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Published:09/02/2011

The selected worked solutions for New Q Maths 12A, 12B and 12C are all contained on this DVD for Year 12. The solutions have been chosen to assist students with the middle level to difficult questions in the textbooks. They are representative and provide students with an opportunity to consolidate and apply the approach they develop to other problems of the same type. A large number of problem-solving and modeling questions have accordingly been included in the selection. The solutions are presented in the same way as the examples in the textbook, with explanation on the left and the mathematical steps on the right.

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• School site licences available for schools that have adopted any of the New Q Maths 11 and 12 textbooks.

eBook features include:

• Adobe annotation tools are enabled, allowing the user to highlight text and add notes and links to their own files and save their annotations

• A recent version of Adobe Reader is sufficient for this, which is a free download from the Adobe site

• Printing enabled

• Bookmarks for navigation

• School site licences available for schools that have adopted any of the New Q Maths 11 and 12 textbooks.

STUDENTS:

PRODUCT:

New Q Maths 12A Selected Worked Solutions

Chapter 1 Navigation I

Exercise 1.1: 3a,b, 4a,b,c, 5a,b,c, 6a,b,c

Exercise 1.2: 1a,c, 2a, 3a, 4a

Chapter 2 Land measurement I

Exercise 2.1: 1a, 2a, 5a,b,c, 7, 8a, 9, 11, 12, 13, 14a

Exercise 2.2; 1, 3, 4

Exercise 2.3: 1, 3, 5a,b,c,d, 8, 9

Exercise 2.5: 1, 2, 5

Chapter 3 Simple and compound interest

Exercise 3.1: 5a,b,c, 7, 8, 12, 13, 14, 19, 20

Exercise 3.2: 2, 5, 6, 11a, 13a,b, 14, 17, 18a,b

Exercise 3.3: 2a, 3, 5, 7, 10

Exercise 3.4: 1a, 3

Chapter 4 Exploring data I

Exercise 4.1: 1a, 2a, 5a, 6, 8a,b

Exercise 4.2: 2, 4a, 6a, 7, 10a,b

Exercise 4.3: 1a, 5, 7, 9, 11

Chapter 5 Depreciation and growth of money

Exercise 5.1: 1, 3, 4a,b,c, 7, 8

Exercise 5.2: 1a,b,c,d, 5, 7, 8a,b

Exercise 5.3: 1, 2, 5, 8, 14, 15a,b, 18a,b,c

Exercise 5.4: 2, 4a, 9, 10

Chapter 6 Exploring data II

Exercise 6.1: 1a,b,c,d,e,f, 81,b, 10a,b

