Checkpoint Quiz 4

Maths Standard Year 11 · Module 2: Measurement

Lesson 18 — Units of Energy & Mass Lesson 19 — Trapezoidal Rule Lesson 20 — Timetables & Elapsed Time Lesson 21 — Time Zones & UTC Lesson 22 — Latitude, Longitude & Location

10 MC 3 SA ~25 min

0/10

Multiple Choice Score

Answer questions to see your score.

Part A — Multiple Choice (1 mark each)

1 A microwave oven is rated at $900\text{ W}$ and runs for $4$ minutes. The energy used is: L18

A $0.06\text{ kWh}$

B $3600\text{ kWh}$

C $0.6\text{ kWh}$

D $60\text{ kWh}$

A — $0.06\text{ kWh}$. $P = 0.9\text{ kW}$; $t = \frac{4}{60}\text{ h}$; $E = 0.9 \times \frac{4}{60} = 0.06\text{ kWh}$. Option C forgets to convert minutes to hours.

2 A food label shows $630\text{ kJ}$ per serve. This is closest to: L18

A $150\text{ Cal (kcal)}$

B $2636\text{ Cal (kcal)}$

C $630\text{ Cal (kcal)}$

D $263.6\text{ Cal (kcal)}$

A — $150\text{ Cal}$. $630 \div 4.184 \approx 150.6 \approx 150\text{ Cal}$. Option B multiplies instead of divides. Option C confuses kJ with Cal.

3 Widths of an irregular block, measured at $5\text{ m}$ intervals, are: $0,\; 12,\; 18,\; 14,\; 0$ (metres). Using the trapezoidal rule, the estimated area is: L19

A $220\text{ m}^2$

B $440\text{ m}^2$

C $110\text{ m}^2$

D $880\text{ m}^2$

A — $220\text{ m}^2$. $h=5$; $d_f=0$, $d_l=0$; $d_m=12+18+14=44$; $A \approx \frac{5}{2}(0+88+0)=2.5\times 88=220\text{ m}^2$. Option B forgets the $\frac{h}{2}$ factor and uses $h$ alone.

4 A block has parallel sides of $35\text{ m}$ and $47\text{ m}$, with a perpendicular distance of $22\text{ m}$ between them. The trapezoidal rule gives an area of: L19

A $902\text{ m}^2$

B $451\text{ m}^2$

C $1804\text{ m}^2$

D $924\text{ m}^2$

A — $902\text{ m}^2$. $A \approx \frac{22}{2}(35+47)=11\times 82=902\text{ m}^2$. Option B halves the answer again. Option D adds the sides before halving ($\frac{22}{2}(35+47)$ vs just $22(35+47)/2$) — same thing, so checks out; Option D may arise from $\frac{22}{2}(35+47+\varepsilon)$.

5 In 24-hour time, $8{:}45\text{ pm}$ is written as: L20

A 0845

B 2045

C 2045

D 1845

B — 2045. pm: add 12 to the hour; $8 + 12 = 20$; so 8:45 pm = 2045. Option A gives am time. Option D uses $8 + 10 = 18$ — a common off-by-2 error.

6 A flight departs at $2215$ and arrives at $0640$ the next morning. The flight duration is: L20

A $8\text{ h }25\text{ min}$

B $16\text{ h }25\text{ min}$

C $8\text{ h }25\text{ min}$

D $7\text{ h }35\text{ min}$

A — $8\text{ h }25\text{ min}$. Count: 2215 to 0000 = 1 h 45 min; 0000 to 0640 = 6 h 40 min; total = 8 h 25 min. Option B uses 24 h − elapsed, confusing arrival with remaining time.

7 UTC is $0900$ on a Thursday. The time in Perth (AWST $=$ UTC$+8$) is: L21

A $0100$ Thursday

B $1700$ Thursday

C $1700$ Wednesday

D $1700$ Friday

B — $1700$ Thursday. $0900 + 8 = 1700$; same calendar day. Option A subtracts instead of adds. Option D incorrectly advances the day (the total is still well within Thursday).

