Part a (2 marks)

Award the 2 available marks for the following observable evidence: substitutes the two adjacent sides and included angle into frac12absin C; reports 23.9text( m)² with correct units.

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part b (3 marks)

Award the 3 available marks for the following observable evidence: forms the cosine-rule expression with the included 58^circ angle; evaluates the positive square root 7.47009ldots; reports 7.47text( m).

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part c (2 marks)

Award the 2 available marks for the following observable evidence: uses the unrounded third side to obtain the complete perimeter; applies the 1.05 allowance and reports 23.7text( m).

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part a (1 mark)

Award the 1 available mark for the following observable evidence: states h=5text( m).

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part b (4 marks)

Award the 4 available marks for the following observable evidence: uses the factor h / 3=5 / 3; assigns weight 4 to ordinates 5.4,8.6,4.1; assigns weight 2 to ordinates 7.8,7.2; obtains 170.666ldotstext( m)², hence 171text( m)^2.

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part c (2 marks)

Award the 2 available marks for the following observable evidence: divides the unrounded square-metre area by 10000; reports 0.0171text( ha).

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part d (3 marks)

Award the 3 available marks for the following observable evidence: applies the 1.08 contingency to the unrounded area; divides by 120text( m)² per bag; rounds 1.536 upwards to 2 bags.

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part a (3 marks)

Award the 3 available marks for the following observable evidence: selects V=pi r^2h; substitutes r=1.2 and h=2.4; reports 10.857text( m)^3.

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part b (3 marks)

Award the 3 available marks for the following observable evidence: uses frac23pi r³ for the hemisphere; adds the hemisphere to the cylinder; reports 14.476text( m)^3.

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part c (3 marks)

Award the 3 available marks for the following observable evidence: converts the unrounded total from cubic metres to litres; applies the 0.82 usable fraction; reports 11871text( L).

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part d (2 marks)

Award the 2 available marks for the following observable evidence: divides usable capacity by 110text( L / min); rounds upwards to 108 minutes.

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part e (2 marks)

Award the 2 available marks for the following observable evidence: identifies wall thickness as the excluded material; states that external dimensions would overestimate usable capacity.

Acceptable alternatives: Accept an equivalent measurement formula or decomposition that uses the same dimensions and produces the same physical quantity.; Accept consequential values from a clearly shown earlier result when later units, rounding and practical interpretation are consistent.

Do not credit by itself: Do not credit a formula using incompatible dimensions, an incorrect trigonometric angle, or a conversion between unlike units.; Do not accept premature rounding that changes a whole-item decision, coverage allowance, capacity or stated tolerance.

Part a (2 marks)

Award the 2 available marks for the following observable evidence: identifies all 360 learners as the population; identifies weekly travel time as the variable.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part b (3 marks)

Award the 3 available marks for the following observable evidence: calculates the day-shift allocation 24; calculates the evening-shift allocation 16; calculates the weekend allocation 8.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part c (2 marks)

Award the 2 available marks for the following observable evidence: identifies voluntary-response or response-time bias; explains how respondents may differ in travel experience.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part d (1 mark)

Award the 1 available mark for the following observable evidence: proposes random selection within every stratum.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part a (2 marks)

Award the 2 available marks for the following observable evidence: places every leaf beside the correct tens stem in ascending order; includes a correct key such as 2|4=24 minutes.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part b (3 marks)

Award the 3 available marks for the following observable evidence: identifies minimum 18 and maximum 48; calculates median 26; calculates Q_1=23 and Q_3=30.5.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part c (2 marks)

Award the 2 available marks for the following observable evidence: calculates IQR=7.5 and upper fence 41.75; correctly classifies 48 as an outlier.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part d (2 marks)

Award the 2 available marks for the following observable evidence: states the median 26 and IQR 7.5 in context; describes the right skew or high outlier.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part a (4 marks)

Award the 4 available marks for the following observable evidence: enters all eight x-values as the explanatory variable; enters the paired y-values as the response variable; selects linear regression; reports a=6.345 and b=3.869.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part b (3 marks)

Award the 3 available marks for the following observable evidence: reports r=0.9975; reports r²=0.9950; interprets r² using task variation and training time.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part c (2 marks)

Award the 2 available marks for the following observable evidence: calculates the unrounded prediction 29.5595ldots; uses observed minus predicted to obtain -0.560.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part d (4 marks)

Award the 4 available marks for the following observable evidence: substitutes x=12 in the unrounded model; reports 52.8 tasks; identifies extrapolation beyond 9 hours; states a contextual limitation such as fatigue, saturation or a finite task pool.

Acceptable alternatives: Accept direct approved-calculator output when the entered data, variable order and requested statistic or regression model are identified.; Accept an equivalent statistically valid explanation that refers explicitly to sampling, distribution, residual, correlation or model range as required.

Do not credit by itself: Do not credit a biased or non-random selection method as representative without a valid limitation.; Do not swap explanatory and response variables, confuse correlation with causation, reverse the residual sign, or extrapolate without evaluating reliability.

Part a (2 marks)

Award the 2 available marks for the following observable evidence: identifies the multiplier 1.032; uses exponent 4 with the current 420 cost.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part b (3 marks)

Award the 3 available marks for the following observable evidence: evaluates the compound-inflation expression; retains sufficient precision; reports 476.40.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part c (2 marks)

Award the 2 available marks for the following observable evidence: compares 450 with the projected unrounded cost; states the 26.40 shortfall and insufficiency.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part a (2 marks)

Award the 2 available marks for the following observable evidence: states monthly rate 0.0045; states 72 deposits.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part b (4 marks)

Award the 4 available marks for the following observable evidence: uses an ordinary-annuity future-value model; uses payment 350 and rate 0.0045; uses 72 periods with zero initial value; reports 29683.32.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part c (2 marks)

Award the 2 available marks for the following observable evidence: multiplies the ordinary-annuity value by 1.0045 to obtain 29816.90; finds the increase 133.57.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part d (2 marks)

Award the 2 available marks for the following observable evidence: states that each deposit is invested one month longer; distinguishes timing from total contributions.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part a (2 marks)

Award the 2 available marks for the following observable evidence: calculates first-month interest 1400; applies the repayment after interest to obtain 279550.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part b (4 marks)

Award the 4 available marks for the following observable evidence: uses monthly rate 0.005; uses 60 end-of-month repayments; uses opposite signs for the loan and repayments; reports 248603.49.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part c (4 marks)

Award the 4 available marks for the following observable evidence: uses the unrounded balance as present value; uses monthly rate 0.0055; uses 180 remaining months and zero future value; reports 2179.29.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.

Part d (3 marks)

Award the 3 available marks for the following observable evidence: models 180 payments of 1850 at monthly rate 0.0055; obtains a positive balance near 100820.29; concludes that the loan is not cleared.

Acceptable alternatives: Accept a financial solver, recurrence, table or explicit annuity equation using the correct periodic rate, period count and payment timing.; Accept an alternative cash-flow sign convention when inflows and outflows remain consistently opposite and the contextual conclusion is unchanged.

Do not credit by itself: Do not use a nominal annual rate as the periodic rate, an incorrect payment count, or beginning-of-period timing when end-of-period timing is stated.; Do not accept inconsistent financial-solver signs or a comparison that ignores fees, inflation, remaining balance or the stated time horizon.