balanced equation: \(\text{Mg(s)} + \text{H}_2\text{SO}_4\text{(aq)} \rightarrow \text{MgSO}_4\text{(aq)} + \text{H}_2\text{(g)}\)

**(b)**
1. Convert the volume of hydrogen gas to \(\text{dm}^3\):
\(240\text{ cm}^3 = \frac{240}{1000} = 0.24\text{ dm}^3\)
2. Calculate the moles of \(\text{H}_2\):
\(\text{Moles of } \text{H}_2 = \frac{0.24\text{ dm}^3}{24.0\text{ dm}^3/\text{mol}} = 0.010\text{ mol}\)
3. From the chemical equation, the mole ratio of \(\text{Mg} : \text{H}_2\) is \(1 : 1\).
Therefore, moles of \(\text{Mg} = 0.010\text{ mol}\).
4. Calculate the mass of \(\text{Mg}\):
\(\text{Mass} = 0.010\text{ mol} \times 24\text{ g/mol} = 0.24\text{ g}\)

**(c)**
1. From the equation, the mole ratio of \(\text{H}_2\text{SO}_4 : \text{Mg}\) is \(1 : 1\).
Therefore, moles of \(\text{H}_2\text{SO}_4 = 0.010\text{ mol}\).
2. Calculate the volume of sulfuric acid in \(\text{dm}^3\):
\(\text{Volume} = \frac{\text{Moles}}{\text{Concentration}} = \frac{0.010\text{ mol}}{0.50\text{ mol/dm}^3} = 0.020\text{ dm}^3\)
3. Convert volume to \(\text{cm}^3\):
\(0.020\text{ dm}^3 \times 1000 = 20\text{ cm}^3\)

**(d)**
Visible changes include: effervescence / bubbles of gas, the magnesium ribbon dissolving / disappearing, or the reaction mixture getting hot.

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(a)
- Correct chemical formulas of reactants and products: \(\text{Mg} + \text{H}_2\text{SO}_4 \rightarrow \text{MgSO}_4 + \text{H}_2\) [1]
- Correctly balanced equation [1]
- Correct state symbols: \(\text{(s)}\), \(\text{(aq)}\), \(\text{(aq)}\), \(\text{(g)}\) [1]

(b)
- Calculate moles of gas: \(\frac{240}{24000} = 0.010\text{ mol}\) [1]
- Deduced mole ratio of 1:1, so moles of Mg = 0.010 mol [1]
- Calculate mass of Mg: \(0.010 \times 24 = 0.24\text{ g}\) [1]

(c)
- Moles of sulfuric acid = 0.010 mol [1]
- Calculate volume in \(\text{dm}^3\): \(\frac{0.010}{0.50} = 0.020\text{ dm}^3\) [1]
- Convert to \(\text{cm}^3\): \(20\text{ cm}^3\) [1] (Allow error carried forward from previous steps)

(d)
- Any one valid visible change: effervescence / bubbles / gas evolved / magnesium dissolves / solid disappears / test tube gets hot [1]
PastPaper.question 2 · structured
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A student titrates \(25.0\text{ cm}^3\) of sodium hydroxide solution, \(\text{NaOH}\), against dilute hydrochloric acid, \(\text{HCl}\), of concentration \(0.15\text{ mol/dm}^3\).

The average titration volume (titre) of hydrochloric acid required for complete neutralization is \(22.0\text{ cm}^3\).

(a) Write the balanced chemical equation for the neutralization reaction. State symbols are not required. [2]

(b) Calculate the number of moles of \(\text{HCl}\) used in the titration. [2]

(c) Determine the concentration of the sodium hydroxide solution in \(\text{mol/dm}^3\). [3]

(d) Calculate the concentration of the sodium hydroxide solution in \(\text{g/dm}^3\).
[\(M_r\) of \(\text{NaOH} = 40.0\)] [3]
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**(a)**
The neutralization of sodium hydroxide by hydrochloric acid produces sodium chloride and water:
\(\text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O}\)