Exercise 6.2: 1a,b,c,d,e, 2a,b,c, 4, 9, 11a,b, 14, 17

Exercise 6.3; 1a,b,c,d,e, 3a,b, 15a,b,c

Chapter 7 Linear programming I

Exercise 7.1: 6a,b,c,d, 7a,b,c,d, 9a,b,c,d,e,f

Exercise 7.2: 1a, 2,4,6

Exercise 7.3: 1a,b,c,d, 3a,b,c,d, 4a,b,c,d

Chapter 8 Networks and queuing I

Exercise 8.1: 3a, 4, 6a

Exercise 8.2: 1a, 3a,b

Exercise 8.3: 1a, 2, 4a,b, 5, 6

Chapter 9 Data models I

Exercise 9.1: 4a,b,c,d,e,f, 6, 7, 8, 9

Exercise 9.2: 3, 6, 8, 10, 11, 14, 16

Exercise 9.3: 2a,b,c,d, 6a,b, 8, 11a,b

Chapter 10 Navigation II

Exercise 10.1: 1a, 2a, 3a,b,c,d,e,f, 4a,b,c, 5a,c, 6a,c, 8, 9a,b

Exercise 10.4: 1a, 2a, 4, 7, 8

Exercise 10.5: 1a, 2a, 4

Chapter 11 Land measurement II

Exercise 11.1: 3a,b,c, 4a,b,c, 5a,b,c,d,e,f

Exercise 11.2: 1a,b,c(i),d(i), 3a,b, 5a,b,c,d,e,f, 9

Exercise 11.3: 1a,b,c,d,e,f, 2a,b,c,f, 5

Chapter 12 Loans and credit

Exercise 12.1: 1, 6, 11, 14

Exercise 12.2: 1a, 2a,b, 3a, 4, 6

Exercise 12.3: 3a,b,c, 6

Chapter 13 Exploring data III

Exercise 13.1: 1, 3, 7

Exercise 13.2: 1a,b,c, 4a,b,c,d,e,f

Exercise 13.3: 2a,b,c, 5, 9a,b,c,d

Exercise 13.4: 1a,b, 2a,b, 4a,b,c, 6, 7

Chapter 14 Investing money

Exercise 14.1: 2a,b, 5

Exercise 14.2: 1a,b, 2a, 3a, 4a, 5a,b, 7

Exercise 14.3: 1a,b,c,d,e, 2a,b,c, 4a,b,c,d, 5a,b, 9, 10, 12

Exercise 14.4: 1, 4, 8a,b

Chapter 15 Linear programming II

Exercise 15.1: 2, 4

Exercise 15.2: 1a,b,c, 4a,b,c,

6a,b,c, 8a,b,c

Exercise 15.3: 1a,b,c,d,e,

3a,b,c,d,e,f,g,h

Chapter 16 Networks and queuing II

Exercise 16.1: 1, 3

Exercise 16.2: 1a, 2a,b, 4a,b,c,d

Exercise 16.4: 1a,b, 3, 4

Exercise 16.5: 1a(i),b, 2a,b,c,d, 7a,b,c, 8a,b,c

Chapter 17 Data models II

Exercise 17.1: 2, 4

Exercise 17.2: 9a,b, 11a,b, 12, 13

Exercise 17.3: 1a,b, 2a,b,c, 4a,b,c, 7

New Q Maths 12B Selected Worked Solutions

Chapter 1 Quadratic, cubic and polynomial functions

Exercise 1.1: 2a,c, 3a,d, 7a,d, 9b,c,d, 11

Exercise 1.2: 3a,b, 4a,e,i

Exercise 1.3: 1a,b,e, 2b, 3, 4

Exercise 1.4: 2a, 9a,b, 10a,b, 11a,b,e, 14, 16a,b,c,d,e

Exercise 1.5: 1a,b,c,d, 3a, 5a,c,e, 6a, 7a, 10a,b, 11

Exercise 9.5: 2a,e, 3a,b,c,d,e, 8a,b,c,d,e,f

Chapter 2 Derivatives of sine and cosine

Exercise 2.1: 3a, 4a, 8b, 9a, 11a, 14a, 15a, 16a, 17a,d,e, 19a,b, 20, 21a,b,c, 23a,b,c,d

