Marks will be allocated for good mathematical communication as well as the correct answers. Table 1 shows the gender breakdown and different age groups of dancers attending a salsa dance session. Table 1 The number of dancers att

Question 1

Marks will be allocated for good mathematical communication as well as the correct answers.

Table 1 shows the gender breakdown and different 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.

 (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 finds 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% off 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 first saw it at.

(i) Calculate what price the sofa would be after a 5% discount from

the first 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 finds the length is 168.5 cm.

(i) Round 168.5 cm to 3 significant figures.

(ii) Round 168.5 cm to 2 significant figures.

(iii) Round 168.5 cm to 1 significant figure.

(iv) Gareth accidentally wrote the measurement down as 165.8 cm.

Which one of the above roundings will give a different 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 first 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.

B

(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 find 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 flying hours for the return trip.

(i) Jane plans to fly from London to Lisbon, a return trip involving

5 hours 40 minutes flying time, and she would like to take

2 pieces of checked luggage. Use the formula to find the extra cost

involved in using a budget airline for such a trip.

(ii) Jane finds return flights 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 off choosing the standard airline.

(iii) Airlines offer 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 filled 18 of them with cappuccino

truffle. I filled the remaining ones with orange lacquer truffle,

except for the three which disintegrated and I ate. How many

complete orange lacquer truffles 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.

T