**(b)**
1. Convert the volume of hydrochloric acid from \(\text{cm}^3\) to \(\text{dm}^3\):
\(22.0\text{ cm}^3 = \frac{22.0}{1000} = 0.0220\text{ dm}^3\)
2. Calculate the moles:
\(\text{Moles of HCl} = \text{concentration} \times \text{volume} = 0.15\text{ mol/dm}^3 \times 0.0220\text{ dm}^3 = 0.0033\text{ mol}\)

**(c)**
1. Identify the stoichiometry of the reaction:
From the balanced equation, \(1\text{ mol}\) of \(\text{NaOH}\) reacts with \(1\text{ mol}\) of \(\text{HCl}\).
Therefore, moles of \(\text{NaOH}\) in \(25.0\text{ cm}^3 = 0.0033\text{ mol}\).
2. Calculate the concentration of \(\text{NaOH}\):
\(\text{Volume of NaOH in dm}^3 = \frac{25.0}{1000} = 0.0250\text{ dm}^3\)
\(\text{Concentration} = \frac{\text{Moles}}{\text{Volume}} = \frac{0.0033\text{ mol}}{0.0250\text{ dm}^3} = 0.132\text{ mol/dm}^3\) (or \(0.13\text{ mol/dm}^3\))

**(d)**
1. Use the conversion formula:
\(\text{Concentration in g/dm}^3 = \text{Concentration in mol/dm}^3 \times M_r\)
2. Substitute the values:
\(0.132\text{ mol/dm}^3 \times 40.0\text{ g/mol} = 5.28\text{ g/dm}^3\)

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(a)
- Correct chemical formulas of reactants: \(\text{NaOH} + \text{HCl}\) [1]
- Correct chemical formulas of products: \(\text{NaCl} + \text{H}_2\text{O}\) [1]

(b)
- Conversion of volume to \(\text{dm}^3\): \(\frac{22.0}{1000} = 0.0220\text{ dm}^3\) [1]
- Calculation of moles of \(\text{HCl}\): \(0.15 \times 0.0220 = 0.0033\text{ mol}\) [1]

(c)
- Deducing 1:1 mole ratio, so moles of NaOH = 0.0033 mol [1]
- Conversion of sodium hydroxide volume to \(\text{dm}^3\): \(\frac{25.0}{1000} = 0.0250\text{ dm}^3\) [1]
- Calculate concentration of sodium hydroxide: \(\frac{0.0033}{0.0250} = 0.132\text{ mol/dm}^3\) [1] (Accept \(0.13\text{ mol/dm}^3\))

(d)
- Recognize formula: \(\text{conc in g/dm}^3 = \text{conc in mol/dm}^3 \times M_r\) [1]
- Correct calculation process: \(0.132 \times 40.0\) [1]
- Correct final answer with correct units: \(5.28\text{ g/dm}^3\) [1] (Allow ECF from (c): e.g., if concentration is \(0.13\text{ mol/dm}^3\), then answer is \(5.2\text{ g/dm}^3\))
PastPaper.question 3 · Structured Theory
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A student investigates the reaction between solid copper(II) carbonate and dilute hydrochloric acid.

(a) Write the balanced chemical equation, including state symbols, for this reaction. [3]

(b) In an experiment, the student reacts 6.20 g of copper(II) carbonate, \(\text{CuCO}_3\), with an excess of dilute hydrochloric acid. Calculate the theoretical mass of copper(II) chloride, \(\text{CuCl}_2\), produced in this reaction.
Relative atomic masses (\(A_r\)): \(\text{Cu} = 64\), \(\text{C} = 12\), \(\text{O} = 16\), \(\text{H} = 1\), \(\text{Cl} = 35.5\).
Show your working. [4]

(c) The actual mass of copper(II) chloride obtained by the student is 5.40 g. Calculate the percentage yield of copper(II) chloride. [2]

(d) Suggest one practical reason why the actual yield of copper(II) chloride is less than the theoretical yield. [1]
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(a) The balanced chemical equation with state symbols is:
\(\text{CuCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CuCl}_2\text{(aq)} + \text{CO}_2\text{(g)} + \text{H}_2\text{O(l)}\)