Exercise 2.2: 2a,f,g,l, 5a,d,g, 6a,b,f, 9a,b,c

Exercise 2.3: 1a,e, 2a,c,f, 3c,f, 4

Exercise 2.4: 1, 3a,b,c, 5, 6, 9a,b, 10

Chapter 3 Exponential and logarithmic functions and derivatives

Exercise 3.1: 1a, 2a,b, 5d,f, 6a,c,l,j, 7a,d, 8a,d, 10a, 13a,e, 14a

Exercise 3.2: 3a,d,e, 5a,f,g, 6b, 8a,b,d,e,j, 10a,b,e,h,n,o,t

Exercise 3.3: 1a,f, 2d,e, 3a,b,e,g, 4a,b,c, 5a, 6a,b,c

Exercise 3.4: 1a,b,d,g, 2a,c,e, 3, 4a,e, 5a,g,j,m,n, 6g,h, 7

Exercise 3.5: 4a,c,d,h, 5a,b,f

Exercise 3.6: 4a,c,e,h, 5b,c,f

Exercise 3.7: 2a,b, 3, 4a,b,c, 5a,b, 7, 9, 12

Chapter 4 Integration

Exercise 4.1: 1a, 3a, 5a

Exercise 4.2: 1a,d,g,k, 2a, 6

Exercise 4.3: 1a,b,c,h, 3a,g,j, 4, 5, 7

Exercise 4.4: 2a, 6a, 8a, 11a, 12a, 13a, 17, 19

Exercise 4.5: 1a,b,c,d, 3, 6, 8

Chapter 5 Binomial and normal distributions

Exercise 5.1: 1a,b, 3a,b,c, 8, 10

Exercise 5.2: 4, 6, 13, 15a,b, 17, 20, 21, 23, 25

Exercise 5.3: 1a,b,c,d,e, 2a for n=5, 8, 10, 12

Exercise 5.4: 2a,b,c,d,e,f, 6a,b,c,d,e,f, 10a,c, 12a, 13, 16, 18, 19a,b, 22a,b,c, 25

Chapter 6 Optimisation 1

Exercise 6.1: 1a(i),b(i), 6a,b,c,d,e,f, 9a,b,c,d,e,f,

11a,b,c,d,e, 13, 14a,b, 17, 18

Exercise 6.2: 1, 3, 5

Exercise 6.3: 1a,d, 2f,g, 3

Exercise 6.4: 1, 2, 9, 12, 13, 14

Chapter 7 Practical integration techniques

Exercise 7.1: 1a, 9a

Exercise 7.2: 1a, 3a,b, 4, 7, 8, 10, 11a,b,c, 13, 14

Chapter 8 Financial applications

Exercise 8.1: 4, 5, 6, 7, 11, 12a, 13a, 14, 16a, 19a,b,c, 20a,b,c,d, 23, 25, 26

Exercise 8.2; 1a, 2a, 3a, 4a, 5a, 6, 9, 10, 11a, 13a,b, 14

Exercise 8.3: 1, 5, 9a, 11, 12

Exercise 8.4: 1, 3, 4, 8, 9, 11a

Exercise 8.5: 1a, 2a, 3a, 4a, 5a, 7, 8, 11, 12

Exercise 8.6: 1a, 2a, 3a, 4a,b, 6, 7a,b, 8a,b, 11a,b,c,d, 12, 17, 19, 21a,b,c,d,e,f, 23a,b,c,d

