Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates annual income 920 × 52=$47,840; divides the annual income by 12; states $3986.67 per month. Accept $3986.67; allow $3986.66 only when the candidate explicitly truncates rather than rounds. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Acceptable alternatives: an equivalent calculation using 920 × 52 / 12

Do not credit by itself: a response that omits the required evidence for convert weekly income to a monthly spreadsheet input; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: totals the four car costs as $830; totals all car-option expenses as $3100; subtracts expenses from income to obtain a $886.67 surplus. Accept $886.67 to the nearest cent. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: omitting registration, insurance or maintenance; adding the surplus to expenses

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: totals public-transport expenses as $2460; calculates the public-transport surplus as $1526.67; calculates the surplus advantage as $640.00; recommends public transport on financial grounds and identifies one relevant non-financial consideration. Accept money values within one cent and any context-relevant non-financial consideration. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Acceptable alternatives: a car recommendation supported by a clearly stated non-financial priority despite its lower supplied surplus

Do not credit by itself: a response that omits the required evidence for compare budget options and justify a practical recommendation; an unsupported final answer with no assessable calculation or interpretation

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: states that the direction is negative; states that the form is approximately linear; states that the association is strong. Accept equivalent statistical language; no numerical tolerance is required. Do not apply consequential marking because this part is independently determined from the supplied information.

Do not credit by itself: claiming that the association proves activity caused the lower heart rate

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates the change in heart rate as -14 and activity as 5; obtains m=-2.8 beats per minute per activity hour; substitutes a point to obtain b=83.6. Accept m and b within 0.1 when supported by the stated endpoint method. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Acceptable alternatives: an equivalent two-point equation converted to slope-intercept form

Do not credit by itself: a response that omits the required evidence for calculate and interpret a fitted line from two data points; an unsupported final answer with no assessable calculation or interpretation

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: substitutes x=5.5 into the fitted model; calculates 68.2 beats per minute; identifies the prediction as interpolation within the observed range; states that uncontrolled variables or observational data prevent a causal conclusion. Accept 68 to 68.5 beats per minute if the candidate used a defensible rounded fitted line. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: treating the model as an exact biological rule; stating causation without experimental evidence

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates maximum heart rate 178 beats per minute; calculates lower limit 115.7 beats per minute; calculates upper limit 142.4 beats per minute. Accept the target range rounded to 116-142 beats per minute when the unrounded limits are shown. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate percentage limits for a target rate; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: uses a conversion factor of 3; calculates 144 beats per minute; states that the rate is 1.6 beats per minute above the upper target limit. Accept 'about 2 beats per minute above' when whole-number target limits are used consistently. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for convert a pulse count to a rate and compare limits; an unsupported final answer with no assessable calculation or interpretation

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: converts the two-minute count to 117 beats per minute; identifies two minutes as the first target-range reading; calculates the average rate of decrease as 11 beats per minute per minute; states a valid physiological or measurement limitation. Accept an equivalent limitation concerning the estimated maximum-heart-rate rule or pulse-count precision. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for interpret a recovery-rate sequence; an unsupported final answer with no assessable calculation or interpretation

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates Route A's transfer as 8 minutes; calculates Route B's transfer as 10 minutes; correctly compares both transfers with the 10-minute rule. Exact minute values are required. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate timetable transfer intervals; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: states Route A arrival as 08:22 with an 18-minute buffer; adds the 8-minute walk to obtain Route B arrival at 08:36; calculates Route B's buffer as 4 minutes. Exact clock times and minute intervals are required; accept equivalent 12-hour notation. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for combine timetable and walking times; an unsupported final answer with no assessable calculation or interpretation

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: identifies that Route A arrives earlier; identifies that Route A fails the connection rule; recommends Route B because it meets the rule and arrives before 08:40; states one relevant timetable, walking-time or service-reliability assumption. Accept a Route A recommendation only if the candidate explicitly rejects or changes the supplied 10-minute reliability rule; otherwise Route B is required. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: choosing only the earliest arrival without applying the connection rule

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates the overtime rate as $47.25; calculates ordinary and overtime earnings; adds the earnings to obtain gross pay of $1433.25. Accept money values to the nearest cent. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate ordinary and overtime earnings; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: subtracts $85 from gross pay; obtains taxable income of $1348.25; selects $310 from the correct PAYG row. Exact money values are required from the supplied table. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: using gross pay rather than supplied taxable income to select the table row