(b) Step 1: Calculate the relative formula mass (\(M_r\)) of \(\text{CuCO}_3\) and \(\text{CuCl}_2\):
\(M_r(\text{CuCO}_3) = 64 + 12 + (3 \times 16) = 124\)
\(M_r(\text{CuCl}_2) = 64 + (2 \times 35.5) = 135\)

Step 2: Calculate the number of moles of \(\text{CuCO}_3\) reacted:
\(\text{Moles of CuCO}_3 = \frac{\text{mass}}{\text{formula mass}} = \frac{6.20}{124} = 0.050\text{ mol}\)

Step 3: Determine the moles of \(\text{CuCl}_2\) formed:
From the balanced equation, \(1\text{ mol}\) of \(\text{CuCO}_3\) produces \(1\text{ mol}\) of \(\text{CuCl}_2\).
Therefore, \(\text{moles of CuCl}_2 = 0.050\text{ mol}\).

Step 4: Calculate the theoretical mass of \(\text{CuCl}_2\):
\(\text{Mass} = 0.050\text{ mol} \times 135\text{ g/mol} = 6.75\text{ g}\).

(c) Percentage yield calculation:
\(\text{Percentage yield} = \frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100\% = \frac{5.40}{6.75} \times 100\% = 80.0\%\)

(d) Acceptable reasons include: loss of product during transfer, filtration, or evaporation; incomplete reaction; or side reactions occurring.

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(a) [3 marks total]
- Correct chemical formulae of reactants and products: \(\text{CuCO}_3 + 2\text{HCl} \rightarrow \text{CuCl}_2 + \text{CO}_2 + \text{H}_2\text{O}\) [1]
- Equation fully balanced [1]
- All state symbols correct: \(\text{CuCO}_3\text{(s)}\), \(\text{HCl(aq)}\), \(\text{CuCl}_2\text{(aq)}\), \(\text{CO}_2\text{(g)}\), \(\text{H}_2\text{O(l)}\) [1]

(b) [4 marks total]
- Correct \(M_r\) values calculated (\(\text{CuCO}_3 = 124\) and \(\text{CuCl}_2 = 135\)) [1]
- Correct conversion of 6.20 g of \(\text{CuCO}_3\) to 0.050 mol [1]
- Deduces 0.050 mol of \(\text{CuCl}_2\) is produced (1:1 ratio) [1]
- Correct theoretical mass of 6.75 g [1]

(c) [2 marks total]
- Correct formula for percentage yield and substitution of values: \(\frac{5.40}{6.75} \times 100\) [1]
- Correct answer: 80.0% (or 80%) [1]

(d) [1 mark total]
- Accept any one valid reason: some product left on the filter paper or beaker / loss during transfer / evaporation / incomplete reaction. Reject: general 'experimental error' / 'human error' (unless specified as spilling).
PastPaper.question 4 · Structured Theory
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Aqueous copper(II) sulfate is electrolysed using inert carbon (graphite) electrodes.

(a) State the visual observation made during this electrolysis at:
(i) the anode (positive electrode) [1]
(ii) the cathode (negative electrode) [1]

(b) Write the ionic half-equation, including state symbols, for the reaction occurring at:
(i) the cathode [2]
(ii) the anode [2]

(c) Explain why the blue color of the copper(II) sulfate solution gradually fades during the electrolysis. [2]

(d) The inert carbon electrodes are now replaced with copper electrodes.
(i) Describe how the observation at the anode changes when copper electrodes are used instead of carbon. [1]
(ii) State what happens to the intensity of the blue color of the solution when copper electrodes are used. [1]
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(a) (i) Effervescence / bubbles of a colorless gas (oxygen) are formed.
(ii) A pink / brown / red-brown solid (copper metal) is deposited on the electrode.

