Compound Measures: WJEC GCSE Numeracy Higher November 2016 Unit 1 Q7

Numeracy Higher November 2016 Unit 1 Q7

WJECHigherCurrent spec12 marksCompound Measures Drawing & Using Graphs Units & Time

7. Siân went for a ride on her bike.

She started her ride at 14:00.
The graph below shows information about her bike ride.

Velocity (km/h, 0 to 20) against Time (14:00 to 17:00): a curve starting at 0 at 14:00, rising slowly then steeply between about 14:30 and 15:00, peaking at 19 km/h around 15:10 to 15:20, falling to 14 km/h at 16:00, 12 km/h at 16:30 and to 0 at 17:00

(a)

During which quarter-hour period was Siân’s acceleration the greatest? [1]

(b)

At about what time did Siân stop accelerating? [1]

(c)

Siân usually finds cycling at a velocity of 18 km/h very comfortable.
Express 18 km/h in metres per second. [2]

(d)

Using her velocities at 14:00, 15:00 and 16:00, calculate an estimate for the total distance Siân travelled between 14:00 and 16:00. [3]

Distance travelled …………… km

(e)

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Siân estimated the distance she travelled between 16:00 and 17:00 as 5 miles.
Is Siân’s estimate reasonable?
You must justify your answer and show your working. [3 + 2 OCW]

Scheme	Marks	Comments
14:30 to 14:45	B1	Accept any ¼ hour period within 14:27 to 14:57 inclusive Allow e.g. 2:30(p.m.) to 2:45(p.m.)

Scheme	Marks	Comments
Answer in the range 15:09 to 15:15 inclusive	B1	Allow e.g. 3:09(p.m.) to 3:15(p.m.) inclusive

Scheme	Marks	Comments
\(\dfrac{18 \times 1000}{60 \times 60}\)	M1	Or equivalent e.g. 18 × 5 ÷ 18
5 (metres per second)	A1

Mark scheme (d)

Scheme	Marks	Comments
		Do not penalise a more accurate estimate that uses the velocities at 14:00, 15:00 and 16:00, e.g. using ½-hour intervals.
½ × 18 + ½ × 1 × (18 + 14) (= 9 + 16)	M2	M1 for one of the two areas correct in the sum, OR M1 for 1 slip in reading If a more accurate estimate used, M2 for a full correct method M1 for a full method with at least 1 correct area calculation A1 is dependent on M2 being awarded
25 (km)	A1	No FT from M1 Alternative method: M2 for ½×1×((0+)14+2(18)) Award M1 if 1 error made A1 for 25 (km) No FT from M1

Mark scheme (e)

Scheme	Marks	Comments
Shows the distance travelled from the graph, e.g. ½ × 1 × 14 (= 7 km) or ½ × ½ × (14 + 12) + ½ ×½ × 12 (= 9.5 km)	M1
Distance from the graph 7 (km) to 12 (km)	A1	If units are given they must be correct Must follow their working correctly
Shows use of 5 miles ≈ 8 km with a comparison conclusion, e.g. ‘7 km is reasonably close 8 km which is 5 miles’, ‘not really as 5 miles ≈ 8 km, so 9.5 km is a greater distance’	E1	Depends on M1 previously awarded Need sight of conversion 5 miles ≈ 8 km, or equivalent For this question, accept use of 3 miles is approximately 5 km
Organisation and communication	OC1	Organisation and communication For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanations and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means
Accuracy of writing	W1	Accuracy of writing For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc.