Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Identifies the slope as the predicted change in score for one additional training session.
2. Uses the numerical slope 2.3 with score-point units.
3. States that each additional session is associated with a predicted increase of 2.3 score points.

Do not credit by itself: Omitting or contradicting this required achievement: Identifies the slope as the predicted change in score for one additional training session. Stating a result without establishing: States that each additional session is associated with a predicted increase of 2.3 score points.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Substitutes x=6 into 18.4+2.3x.
2. Obtains the fitted score 32.2.
3. Calculates observed minus fitted, 31-32.2=-1.2 points.

Do not credit by itself: Omitting or contradicting this required achievement: Substitutes x=6 into 18.4+2.3x. Stating a result without establishing: Calculates observed minus fitted, 31-32.2=-1.2 points.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Notes that 30 sessions is outside the observed range 2 to 10.
2. Classifies use at x=30 as substantial extrapolation.
3. States the assumption that the fitted linear pattern continues beyond the observed range.
4. Concludes that the prediction is unsupported or unreliable despite being calculable.

Do not credit by itself: Omitting or contradicting this required achievement: Notes that 30 sessions is outside the observed range 2 to 10. Stating a result without establishing: Concludes that the prediction is unsupported or unreliable despite being calculable.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Adds the urban counts 42+18.
2. Adds the rural counts 12+28.
3. States the row totals as urban 60 and rural 40.

Do not credit by itself: Omitting or contradicting this required achievement: Adds the urban counts 42+18. Stating a result without establishing: States the row totals as urban 60 and rural 40.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Calculates the urban conditional percentage 42 / 60 × 100.
2. Calculates the rural conditional percentage 12 / 40 × 100.
3. States urban 70% and rural 30%.

Do not credit by itself: Omitting or contradicting this required achievement: Calculates the urban conditional percentage 42 / 60 × 100. Stating a result without establishing: States urban 70% and rural 30%.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Compares the conditional bus-use percentages using the 40-percentage-point difference.
2. Concludes that location and travel mode appear associated.
3. Recognises that the survey is observational rather than a controlled experiment.
4. Explains that confounding or other group differences prevent a causal conclusion.

Do not credit by itself: Omitting or contradicting this required achievement: Compares the conditional bus-use percentages using the 40-percentage-point difference. Stating a result without establishing: Explains that confounding or other group differences prevent a causal conclusion.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Identifies the initial value V_0=28000.
2. Converts 16% depreciation to the multiplier 1-0.16=0.84.
3. Writes V_n=28000(0.84)^n.

Do not credit by itself: Omitting or contradicting this required achievement: Identifies the initial value V_0=28000. Stating a result without establishing: Writes V_n=28000(0.84)^n.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Substitutes n=3 into 28000(0.84)^n.
2. Evaluates the unrounded value 16595.712.
3. Rounds to $16,596.

Do not credit by itself: Omitting or contradicting this required achievement: Substitutes n=3 into 28000(0.84)^n. Stating a result without establishing: Rounds to $16,596.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Calculates the three-year loss 28000-16595.712=11404.288.
2. Expresses the loss as 11404.288 / 28000 × 100approx40.73%.
3. Identifies the constant annual percentage-depreciation assumption.
4. Limits the model's reasonableness to a period in which the 16% rate remains plausible.

Do not credit by itself: Omitting or contradicting this required achievement: Calculates the three-year loss 28000-16595.712=11404.288. Stating a result without establishing: Limits the model's reasonableness to a period in which the 16% rate remains plausible.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Interprets 1.004 as a monthly growth factor.
2. Converts the growth factor to 0.4% monthly interest.
3. Interprets the subtraction as an $850 monthly repayment after interest.

Do not credit by itself: Omitting or contradicting this required achievement: Interprets 1.004 as a monthly growth factor. Stating a result without establishing: Interprets the subtraction as an $850 monthly repayment after interest.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Calculates first-month interest 0.004(24000)=96.
2. Uses the operation order 24000+96-850.
3. Obtains B_1=$23,246.