Chapter 9 Graphs and transformations

Exercise 9.1: 5a,b,c, 6b, 7a,g, 10a, 11a, 12a,b

Exercise 9.2: 1a,b,c,d, 2a,b,c,d, 5a,b,c, 7a,b,c,d,e,f,g

Exercise 9.3: 1a,c,d, 2a, 3a,b,c, 7a,b, 8a,b

Exercise 9.4: 1a,f,h, 3a,e

Chapter 10 Trigonometric equations

Exercise 10.1: 3a,b, 4a, 5a, 6a, 7a, 10a,d, 11a, 12b, 14a, 15a, 16a

Exercise 10.2: 1a,b,c, 2a,d, 3a,b,c,d, 6a, 7a, 8a,d

Exercise 10.3: 1a,b, 3a,b, 5, 7a,b,c, 8a,d, 9a,b, 10b,c,e, 11a,b,e, 12a,c

Exercise 10.4: 1a,c,h, 4a, 5a, 6a, 7a, 8a, 9a,d, 11a,e

Chapter 11 Optimisation II

Exercise 11.1: 1a,b, 2, 3, 6, 8a,b, 9, 11, 12, 15

Exercise 11.2: 1, 2, 4, 6, 7, 10, 13

Exercise 11.3; 1, 3a,b, 5

New QMaths 12C Selected Worked Solutions

Chapter 1 Finite Directions

Exercise 1.1: 2d, 4a, 6c, 7a, 13

Exercise 1.2: 1a, 2, 4, 6, 8, 10

Exercise 1.3; 1, 5, 7

Chapter 2 Products of vectors

Exercise 2.1: 1a,b, 2a,b, 4a,b, 7, 8, 10, 11, 13, 16, 18

Exercise 2.2: 2a, 3a, 6a, 7a,d, 10a,b, 11a,b,c, 12, 14, 17a, 19a

Exercise 2.3: 1, 3,7, 10, 11, 13, 14, 16a,b,c, 18, 20, 21, 23

Chapter 3 De Moivre's theorem

Exercise 3.1: 2a, 4a,b, 5e, 7, 9, 10

Exercise 3.2: 1a, 2a,b, 6a,c, 7a, 9a, 10, 11b

Exercise 3.3: 1a,b,c, 3a, 4a, 6a, 7

Exercise 3.4: 1a,b,c, 2a,b,c, 4a,b, 5a, 6, 8, 10a,c, 11b, 12a, 14a,b, 17a

Exercise 3.5: 3a,b,c, 4a,b, 5a,c, 8a,b, 9a, 10a, 14a, 15a,b, 19a, 20

Chapter 4 Integration techniques

Exercise 4.1: 1a, 3a,f, 4a,b,c, 6

Exercise 4.2: 1a, 2a, 3, 6

Exercise 4.3: 1a,d, 2a, 3a,b

Chapter 5 Linear programming I

Exercise 5.1: 4, 5, 7,10, 12

Exercise 5.2: 1,2, 4, 5, 6

Exercise 5.3: 1a,b,c, 4a,b,c, 6, 8, 9

Chapter 6 Conics I

Exercise 6.1: 2a,b,d,e, 3a, 6a,d, 7, 10

Exercise 6.2: 1a, 2a, 3a, 5, 6, 7a, 8a, 9a,c, 10a, 12, 13, 15a,d

Exercise 6.3: 1a,d, 3a, 5a, 7, 8

Exercise 6.4: 1a, 2a, 3a, 4a, 6a, 8, 10a,b, 12a,b,c,d

Exercise 6.5: 1a, 2a, 5a, 6a, 8, 9, 10a,b,c

Exercise 6.6: 1, 3, 5, 9, 11, 12

Chapter 7 Dynamics I

Exercise 7.1: 2a,c, 3a, 4a,d,f, 5a,b,c, 6a,b, 9a,b, 11a,b,c,d, 13a,b,c, 14a,b,c

Exercise 7.2: 4a, 6, 8, 11, 13, 17, 18,1a,c,h, 4a, 5a, 6a, 7a, 8a, 9a,d, 11a,e, 20