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: subtracts PAYG and the union fee to obtain $1105.25; calculates 22% of gross pay as $315.32; calculates the difference as $5.32; states that the supplied table amount is lower than the percentage estimate. Accept money values within one cent. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: subtracting the allowable deduction again when calculating net pay

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates the depreciable amount as $13,500; divides by 5 to obtain $2700 per year; writes V_n=18,500-2700n with an appropriate domain. Exact values are required; accept an equivalent recurrence V_(n+1)=V_n-2700, V_0=18,500. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Acceptable alternatives: the equivalent recurrence relation with initial value and yearly decrease

Do not credit by itself: a response that omits the required evidence for calculate and represent straight-line depreciation; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: substitutes n=3 to obtain $10,400; substitutes n=5 to obtain $5000; states that the second result verifies the residual-value condition. Exact dollar values are required. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for substitute into a straight-line depreciation rule; an unsupported final answer with no assessable calculation or interpretation

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: forms or tests the inequality 18,500-2700n<8000; identifies the first whole year as 4; verifies V_4=$7700; explains that straight-line uses a constant dollar decrease rather than a constant percentage. Year 4 and $7700 are exact; accept trial-and-check using year 3 and year 4. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Acceptable alternatives: a year-by-year table that correctly identifies year 4

Do not credit by itself: a response that omits the required evidence for solve a depreciation threshold and distinguish depreciation models; an unsupported final answer with no assessable calculation or interpretation

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates both shift totals as 60 and 40; calculates both outcome totals as 78 and 22; checks the grand total as 100. Exact counts are required. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate marginal totals in a two-way table; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: uses 12 / 60 for the day shift; uses 10 / 40 for the night shift; states the conditional percentages as 20% and 25%. Exact percentages are expected; accept equivalent decimals 0.20 and 0.25 when labelled. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate conditional percentages from a two-way table; an unsupported final answer with no assessable calculation or interpretation

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: compares 25% with 20%; calculates a rate ratio of 1.25 or a 5-percentage-point difference; rejects the claim that the rate is twice as high; selects and justifies a suitable comparative display. Accept 1.25 times or a 5-percentage-point comparison; the display must compare conditional rates rather than raw counts. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Acceptable alternatives: a correctly labelled percentage bar chart or dot plot

Do not credit by itself: a response that omits the required evidence for evaluate a conditional-rate claim and choose a graph; an unsupported final answer with no assessable calculation or interpretation

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: selects the 120 / 360 sector fraction; calculates arc length 3piapprox9.42 m; calculates area 6.75piapprox21.21 m^2. Accept arc length within 0.01 m and area within 0.02 square metres. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate sector arc length and area; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: calculates full-circle area 20.25π m²; subtracts the coated sector area; states remainder 13.5piapprox42.41 m^2. Accept a remainder within 0.02 square metres. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate a complementary sector area; an unsupported final answer with no assessable calculation or interpretation

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: applies the 1.08 waste factor to obtain about 22.90 m²; divides by 5 m² per kit; rounds 4.5804ldots up to 5 whole kits; calculates total cost $700. Accept 5 kits and $700 from consistent use of the unrounded sector area. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: using ordinary money rounding on a theoretical per-square-metre cost; rounding the kit count down

Part a (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: converts the 8 m length to 8 cm; converts the 6 m width to 6 cm; converts the 3.2 m height to 3.2 cm. Exact scale dimensions are required. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for convert actual dimensions for a scale drawing; an unsupported final answer with no assessable calculation or interpretation

Part b (3 marks)

Award one mark for each observable checkpoint, to a maximum of 3: converts the door width to 1.8 cm; converts the door height to 2.1 cm; identifies required scale, dimension and elevation labels. Exact scaled dimensions are required; accept standard equivalent building-plan conventions. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Acceptable alternatives: a correctly dimensioned sketch using an equivalent conventional door placement

Do not credit by itself: a response that omits the required evidence for apply scale and building-drawing conventions; an unsupported final answer with no assessable calculation or interpretation

Part c (4 marks)

Award one mark for each observable checkpoint, to a maximum of 4: calculates four-wall area as 89.6 m²; subtracts door area 3.78 m² to obtain 85.82 m²; applies the 10% allowance to obtain 94.402 m²; reports approximately 94.4 m² with units without inventing a purchase increment. Accept the exact requirement 94.402 square metres or 94.4 square metres to one decimal place. Apply consequential marking to a correct later method that uses an earlier incorrect value, unless the error makes the later work materially easier.

Do not credit by itself: a response that omits the required evidence for calculate wall area from a building plan and apply waste; an unsupported final answer with no assessable calculation or interpretation