(a) The table shows the temperature at noon each day for one week in a city.
Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
5°C | 2°C | −3°C | −1°C | 0°C | 1°C | −2°C |
(i) Which day had the lowest noon temperature?
(ii) Find the difference between the noon temperatures on Tuesday and Wednesday.
(iii) Write these seven temperatures in order, starting with the lowest.
(iv) On Sunday the noon temperature was −2°C.
The next day the noon temperature fell by 4°C.
Find the noon temperature on the next day.
(b) The number of houses in the city is 1,935,364.
Write this number correct to the nearest million.
(c) The height, h metres, of a tower in the city is 120m, correct to the nearest 10m.
Complete this statement about the value of h.
(d) The diagram shows the cross section of a circular tunnel in the city.
Calculate the shaded area.
▶️ Answer/Explanation
(a)(i) Ans: Wednesday
The lowest temperature was −3°C on Wednesday.
(a)(ii) Ans: 5°C
Difference: 2°C (Tuesday) − (−3°C) (Wednesday) = 5°C
(a)(iii) Ans: −3, −2, −1, 0, 1, 2, 5
Ordered temperatures: −3°C, −2°C, −1°C, 0°C, 1°C, 2°C, 5°C
(a)(iv) Ans: −6°C
Sunday: −2°C
Next day: −2°C − 4°C = −6°C
(b) Ans: 2,000,000
1,935,364 rounded to nearest million: 2 million (since 935,364 ≥ 500,000)
(c) Ans: 115 ≤ h < 125
120m to nearest 10m means: 115m ≤ h < 125m
(d) Ans: 28.3 m²
Shaded area = Area of square − Area of circle
= (8×8) − (π×4²) = 64 − 16π ≈ 28.3 m²
(a) Hillibar Station (1047m) and Sular Junction (297m):
(i) Calculate height difference.
(ii) Temperature falls 1°C per 100m. If Sular Junction is 19°C, find Hillibar’s temperature.
(iii) Round 297 to nearest ten.
(iv) Round 1047 to nearest hundred.
(b) Time calculations:
(i) Kim arrives at Hillibar at 12:35; taxi takes 27 mins. Find arrival time at hotel.
(ii) Henry’s walk to Sular Junction takes 17 mins. Must arrive by 10:43. Find latest departure time.
(c) Train timetable:
(i) Complete missing times.
(ii) Calculate average speed for 64km journey.
(iii) Joel arrives at Sular Junction at 11:48. Find next departure to Hillibar.
▶️ Answer/Explanation
(a)(i) Ans: 750m
1047m – 297m = 750m difference
(a)(ii) Ans: 11.5°C
Temperature drop: (750m ÷ 100) × 1°C = 7.5°C
19°C – 7.5°C = 11.5°C
(a)(iii) Ans: 300
297 rounded to nearest ten: look at units digit (7 ≥ 5) → round up to 300
(a)(iv) Ans: 1000
1047 rounded to nearest hundred: look at tens digit (4 < 5) → round down to 1000
(b)(i) Ans: 13:02
12:35 + 27 minutes = 13:02 (add 25 mins to make 13:00, then remaining 2 mins)
(b)(ii) Ans: 10:26
10:43 – 17 minutes = 10:26 (subtract 3 mins to make 10:40, then remaining 14 mins)
(c)(i) Ans: 16:24
From timetable pattern: 08:00 → 09:36 (1h36m journey)
14:48 + 1h36m = 16:24
(c)(ii) Ans: 40 km/h
Speed = Distance ÷ Time
64km ÷ 1.6h (1h36m) = 40 km/h
(c)(iii) Ans: 12:32
From timetable: after 11:48, next departure is at 12:32 (following the 2h24m interval pattern)