Exercise 7.3: 3a,b,c,d,e, 5a, 7a,b,c, 9a,b, 16, 17

Exercise 7.4: 1a,b,c, 4a, 6a,b, 8a,b, 10, 15a,b, 16a,b,c,d

Chapter 8 Advanced periodic and exponential functions I

Exercise8.1; 1, 3, 6, 15, 16, 18, 20

Exercise 8.2: 1a, 3a, 4a, 5,9, 11,13, 16, 19, 21, 24, 26

Exercise 8.3: 1a(i),(ii),b(i),(ii), 3, 7, 8, 12, 14, 17a,b,c, 19, 20

Chapter 9 Introductory modelling with probability I

Exercise 9.1: 2e,g,h, 4, 5a, 6a, 7, 9

Exercise 9.2: 1, 2, 4, 5, 6, 10a,b, 11a(i),(ii),b, 13

Exercise 9.3: 2a,b,c, 4, 6, 8, 9a,b,c,d,e,f, 11, 13

Chapter 10 Introduction to number theory I

Exercise 10.1: 1, 3, 5, 9, 11, 13, 16, 18, 20, 22, 24

Exercise 10.2: 4, 5, 6, 8a, 9a, 11, 13a,b, 15, 19, 21a,b

Exercise 10.3: 2a, 3a,b, 11, 12, 14

Chapter 11 Advanced differential calculus

Exercise 11.1: 1, 7, 8, 10, 12, 13, 15

Exercise 11.2: 1a, 2, 4, 6, 8, 9, 13, 16a,b

Exercise 11.3: 1a, 2, 4, 6, 8, 11

Chapter 12 Matrices and determinants

Exercise 12.1: 1a,e,i

Exercise 12.2: 1e,i, 2a,c

Exercise 12.3: 1a, 2a,e

Chapter 13 Approximation methods in calculus

Exercise 13.1: 1, 3a, 7a,b,c,d,e, 9, 11a, 13

Exercise 13.2: 1a, 2a(i), 4, 5a

Exercise 13.3: 1, 2, 6

Exercise 13.4: 1, 4a,b, 9

Exercise 13.5: 2a,b, 4, 6a,b, 8

Chapter 14 Linear programming II

Exercise 14.1: 1a,e, 2

Exercise 14.2: 1a,b, 3a, 8a,b

Exercise 14.3: 1, 3

Exercise 14.4: 1, 3, 7, 8

Chapter 15 Conics II

Exercise 15.1: 3a,c,e,f, 4a,b,d,e, 6a,c, 7

Exercise 15.2: 1a, 2a, 3a,c, 6, 7

Exercise 15.3: 1a, 3a, 4, 5a,b, 7, 9, 11, 13, 16, 17

Exercise 15.4: 1a, 3a, 5a, 6a, 9, 11, 12

Exercise 15.5: 1a, 3, 5a, 10, 11, 15a,b

Chapter 16 Dynamics II

Exercise 16.1: 2, 3a,b,c, 7a,b,c,d,e, 10a,b, 11a,b,c

Exercise 16.2: 1a,b,d, 2a, 3a,c, 4a,c, 5, 6, 7, 8, 11, 12a,b, 12, 13

Exercise 16.3: 1a,b(i), 3a, 4, 5, 6a,b,c, 9a,b,c,d, 12a,b

Exercise 16.4: 1a,b, 2, 4, 5, 7, 10, 13a,b, 16, 19

Chapter 17 Advanced periodic and exponential functions II

Exercise 17.1: 1a, 2, 5, 7a,b,c, 9

Exercise 17.2: 1a,b, 3a, 4a,b,d, 5a,b,c

Exercise 17.3: 1, 3, 5a,b, 7

Chapter 18 Introductory modelling with probability II

Exercise 18.1: 1a,b,f, 4a,b,c,d, 6a,b,c, 7

Exercise 18.2: 1, 2, 3a, b(i), 5, 6, 7a, 9, 11, 12

Exercise 18.3: 2a,b, 4a, 5, 6, 7a, 9, 12a, 15a,b,c

Chapter 19 Introduction to number theory II

Exercise 19.1: 1a,b,c,d, 4a,c, 7, 9, 11, 13, 15, 17, 19, 20

Exercise 19.2: 1a,c, 2a, 4, 6, 8, 10, 11, 12

Exercise 19.3: 1a,b, 2a, 3, 5, 6, 7, 9