Do not credit by itself: Omitting or contradicting this required achievement: Calculates first-month interest 0.004(24000)=96. Stating a result without establishing: Obtains B_1=$23,246.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Substitutes B_1=23246 into the recurrence.
2. Calculates 1.004(23246)=23338.984.
3. Obtains B_2=$22,488.98 to the nearest cent.
4. Explains that the last repayment is reduced when the interest-added balance is below $850.

Do not credit by itself: Omitting or contradicting this required achievement: Substitutes B_1=23246 into the recurrence. Stating a result without establishing: Explains that the last repayment is reduced when the interest-added balance is below $850.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Selects the cosine rule because two sides and the included angle are known.
2. Substitutes BC²=7.2²+9.5²-2(7.2)(9.5)cos58^circ.
3. Obtains BCapprox8.34 km to two decimal places.

Do not credit by itself: Omitting or contradicting this required achievement: Selects the cosine rule because two sides and the included angle are known. Stating a result without establishing: Obtains BCapprox8.34 km to two decimal places.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Selects the cosine rule using AB=7.2, AC=9.5 and the consequential value BCapprox8.34248.
2. Substitutes cos B=(7.2²+8.34248²-9.5²) / (2(7.2)(8.34248)).
3. Obtains angle ABCapprox74.953^circapprox75^circ.

Do not credit by itself: Omitting or contradicting this required achievement: Selects the cosine rule using AB=7.2, AC=9.5 and the consequential value BCapprox8.34248. Stating a result without establishing: Obtains angle ABCapprox74.953^circapprox75^circ.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Selects A=frac12absin C using sides 7.2, 9.5 and included angle 58^circ.
2. Substitutes frac12(7.2)(9.5)sin58^circ.
3. Evaluates the area as approximately 29.0.
4. States the area unit km^2.

Do not credit by itself: Omitting or contradicting this required achievement: Selects A=frac12absin C using sides 7.2, 9.5 and included angle 58^circ. Stating a result without establishing: States the area unit km^2.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Calculates the longitude difference 173^circ-147^circ=26^circ.
2. Converts using 26π / 180=13π / 90.
3. States the decimal angle 0.4538 radians.

Do not credit by itself: Omitting or contradicting this required achievement: Calculates the longitude difference 173^circ-147^circ=26^circ. Stating a result without establishing: States the decimal angle 0.4538 radians.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Uses the parallel-radius relationship r=Rcos(latitude).
2. Substitutes r=6371cos42^circ.
3. Obtains rapprox4735 km.

Do not credit by itself: Omitting or contradicting this required achievement: Uses the parallel-radius relationship r=Rcos(latitude). Stating a result without establishing: Obtains rapprox4735 km.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Selects the arc-length model s=rtheta.
2. Substitutes the small-circle radius and radian angle 6371cos42^circ(13π / 90).
3. Evaluates the distance as approximately 2149.
4. States the distance in kilometres along the parallel.

Do not credit by itself: Omitting or contradicting this required achievement: Selects the arc-length model s=rtheta. Stating a result without establishing: States the distance in kilometres along the parallel.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Assigns B the direct tentative label 7.
2. Assigns C the direct tentative label 4.
3. States the two labels as B=7 and C=4 after considering A.

Do not credit by itself: Omitting or contradicting this required achievement: Assigns B the direct tentative label 7. Stating a result without establishing: States the two labels as B=7 and C=4 after considering A.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Settles C at distance 4 and updates B to 4+2=6.
2. Compares the routes to D, obtaining 6+5=11 via B and 4+8=12 directly via C.
3. States the shortest A-to-D route A-C-B-D with distance 11 km.

Do not credit by itself: Omitting or contradicting this required achievement: Settles C at distance 4 and updates B to 4+2=6. Stating a result without establishing: States the shortest A-to-D route A-C-B-D with distance 11 km.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Updates E from C to label 4+7=11.
2. Shows that the competing route through D is at least 11+3=14.
3. States route A-C-E with distance 11 km.
4. Justifies finality because no unsettled label below 11 can improve E.

