Reference no: EM13967086
Question 1
Marks will be allocated for good mathematical communication as well as the correct answers.
Table 1 shows the gender breakdown and di?erent age groups of dancers
attending a salsa dance session.
Table 1 The number of dancers attending a salsa dance session
Age in years Male Female Total.
|
Age in years
|
Male
|
Female
|
Total
|
|
Under 40
|
14
|
19
|
33
|
|
40-65
|
A
|
8
|
19
|
|
Over65
|
3
|
5
|
8
|
|
Total
|
28
|
32
|
60
|
(a) Calculate the number that should be in the shaded box marked A. Show your working clearly.
(b) Work out the percentage of dancers attending the salsa dance session who are aged under 40 years.
(c) Find the total number of dancers at the salsa dance session who are aged 40 or over. If you were told that only one-third of these dancers (aged 40 or over) are female, would this statement be true? Justify your answer.
(d) Write the number of dancers aged over 65 as a fraction of the total number of dancers attending the salsa dance session. Cancel your fraction down to write it in its simplest form.
(e) 30% of the dancers who attend the salsa dance session also attend a jazz dance session. How many dancers is this?
(f) Next year the teacher plans to increase the total number of dancers attending the salsa dance session from 60 to 70. Calculate the percentage increase in the number of dancers, giving your answer correct to the nearest whole number.
Question 2
Marks will be allocated for good mathematical communication as well as the correct answers.
Gareth wants to buy a new sofa. He ?nds one that he likes at a price of £499. However, when he returns to the store, prices for this make of sofa have risen by 10%.
(a) Calculate the new price of the sofa after the 10% price rise.
(b) The store then holds a sale with 15% o? all sofa prices. Calculate the sale price of the sofa. (Note that this reduction of 15% should be applied to your answer to part (a).
(c) Gareth's friend (wrongly) told him that the price of the sofa in the sale was 5% lower than the price of £499 he ?rst saw it at.
(i) Calculate what price the sofa would be after a 5% discount from the ?rst price of £499.
(ii) Compare this price to your answer to part (b) and explain in words why increasing the price by 10% and then reducing it by 15% is not the same as reducing the price by 5%.
(d) Gareth measures the sofa and ?nds the length is 168.5 cm.
(i) Round 168.5 cm to 3 signi?cant ?gures.
(ii) Round 168.5 cm to 2 signi?cant ?gures.
(iii) Round 168.5 cm to 1 signi?cant ?gure.
(iv) Gareth accidentally wrote the measurement down as 165.8 cm.
Which one of the above roundings will give a di?erent answer for 168.5 cm and 165.8 cm? Explain your answer.
Question 3
Marks will be allocated for good mathematical communication as well as the correct answers.
This question concerns a journey from Gravesend to Tonbridge via Sevenoaks. A map with scale 1 : 80 000 is used to determine the distances.
(a) On the map, the distance of the ?rst part of the journey from Gravesend to Sevenoaks is 33.5 cm. Find the corresponding distance on the ground in km.
(b) The total distance from Gravesend to Tonbridge via Sevenoaks is 36 km, and the journey takes 42 minutes. Find the average speed in km/h, to the nearest 10 km/h.
(c) The cost of the petrol for the journey is £1.35 per litre and the car averages 15 km per litre.
(i) Using this information, copy and complete the table below.
|
Number of kilometres travelled
|
0
|
10
|
15
|
20
|
50
|
100
|
150
|
200
|
|
Cost of Petrol (£)
|
0.00
|
0.90
|
1.35
|
1.80
|
|
|
|
|
(ii) Draw a graph to illustrate this information. The vertical axis should show the cost of petrol in pounds, and the horizontal axis should show the number of kilometres travelled. Mark the points clearly and join them up with a line.
(iii) Explain how you could use your graph to ?nd the number of kilometres that the car could travel on average for £12.
(iv) Construct a formula for the cost in pounds, C, of travelling x kilometres.
Question 4
Marks will be allocated for good mathematical communication as well as the correct answers.
(a) Jane is planning a trip abroad. Her friend tells her about a formula that she can use to estimate the extra (hidden) costs, E, in pounds, involved in using a budget airline rather than a standard airline.
E = 18l + 4h,
where l is the number of pieces of checked luggage she wishes to take, and h is the number of ?ying hours for the return trip.
(i) Jane plans to ?y from London to Lisbon, a return trip involving 5 hours 40 minutes ?ying time, and she would like to take 2 pieces of checked luggage. Use the formula to ?nd the extra cost involved in using a budget airline for such a trip.
(ii) Jane ?nds return ?ights advertised from London to Lisbon costing £63 for a budget airline and £104 for a standard airline.
Assuming that the formula holds, explain why she would be better o? choosing the standard airline.
(iii) Airlines o?er fares for adults, children and infants, where an adult is anyone aged 12 years or over, and an infant is under 2 years old. If a represents the age of a child in years, give a double inequality to describe the age restriction for child fares.
(b) Consider the formula N = 16 - n2 - 3n.
Find the value of N when n = -1.5, showing your working clearly.
Question 5
Marks will be allocated for good mathematical communication as well as the correct answers.
In this question, you are asked to comment on a student's incorrect attempt at answering the following question:
I made 35 chocolate cases and ?lled 18 of them with cappuccino tru?e. I ?lled the remaining ones with orange lacquer tru?e, except for the three which disintegrated and I ate. How many complete orange lacquer tru?es did I succeed in making?
The student's incorrect solution is below:
35 -18 - 3 = 35 -15 = 20
(a) Write out your own solution to the question, showing your working in Full.
(b) The student has made a mistake in the arithmetic in the line 35 - 18 - 3 = 35 - 15 = 20.
Where does the mistake lie? Explain, as if directly to the student, why their working is incorrect.