(b) (i) \(\text{Cu}^{2+}\text{(aq)} + 2\text{e}^- \rightarrow \text{Cu(s)}\)
(ii) \(4\text{OH}^-\text{(aq)} \rightarrow \text{O}_2\text{(g)} + 2\text{H}_2\text{O(l)} + 4\text{e}^-\)
(Alternatively: \(2\text{H}_2\text{O(l)} \rightarrow \text{O}_2\text{(g)} + 4\text{H}^+\text{(aq)} + 4\text{e}^-\))

(c) The blue color of the solution is due to the presence of aqueous copper(II) ions, \(\text{Cu}^{2+}\text{(aq)}\). As these ions are discharged at the cathode to form copper atoms, they are removed from the solution. Since the carbon anodes are inert, they do not replace these copper ions, so the concentration of \(\text{Cu}^{2+}\) ions decreases, causing the blue color to fade.

(d) (i) The copper anode dissolves / becomes smaller / decreases in mass, and no bubbles of gas are produced.
(ii) The intensity of the blue color remains constant (unchanged).

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(a) [2 marks total]
(i) Bubbles / effervescence / gas released [1]
(ii) Pink / brown / red-brown solid deposit [1]

(b) [4 marks total]
(i) \(\text{Cu}^{2+}\text{(aq)} + 2\text{e}^- \rightarrow \text{Cu(s)}\)
- Correct species (reactants and products) [1]
- Fully balanced with state symbols [1]
(ii) \(4\text{OH}^-\text{(aq)} \rightarrow \text{O}_2\text{(g)} + 2\text{H}_2\text{O(l)} + 4\text{e}^-\) (or equivalent)
- Correct species (reactants and products) [1]
- Fully balanced with state symbols [1]

(c) [2 marks total]
- Identifies that blue color is due to \(\text{Cu}^{2+}\) ions [1]
- Explains that the concentration of \(\text{Cu}^{2+}\) decreases as they are discharged at the cathode / not replaced [1]

(d) [2 marks total]
(i) Anode dissolves / decreases in mass / no bubbles of gas observed [1]
(ii) Color intensity remains the same / does not change [1]

Section 3: Physics

Answer all questions in this section. Questions cover forces, electricity, electromagnetism, thermal, and nuclear physics.
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PastPaper.question 1 · Mathematical Calculations
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An electric toy car of mass 0.50 kg starts from rest and accelerates uniformly to a velocity of 4.0 m/s in 2.0 s. It then travels at this constant velocity of 4.0 m/s for 5.0 s. (a) Calculate the acceleration of the toy car during the first 2.0 s. [2 marks] (b) Calculate the total distance traveled by the toy car during the entire 7.0 s journey. [4 marks] (c) Calculate the kinetic energy of the toy car while traveling at its constant velocity. [2 marks] (d) Calculate the useful power developed by the motor during the acceleration phase, assuming no energy losses. [2 marks]
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For (a): Use the acceleration formula: \(a = \frac{v - u}{t}\). Substituting the values: \(a = \frac{4.0 - 0}{2.0} = 2.0\text{ m/s}^2\). For (b): The total distance is the sum of distance in the acceleration phase and distance in the constant velocity phase. Distance 1 = area under the speed-time graph = \(0.5 \times 2.0\text{ s} \times 4.0\text{ m/s} = 4.0\text{ m}\). Distance 2 = \(5.0\text{ s} \times 4.0\text{ m/s} = 20.0\text{ m}\). Total distance = \(4.0 + 20.0 = 24.0\text{ m}\). For (c): Use the kinetic energy formula: \(E_k = \frac{1}{2}mv^2\). Substituting the values: \(E_k = 0.5 \times 0.50\text{ kg} \times (4.0\text{ m/s})^2 = 4.0\text{ J}\). For (d): Power is work done divided by time taken: \(P = \frac{W}{t}\). Here, work done is equal to the increase in kinetic energy: \(W = 4.0\text{ J}\) over a time of \(2.0\text{ s}\). Therefore, \(P = \frac{4.0\text{ J}}{2.0\text{ s}} = 2.0\text{ W}\).

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(a) 1 mark for formula or substitution: \(a = (4.0 - 0)/2.0\); 1 mark for correct value with unit: \(2.0\text{ m/s}^2\). (b) 1 mark for calculating distance during acceleration: \(4.0\text{ m}\); 1 mark for calculating distance during constant speed: \(20\text{ m}\); 1 mark for adding the distances; 1 mark for correct total: \(24\text{ m}\). (c) 1 mark for formula or substitution: \(E_k = 0.5 \times 0.50 \times 4.0^2\); 1 mark for correct value: \(4.0\text{ J}\). (d) 1 mark for power formula: \(P = E/t\) or substitution; 1 mark for correct value: \(2.0\text{ W}\).
PastPaper.question 2 · Mathematical Calculations
10 PastPaper.marks
A student sets up an electrical circuit with a 12 V d.c. power supply connected to a network of resistors. Resistor R1, with a resistance of 2.0 ohms, is connected in series with a parallel combination of two resistors, R2 (12 ohms) and R3 (6.0 ohms). (a) Calculate the combined resistance of the parallel combination of R2 and R3. [2 marks] (b) Calculate the total resistance of the entire circuit. [2 marks] (c) Calculate the current flowing through resistor R1. [2 marks] (d) Calculate the potential difference across resistor R1. [2 marks] (e) Calculate the electrical energy converted to thermal energy in resistor R1 in 10 minutes. [2 marks]
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For (a): The formula for parallel resistors is \(\frac{1}{R_p} = \frac{1}{R_2} + \frac{1}{R_3}\). Substituting the values: \(\frac{1}{R_p} = \frac{1}{12} + \frac{1}{6.0} = \frac{3}{12}\), so \(R_p = 4.0\ \Omega\). For (b): The total resistance is the sum of R1 and the parallel combination: \(R_{total} = R_1 + R_p = 2.0 + 4.0 = 6.0\ \Omega\). For (c): The current through R1 is the total current of the circuit, given by Ohm's Law: \(I = \frac{V}{R_{total}} = \frac{12\text{ V}}{6.0\ \Omega} = 2.0\text{ A}\). For (d): The potential difference across R1 is \(V_1 = I \times R_1 = 2.0\text{ A} \times 2.0\ \Omega = 4.0\text{ V}\). For (e): First convert time to seconds: \(10\text{ minutes} = 600\text{ s}\). Energy converted is \(E = I^2 \times R_1 \times t = (2.0)^2 \times 2.0 \times 600 = 8.0 \times 600 = 4800\text{ J}\) (or \(4.8\text{ kJ}\)).

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(a) 1 mark for formula or substitution: \(1/R = 1/12 + 1/6\); 1 mark for correct value: \(4.0\ \Omega\). (b) 1 mark for adding resistances: \(2.0 + 4.0\); 1 mark for correct total: \(6.0\ \Omega\). (c) 1 mark for Ohm's law: \(I = V/R\); 1 mark for correct value: \(2.0\text{ A}\). (d) 1 mark for potential difference formula or substitution: \(2.0 \times 2.0\); 1 mark for correct value: \(4.0\text{ V}\). (e) 1 mark for converting time to seconds (600 s) and choosing energy formula \(E = Pt\) or \(E = I^2 R t\); 1 mark for correct value: \(4800\text{ J}\) (or \(4.8\text{ kJ}\)).
PastPaper.question 3 · Recall & Diagrams
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An experiment is designed to investigate the electrical properties of an unknown resistor, \(R\). (a) Describe how to connect a voltmeter and an ammeter to measure the resistance of resistor \(R\) in a circuit containing a power supply. State whether each meter is connected in series or in parallel with \(R\). [2 marks] (b) Describe the difference in the circuit symbols for a variable resistor and a thermistor. [2 marks] (c) The current through resistor \(R\) is measured as \(0.50\text{ A}\) when the potential difference across it is \(3.0\text{ V}\). Calculate the resistance of \(R\). State the formula used and show your working. [2 marks] (d) Describe the shape of a current-voltage (\(I\)-\(V\)) graph for: (i) a filament lamp, explaining why it has this shape [3 marks], and (ii) a fixed resistor at constant temperature [1 mark].
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For (a), the voltmeter must be connected in parallel across the resistor \(R\), and the ammeter must be connected in series with the resistor \(R\). For (b), a variable resistor is represented by a standard rectangle with a diagonal arrow pointing through it, whereas a thermistor is represented by a rectangle with a diagonal line that has a flat horizontal section at its bottom-left end. For (c), we use the Ohm's law formula: \(R = \frac{V}{I}\). Substituting the given values: \(R = \frac{3.0\text{ V}}{0.50\text{ A}} = 6.0\ \Omega\). For (d)(i), the graph is a curve with a decreasing gradient as the potential difference increases (forming an S-shape through the origin). This occurs because a higher current increases the temperature of the filament, which increases the lattice vibrations of the metal atoms and consequently increases its resistance. For (d)(ii), the graph is a straight line of constant positive gradient passing through the origin, indicating that current is directly proportional to potential difference.