Do not credit by itself: Omitting or contradicting this required achievement: Updates E from C to label 4+7=11. Stating a result without establishing: Justifies finality because no unsettled label below 11 can improve E.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Uses A's finish at 3 to give C: ES=3, EF=7.
2. Uses B's finish at 8 and C's finish at 7 to set E: ES=max(8,7)=8.
3. States E: EF=8+3=11.

Do not credit by itself: Omitting or contradicting this required achievement: Uses A's finish at 3 to give C: ES=3, EF=7. Stating a result without establishing: States E: EF=8+3=11.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Finds D: ES=8, EF=10 from its two predecessors.
2. Sets F: ES=max(10,11)=11.
3. States the minimum project duration EF_F=15 days.

Do not credit by itself: Omitting or contradicting this required achievement: Finds D: ES=8, EF=10 from its two predecessors. Stating a result without establishing: States the minimum project duration EF_F=15 days.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Completes the backward pass to identify zero float for A, B, E and F.
2. Identifies A-B-E-F as the critical path.
3. States that B has 0 days float.
4. Checks that C and D each have 1 day float, consistent with the critical-path result.

Do not credit by itself: Omitting or contradicting this required achievement: Completes the backward pass to identify zero float for A, B, E and F. Stating a result without establishing: Checks that C and D each have 1 day float, consistent with the critical-path result.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Uses vertex order A, B, C, D with zeros on the diagonal.
2. Places symmetric ones for edges AB,AC,BC,CD and zeros for absent edges.
3. Writes the complete matrix begin(bmatrix)0&1&1&01&0&1&01&1&0&10&0&1&0end(bmatrix).

Do not credit by itself: Omitting or contradicting this required achievement: Uses vertex order A, B, C, D with zeros on the diagonal. Stating a result without establishing: Writes the complete matrix begin(bmatrix)0&1&1&01&0&1&01&1&0&10&0&1&0end(bmatrix).

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Counts degrees A=2 and B=2.
2. Counts degrees C=3 and D=1.
3. States the complete ordered degree list 2,2,3,1.

Do not credit by itself: Omitting or contradicting this required achievement: Counts degrees A=2 and B=2. Stating a result without establishing: States the complete ordered degree list 2,2,3,1.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. Identifies C and D as the only odd-degree vertices.
2. Concludes that an Euler trail exists but an Euler circuit does not.
3. Gives a trail such as C-A-B-C-D that uses every edge exactly once.
4. Uses C and D as the two endpoints.

Do not credit by itself: Omitting or contradicting this required achievement: Identifies C and D as the only odd-degree vertices. Stating a result without establishing: Uses C and D as the two endpoints.

Part a (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Uses A_0=0 to calculate A_1=1.004(0)+250=250.
2. Applies interest before the second deposit.
3. Calculates A_2=1.004(250)+250=$501.00.

Do not credit by itself: Omitting or contradicting this required achievement: Uses A_0=0 to calculate A_1=1.004(0)+250=250. Stating a result without establishing: Calculates A_2=1.004(250)+250=$501.00.

Part b (3 marks)

Use the 3 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement. Apply consequential marking only to a later checkpoint that correctly uses the candidate's earlier value; do not restore the mark lost for the original error.

Mark-by-mark checkpoints:

1. Substitutes n=12 into 250(1.004^n-1) / 0.004.
2. Evaluates the geometric accumulation factor without premature rounding.
3. Obtains A_(12)approx$3,066.89.

Do not credit by itself: Omitting or contradicting this required achievement: Substitutes n=12 into 250(1.004^n-1) / 0.004. Stating a result without establishing: Obtains A_(12)approx$3,066.89.

Part c (4 marks)

Use the 4 numbered checkpoints below, awarding one mark only for each independently demonstrated achievement.

Mark-by-mark checkpoints:

1. States the assumption of a constant 0.4% monthly rate.
2. States that every $250 deposit is made on time with no fees or withdrawals.
3. Links suitability to the one-year horizon rather than indefinite extrapolation.
4. Concludes that the estimate is suitable only if the stated conditions are realistic.

Do not credit by itself: Omitting or contradicting this required achievement: States the assumption of a constant 0.4% monthly rate. Stating a result without establishing: Concludes that the estimate is suitable only if the stated conditions are realistic.