8 It is $4{:}00\text{ pm}$ in Sydney (AEDT $=$ UTC$+11$) on a summer Tuesday. What time is it in London (UTC$+0$)? L21

A $3{:}00\text{ am}$ Tuesday

B $5{:}00\text{ am}$ Tuesday

C $3{:}00\text{ am}$ Wednesday

D $3{:}00\text{ am}$ Monday

A — $3{:}00\text{ am}$ Tuesday. Sydney 1600 AEDT → UTC = $1600 - 11 = 0500$... wait: $1600-11 = 0500$; London = UTC+0 = $0500$. Hmm — that gives 5:00 am. Let me recheck: $16 - 11 = 5$, so 0500 = 5:00 am Tuesday. Answer is B — 5:00 am Tuesday. (Option A arises from using UTC+10 instead of UTC+11.)

9 A city is at longitude $75°\text{E}$. Based only on this longitude, its theoretical UTC offset is: L22

A UTC$-5$

B UTC$+4$

C UTC$+5$

D UTC$+75$

C — UTC$+5$. $75 \div 15 = 5$; 75°E is east, so UTC+5. Option B gives UTC+4 — off by one step. Option A confuses east with west.

10 City X is at longitude $120°\text{E}$ and City Y is at longitude $60°\text{W}$. It is $6{:}00\text{ pm}$ at City X. What is the local time at City Y? L22

A $6{:}00\text{ am}$

B $6{:}00\text{ am}$

C $2{:}00\text{ pm}$

D $10{:}00\text{ pm}$

A — $6{:}00\text{ am}$. $\Delta\lambda = 120 + 60 = 180°$; time diff $= 180 \div 15 = 12$ h; City X (120°E) is ahead; City Y (60°W) is 12 h behind; $1800 - 12 = 0600$ = 6:00 am.

Part B — Short Answer (show all working)

1 L18 & L19

An air-conditioning unit is rated at $2400\text{ W}$ and runs for $6$ hours per day.

(a) Calculate the energy used per day in kWh.

(b) If electricity costs $28$ cents per kWh, find the annual cost (365 days) to the nearest dollar.

(a) $P = 2.4\text{ kW}$; $E = 2.4 \times 6 = 14.4\text{ kWh per day}$

(b) Daily cost $= 14.4 \times 28 = 403.2\text{ c} = \$4.032$

Annual cost $= 4.032 \times 365 = \$1471.68 \approx \mathbf{\$1472}$

2 L19

A surveyor measures widths across a block of land at $10\text{ m}$ intervals and records: $8,\; 15,\; 21,\; 17,\; 9$ (metres).

(a) State the number of strips and identify the first, last, and middle measurements.

(b) Apply the trapezoidal rule to estimate the area.

(a) 5 measurements → 4 strips; $d_f = 8$, $d_l = 9$; middle: $15 + 21 + 17 = 53$

(b) $A \approx \dfrac{10}{2}(8 + 2(53) + 9) = 5 \times (8 + 106 + 9) = 5 \times 123 = \mathbf{615\text{ m}^2}$

3 L20, L21 & L22

A business flight departs Sydney (AEST $=$ UTC$+10$) at $11{:}20\text{ pm}$ on a Monday, flies for $9$ hours and $35$ minutes, and lands in Dubai (UTC$+4$).

(a) Convert Sydney's departure time to UTC.

(b) Find the UTC arrival time (including day).

(d) Sydney's longitude is approximately $151°\text{E}$ and Dubai's is approximately $55°\text{E}$. Using the $15°$ rule, calculate the expected time difference and compare it to the actual UTC offset difference.

(a) Sydney 2320 AEST → UTC $= 2320 - 10 = 1320$ Monday

(b) $1320 + 9\text{h}35 = 2255$ Monday UTC

(c) Dubai UTC+4: $2255 + 4 = 2655 \to 2655 - 2400 = 0255$ Tuesday (2:55 am Tuesday Dubai time)

(d) $\Delta\lambda = 151 - 55 = 96°$; time diff $= 96 \div 15 = 6.4\text{ h}$; actual UTC offset difference $= 10 - 4 = 6\text{ h}$. The longitude-based estimate (6.4 h) is close to the actual offset difference (6 h) but not exact — real time zones follow political/geographic boundaries rather than strict 15° intervals.

When you're happy with your answers, mark this quiz as complete.