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(a) Voltmeter connected in parallel across the resistor \(R\) [1 mark]; Ammeter connected in series with the resistor \(R\) [1 mark].
(b) Variable resistor described as a rectangle with a diagonal arrow through it [1 mark]; Thermistor described as a rectangle with a diagonal line having a horizontal step/flat section at the bottom [1 mark].
(c) State formula: \(R = \frac{V}{I}\) [1 mark]; Correct calculation to yield \(6.0\ \Omega\) (accept 6 or 6.0 ohms) [1 mark].
(d)(i) S-shaped curve passing through the origin / curve with a decreasing gradient [1 mark]; current increases the temperature of the filament [1 mark]; higher temperature increases resistance [1 mark].
(d)(ii) Straight line passing through the origin [1 mark].
PastPaper.question 4 · Recall & Diagrams
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A heavy box of mass \(15\text{ kg}\) is dropped from a stationary helicopter. (a) State the difference between a scalar quantity and a vector quantity. Identify which type of quantity velocity is. [2 marks] (b) Describe what features represent the acceleration and the distance travelled on a speed-time graph. [2 marks] (c) Calculate the weight of the box near the Earth's surface. (Take the acceleration of free fall, \(g\), to be \(9.8\text{ m/s}^2\).) [2 marks] (d) Shortly after release, the box experiences an upward air resistance force of \(50\text{ N}\). Calculate the magnitude and state the direction of the resultant force acting on the box. [2 marks] (e) Explain, in terms of the forces acting on the box, how it eventually reaches a constant terminal velocity. [2 marks]
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For (a), a scalar quantity has magnitude only, whereas a vector quantity has both magnitude and direction. Velocity is a vector quantity. For (b), the acceleration is represented by the gradient (slope) of the speed-time graph, and the distance travelled is represented by the total area under the speed-time graph. For (c), the weight is calculated using the formula \(W = m \times g\). Substituting the values: \(W = 15\text{ kg} \times 9.8\text{ m/s}^2 = 147\text{ N}\). For (d), the weight acts downwards (\(147\text{ N}\)) and the air resistance acts upwards (\(50\text{ N}\)). The resultant force is: \(147\text{ N} - 50\text{ N} = 97\text{ N}\) acting downwards. For (e), as the box falls and its speed increases, the upward air resistance force acting on it also increases. Eventually, the magnitude of the upward air resistance becomes equal to the downward weight of the box. At this point, the forces are balanced, the resultant force is zero, and the box stops accelerating, falling at a constant terminal velocity.

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(a) Scalar has magnitude only, vector has magnitude and direction [1 mark]; Velocity is a vector [1 mark].
(b) Acceleration is the gradient (slope) [1 mark]; Distance travelled is the area under the graph [1 mark].
(c) Correct formula used: \(W = m \times g\) [1 mark]; Correct calculation: \(15 \times 9.8 = 147\text{ N}\) [1 mark].
(d) Correct subtraction of forces (\(147 - 50\)) to give \(97\text{ N}\) [1 mark]; Direction stated as downwards [1 mark].
(e) Air resistance increases as speed increases [1 mark]; Air resistance becomes equal to weight, so the resultant force is zero (and acceleration becomes zero) [1 mark].

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