Chapter 1 Navigation I

Exercise 1.1: 3a,b, 4a,b,c, 5a,b,c, 6a,b,c

Exercise 1.2: 1a,c, 2a, 3a, 4a

Chapter 2 Land measurement I

Exercise 2.1: 1a, 2a, 5a,b,c, 7, 8a, 9, 11, 12, 13, 14a

Exercise 2.2; 1, 3, 4

Exercise 2.3: 1, 3, 5a,b,c,d, 8, 9

Exercise 2.5: 1, 2, 5

Chapter 3 Simple and compound interest

Exercise 3.1: 5a,b,c, 7, 8, 12, 13, 14, 19, 20

Exercise 3.2: 2, 5, 6, 11a, 13a,b, 14, 17, 18a,b

Exercise 3.3: 2a, 3, 5, 7, 10

Exercise 3.4: 1a, 3

Chapter 4 Exploring data I

Exercise 4.1: 1a, 2a, 5a, 6, 8a,b

Exercise 4.2: 2, 4a, 6a, 7, 10a,b

Exercise 4.3: 1a, 5, 7, 9, 11

Chapter 5 Depreciation and growth of money

Exercise 5.1: 1, 3, 4a,b,c, 7, 8

Exercise 5.2: 1a,b,c,d, 5, 7, 8a,b

Exercise 5.3: 1, 2, 5, 8, 14, 15a,b, 18a,b,c

Exercise 5.4: 2, 4a, 9, 10

Chapter 6 Exploring data II

Exercise 6.1: 1a,b,c,d,e,f, 81,b, 10a,b

Exercise 6.2: 1a,b,c,d,e, 2a,b,c, 4, 9, 11a,b, 14, 17

Exercise 6.3; 1a,b,c,d,e, 3a,b, 15a,b,c

Chapter 7 Linear programming I

Exercise 7.1: 6a,b,c,d, 7a,b,c,d, 9a,b,c,d,e,f

Exercise 7.2: 1a, 2,4,6

Exercise 7.3: 1a,b,c,d, 3a,b,c,d, 4a,b,c,d

Chapter 8 Networks and queuing I

Exercise 8.1: 3a, 4, 6a

Exercise 8.2: 1a, 3a,b

Exercise 8.3: 1a, 2, 4a,b, 5, 6

Chapter 9 Data models I

Exercise 9.1: 4a,b,c,d,e,f, 6, 7, 8, 9

Exercise 9.2: 3, 6, 8, 10, 11, 14, 16

Exercise 9.3: 2a,b,c,d, 6a,b, 8, 11a,b

Chapter 10 Navigation II

Exercise 10.1: 1a, 2a, 3a,b,c,d,e,f, 4a,b,c, 5a,c, 6a,c, 8, 9a,b

Exercise 10.4: 1a, 2a, 4, 7, 8

Exercise 10.5: 1a, 2a, 4

Chapter 11 Land measurement II

Exercise 11.1: 3a,b,c, 4a,b,c, 5a,b,c,d,e,f

Exercise 11.2: 1a,b,c(i),d(i), 3a,b, 5a,b,c,d,e,f, 9

Exercise 11.3: 1a,b,c,d,e,f, 2a,b,c,f, 5

Chapter 12 Loans and credit

Exercise 12.1: 1, 6, 11, 14

Exercise 12.2: 1a, 2a,b, 3a, 4, 6

Exercise 12.3: 3a,b,c, 6

Chapter 13 Exploring data III

Exercise 13.1: 1, 3, 7

Exercise 13.2: 1a,b,c, 4a,b,c,d,e,f

Exercise 13.3: 2a,b,c, 5, 9a,b,c,d

Exercise 13.4: 1a,b, 2a,b, 4a,b,c, 6, 7

Chapter 14 Investing money

Exercise 14.1: 2a,b, 5

Exercise 14.2: 1a,b, 2a, 3a, 4a, 5a,b, 7

Exercise 14.3: 1a,b,c,d,e, 2a,b,c, 4a,b,c,d, 5a,b, 9, 10, 12

Exercise 14.4: 1, 4, 8a,b

Chapter 15 Linear programming II

Exercise 15.1: 2, 4

Exercise 15.2: 1a,b,c, 4a,b,c,

6a,b,c, 8a,b,c

Exercise 15.3: 1a,b,c,d,e,

3a,b,c,d,e,f,g,h

Chapter 16 Networks and queuing II

Exercise 16.1: 1, 3

Exercise 16.2: 1a, 2a,b, 4a,b,c,d

