Printing: use your browser's print (Ctrl+P / ⌘P). It comes out as exactly 4 A4 sheets (2 pieces of paper double-sided). No answers in here.

time yourself (optional)

Stretch (not recorded)From Sun 18 October, any time1 / 4

Stretch — averages and "per one"

Not recorded. Getting it wrong is fine. Some numbers in the sources are not needed

Name Date

1 · Timing ten swings　[science: pendulums]

Source 1

One swing there and back is so short that timing it once gives a large error. So the time for ten swings was measured three times (a made-up experiment), and one swing is worked out from the records. Every weight was 20 g.

pendulum	length	1st try (s)	2nd try (s)	3rd try (s)
A	25 cm	10.2	9.9	9.9
B	64 cm	16.2	15.9	15.9
C	100 cm	20.4	19.8	19.8

Source 2 — time taken for ten swings (made up)

1Which single measurement of ten swings took the longest: which pendulum, which try, and how many seconds?

2Even out the three times for B (take the mean) to get the time for ten swings. From that, how many seconds is one swing of B?

3Counting from the moment it is released, how many swings does pendulum B make in one minute (60 seconds)? What does the part after the decimal point mean for the pendulum?

4Work out the time for one swing of A and of C. Then: a friend says "if you make the pendulum twice as long, one swing takes twice as long". Is that right? Explain with the numbers for A and C.

time yourself (optional)

Stretch (not recorded)From Sun 18 October, any time2 / 4

Stretch — averages and "per one"

Name Date

2 · Food self-sufficiency　[social studies: food production]

Source 1

In a (made-up) country, the share of the food eaten there that was also made there is called food self-sufficiency. Here we use weight. The country has 4.3 million ha of farmland.
Self-sufficiency (%) = amount made in the country ÷ amount eaten in the country × 100

food	made here (×10,000 t)	eaten here (×10,000 t)
rice	7.2	7.5
wheat	0.9	6.0
soybeans	0.24	3.0
vegetables	13.5	15.0
wheat (ten years ago)	0.6	5.0

Source 2 — this year, and wheat ten years ago (made up)

5This year, which food was eaten in the largest amount? How many ×10,000 t?

6What is the self-sufficiency of rice and of soybeans, in %?

7Wheat self-sufficiency: from what % ten years ago to what % now?

8A friend says: "In ten years the wheat made went up 1.5 times. So the self-sufficiency must have gone up 1.5 times too." Is that right? Explain with numbers from the table.

time yourself (optional)

Stretch (not recorded)From Sun 18 October, any time3 / 4

Stretch — averages and "per one"

Name Date

3 · Solar panels on a roof　[science and social studies: electricity and energy]

Source 1

A (made-up) school put 12.5 m² of solar panels on its roof. The electricity made by 1 m² of panel in a day (in kWh) was measured from Monday to Friday. The school uses 7.5 kWh of electricity a day. The roof slopes at 30°.

Source 2 — the electricity made by 1 m² of panel in a day. The numbers are made up.

9On which day was the least electricity made, and how many kWh was it?

10What is the mean electricity made by 1 m² of panel in a day over the five days, in kWh?

11For the whole 12.5 m² of panels, what is the mean amount made in a day, in kWh?

12A friend says: "The mean amount made (question 11) is more than the 7.5 kWh the school uses a day, so on all five days the school did not need to buy electricity." Is that right? Explain with numbers for particular days.

time yourself (optional)

Stretch (not recorded)From Sun 18 October, any time4 / 4

Stretch — averages and "per one"

Name Date

4 · A train timetable　[social studies: transport]

Source 1

The timetable of a train on a (made-up) line. A to B is 180 km, B to C is 108 km. The train waits a while at B to let a faster train go by. Its top speed is 260 km/h.

station	arrives	leaves
A	—	8:00
B	8:45	8:54
C	9:30	—

Source 2 — the timetable (made up)

13How many minutes does the train stand at station B?

14For A to B and for B to C, what is the speed while the train is running, in km/h?

Turn minutes into hours by dividing by 60 (30 min = 0.5 h).

15From A to C, including the time stopped at B, what is the mean speed in km/h?

16On another day the train ran the 180 km from A to B at 240 km/h on the way there and, because of snow, at 120 km/h on the way back. A friend says: "(240 + 120) ÷ 2 = 180, so the mean speed for the round trip is 180 km/h." Is that right? Work out the round-trip mean speed and give your reason.

The whole round-trip distance ÷ the whole time. Find the time there and the time back separately. Draw it.

1 · Timing ten swings [science: pendulums]

2 · Food self-sufficiency [social studies: food production]

3 · Solar panels on a roof [science and social studies: electricity and energy]

4 · A train timetable [social studies: transport]

1 · Timing ten swings　[science: pendulums]

2 · Food self-sufficiency　[social studies: food production]

3 · Solar panels on a roof　[science and social studies: electricity and energy]

4 · A train timetable　[social studies: transport]