In this section of the syllabus, we have topics about the number systems and notation that we use to describe the world around us, the notions of accuracy, estimation and percentage error and sequences which cross over with the Functions and Modelling section.

Please find links to key chapters from this area of the course below. In addition, here is a growing collection of practice questions for you to use as a review exercise for the whole unit. Currently there are 5 exam style questions worth 38 marks and should be completed in about 40 minutes, before looking at the solutions.

Using the formula for percentage error, The key is to identify the Exact amount as the figure given from ticket sales

c) \(0.919\quad =\quad 9.19\times { 10 }^{ -1 }\)

Shorter P1 style question - 6 marks

On a particular stretch of railway line, there are said to be approximately \(9.62\times { 10 }^{ 5 }\)railway sleepers, spaced at an average of 62.5 cm from center to center.

a) Based on these calculations, what is the length of this stretch of railway to the nearest km ?

b) Given that the actual stretch of railway is exactly 625 km, calculate the percentage error in your answer to part a)

c) Given the exact length of 625km and an approximate spacing of 62.5cm between sleepers, how many gaps would you expect to find on the stretch of railway line? Give you answer in the form \(a\times { 10 }^{ k },\quad where\quad 1\le a<10,\quad k\in Z\)

One might argue about whether or not the track starts and finishes with a sleeper, but I wouldn't make a difference to the answer when given to the nearest km. Follow through marks would be awarded if you used an incorrrect answer to part a)

Now decide, for each of the following statements about these numbers whether they are true or false. (enter either T of F in the cell)

a) All of the numbers listed are Real

b) the number, \(3.\dot { 6 } \) is rational

c) 3 of the nubers belong to the set of integers

d) 2 of the numbers are ratinal but not integers

e) \(\pi \) is the only number that is real, but not rational

f) All natural numbers are integers

a) Yes, all of the numbers are real. There are no examples of complex numbers given

b) Recurring decimas ARE rational, because they can be expressed as fractions

c) Only, -6 and 94 are whole numbers

d) \(7.5\quad and\quad 3.\dot { 6 } \) both belong in this section

e) \(\sqrt { 7 } \) also belongs in this category

f) True - Integers are whole numbers, positive and negative, Natural numbers are whole and positive and so a subset of integers

Shorter P1 style question - 8 marks

Gordie invests 2000 dollars (USD) in an account that pays a nominal interest rate of 5.5% compounded monthly for a period of 4 years. Chris invests the same amount of money at a rate of 5.6% compounding quarterly for the same period.

a) Calculate the amount of money Gordie's investment is worth after 4 years? (give your answer to the nearest dollar

b) Does chris have more or less money? (Enter M or L)

After 4 years, Chris takes out the interest he has earned (to the nearest dollar) and converts ot to Euros for a trip to Paris. the conversion rate is 1USD = xEuros and he receives 448 euros for his dollars

Longer P2 style question - 14 marks (part e) and particularly part f) are a focus for students looking for 6s and 7s)

In this question, give all of your answers to the nearest dollar

Ace and Billy opened a new restaurant opened in Jacksonville and made a profit of 1200 USD in their first week. The profit increased by by 150 USD every week there after.

a) What was the profit made in the 18th week?

b) Calculate the total profit made by the restaurant in the first 20 weeks

Across town, Teddy and Vern opened their own restaurant at the same time. They also made 1200 USD in the first week, but their profits increased by 6% every week.

c) What was the profit in the 18th week of Tedy and Vern's place?

d) What was their total profit for the first 20 weeks?

e) What week was the first week that Teddy and Vern's place made more profit than Ace and Billy's?

f) After how many weeks was Teddy and Vern's total profit bigger than that of Ace and Billy?

a) 18th week profits are USD

b) Total of first 20 weeks profits are USD

c) 18th week profits are USD

d) Total of first 20 weeks profits are USD

e) Teddy and Vern make more profit for the fiorst time in week

f) Tedy and Vern's total profit is bigger for the first time afetr week

a) \({ U }_{ n }={ U }_{ 1 }+d(n-1)\\ { U }_{ 18 }=1200+17x150=3750\)

b) \({ S }_{ n }=\frac { n }{ 2 } ({ 2U }_{ 1 }+d(n-1))\\ { S }_{ 20 }=\frac { 20 }{ 2 } (2\times 1200+150(20-1))\\ { S }_{ 20 }=52500\)

c) \({ U }_{ n }={ U }_{ 1 }\times { r }^{ n-1 }\\ { U }_{ 18 }=1200\times { 1.06 }^{ 18-1 }\\ { U }_{ 18 }=3231.327343=3231\quad (nearest\quad dollar)\)

d) \({ S }_{ n }={ U }_{ 1 }\left( \frac { { r }^{ n }-1 }{ r-1 } \right) \\ { S }_{ 20 }=1200\left( \frac { { 1.06 }^{ 20 }-1 }{ 1.06-1 } \right) \\ { S }_{ 20 }=44142.70944=44143\quad (nearest\quad dollar)\)

When numbers are reported in the news, or as statistical results, they are either displayed exactly, or they are rounded to a certain degree of accuracy. Understanding how and when to do this can give us a deeper insight into the important numbers we run

This is a small sup-topic to introduce or recap numbers in standard form. We will learn how to convert between numbers in standard form and base form, alongside learning how to operate with this succinct and helpful way to express numbers.

This sub topic is about the 4 key sets of numbers that define our number system. Natural numbers, Integers, Rational numbers and Real numbers. This section starts by taking you through the concept of number sets, starting with sets that we...

These are sequences where the difference from one term to the next remains constant, like the one in the title! Arithmetic sequences crop up in all sorts of places and this unit looks at understanding how to generalise, sum and solve problems...

These are sequences where you go from term to term by multiplying by a common ratio. the one in the title has a common ratio of 3 because each term is 3 times bigger than the previous one. Geometric sequences grow exponentially and should be...

Give us feedback

Which of the following best describes your feedback?