Exercise 16.4: 1a,b, 3, 4

Exercise 16.5: 1a(i),b, 2a,b,c,d, 7a,b,c, 8a,b,c

Chapter 17 Data models II

Exercise 17.1: 2, 4

Exercise 17.2: 9a,b, 11a,b, 12, 13

Exercise 17.3: 1a,b, 2a,b,c, 4a,b,c, 7

New Q Maths 12B Selected Worked Solutions

Chapter 1 Quadratic, cubic and polynomial functions

Exercise 1.1: 2a,c, 3a,d, 7a,d, 9b,c,d, 11

Exercise 1.2: 3a,b, 4a,e,i

Exercise 1.3: 1a,b,e, 2b, 3, 4

Exercise 1.4: 2a, 9a,b, 10a,b, 11a,b,e, 14, 16a,b,c,d,e

Exercise 1.5: 1a,b,c,d, 3a, 5a,c,e, 6a, 7a, 10a,b, 11

Exercise 9.5: 2a,e, 3a,b,c,d,e, 8a,b,c,d,e,f

Chapter 2 Derivatives of sine and cosine

Exercise 2.1: 3a, 4a, 8b, 9a, 11a, 14a, 15a, 16a, 17a,d,e, 19a,b, 20, 21a,b,c, 23a,b,c,d

Exercise 2.2: 2a,f,g,l, 5a,d,g, 6a,b,f, 9a,b,c

Exercise 2.3: 1a,e, 2a,c,f, 3c,f, 4

Exercise 2.4: 1, 3a,b,c, 5, 6, 9a,b, 10

Chapter 3 Exponential and logarithmic functions and derivatives

Exercise 3.1: 1a, 2a,b, 5d,f, 6a,c,l,j, 7a,d, 8a,d, 10a, 13a,e, 14a

Exercise 3.2: 3a,d,e, 5a,f,g, 6b, 8a,b,d,e,j, 10a,b,e,h,n,o,t

Exercise 3.3: 1a,f, 2d,e, 3a,b,e,g, 4a,b,c, 5a, 6a,b,c

Exercise 3.4: 1a,b,d,g, 2a,c,e, 3, 4a,e, 5a,g,j,m,n, 6g,h, 7

Exercise 3.5: 4a,c,d,h, 5a,b,f

Exercise 3.6: 4a,c,e,h, 5b,c,f

Exercise 3.7: 2a,b, 3, 4a,b,c, 5a,b, 7, 9, 12

Chapter 4 Integration

Exercise 4.1: 1a, 3a, 5a

Exercise 4.2: 1a,d,g,k, 2a, 6

Exercise 4.3: 1a,b,c,h, 3a,g,j, 4, 5, 7

Exercise 4.4: 2a, 6a, 8a, 11a, 12a, 13a, 17, 19

Exercise 4.5: 1a,b,c,d, 3, 6, 8

Chapter 5 Binomial and normal distributions

Exercise 5.1: 1a,b, 3a,b,c, 8, 10

Exercise 5.2: 4, 6, 13, 15a,b, 17, 20, 21, 23, 25

Exercise 5.3: 1a,b,c,d,e, 2a for n=5, 8, 10, 12

Exercise 5.4: 2a,b,c,d,e,f, 6a,b,c,d,e,f, 10a,c, 12a, 13, 16, 18, 19a,b, 22a,b,c, 25

Chapter 6 Optimisation 1

Exercise 6.1: 1a(i),b(i), 6a,b,c,d,e,f, 9a,b,c,d,e,f,

11a,b,c,d,e, 13, 14a,b, 17, 18

Exercise 6.2: 1, 3, 5

Exercise 6.3: 1a,d, 2f,g, 3

Exercise 6.4: 1, 2, 9, 12, 13, 14

Chapter 7 Practical integration techniques

Exercise 7.1: 1a, 9a

Exercise 7.2: 1a, 3a,b, 4, 7, 8, 10, 11a,b,c, 13, 14

Chapter 8 Financial applications

Exercise 8.1: 4, 5, 6, 7, 11, 12a, 13a, 14, 16a, 19a,b,c, 20a,b,c,d, 23, 25, 26

Exercise 8.2; 1a, 2a, 3a, 4a, 5a, 6, 9, 10, 11a, 13a,b, 14

Exercise 8.3: 1, 5, 9a, 11, 12

Exercise 8.4: 1, 3, 4, 8, 9, 11a

Exercise 8.5: 1a, 2a, 3a, 4a, 5a, 7, 8, 11, 12

Exercise 8.6: 1a, 2a, 3a, 4a,b, 6, 7a,b, 8a,b, 11a,b,c,d, 12, 17, 19, 21a,b,c,d,e,f, 23a,b,c,d

Chapter 9 Graphs and transformations

Exercise 9.1: 5a,b,c, 6b, 7a,g, 10a, 11a, 12a,b

Exercise 9.2: 1a,b,c,d, 2a,b,c,d, 5a,b,c, 7a,b,c,d,e,f,g

Exercise 9.3: 1a,c,d, 2a, 3a,b,c, 7a,b, 8a,b

Exercise 9.4: 1a,f,h, 3a,e

Chapter 10 Trigonometric equations

Exercise 10.1: 3a,b, 4a, 5a, 6a, 7a, 10a,d, 11a, 12b, 14a, 15a, 16a

Exercise 10.2: 1a,b,c, 2a,d, 3a,b,c,d, 6a, 7a, 8a,d

Exercise 10.3: 1a,b, 3a,b, 5, 7a,b,c, 8a,d, 9a,b, 10b,c,e, 11a,b,e, 12a,c

Exercise 10.4: 1a,c,h, 4a, 5a, 6a, 7a, 8a, 9a,d, 11a,e

Chapter 11 Optimisation II

Exercise 11.1: 1a,b, 2, 3, 6, 8a,b, 9, 11, 12, 15

Exercise 11.2: 1, 2, 4, 6, 7, 10, 13

Exercise 11.3; 1, 3a,b, 5

New QMaths 12C Selected Worked Solutions

Chapter 1 Finite Directions

Exercise 1.1: 2d, 4a, 6c, 7a, 13

Exercise 1.2: 1a, 2, 4, 6, 8, 10

Exercise 1.3; 1, 5, 7

Chapter 2 Products of vectors

Exercise 2.1: 1a,b, 2a,b, 4a,b, 7, 8, 10, 11, 13, 16, 18

Exercise 2.2: 2a, 3a, 6a, 7a,d, 10a,b, 11a,b,c, 12, 14, 17a, 19a

Exercise 2.3: 1, 3,7, 10, 11, 13, 14, 16a,b,c, 18, 20, 21, 23

Chapter 3 De Moivre's theorem

Exercise 3.1: 2a, 4a,b, 5e, 7, 9, 10

Exercise 3.2: 1a, 2a,b, 6a,c, 7a, 9a, 10, 11b

Exercise 3.3: 1a,b,c, 3a, 4a, 6a, 7

Exercise 3.4: 1a,b,c, 2a,b,c, 4a,b, 5a, 6, 8, 10a,c, 11b, 12a, 14a,b, 17a

Exercise 3.5: 3a,b,c, 4a,b, 5a,c, 8a,b, 9a, 10a, 14a, 15a,b, 19a, 20

Chapter 4 Integration techniques

Exercise 4.1: 1a, 3a,f, 4a,b,c, 6

Exercise 4.2: 1a, 2a, 3, 6

Exercise 4.3: 1a,d, 2a, 3a,b

Chapter 5 Linear programming I

Exercise 5.1: 4, 5, 7,10, 12

Exercise 5.2: 1,2, 4, 5, 6

Exercise 5.3: 1a,b,c, 4a,b,c, 6, 8, 9

Chapter 6 Conics I

Exercise 6.1: 2a,b,d,e, 3a, 6a,d, 7, 10

Exercise 6.2: 1a, 2a, 3a, 5, 6, 7a, 8a, 9a,c, 10a, 12, 13, 15a,d

Exercise 6.3: 1a,d, 3a, 5a, 7, 8

Exercise 6.4: 1a, 2a, 3a, 4a, 6a, 8, 10a,b, 12a,b,c,d

Exercise 6.5: 1a, 2a, 5a, 6a, 8, 9, 10a,b,c

Exercise 6.6: 1, 3, 5, 9, 11, 12

Chapter 7 Dynamics I

Exercise 7.1: 2a,c, 3a, 4a,d,f, 5a,b,c, 6a,b, 9a,b, 11a,b,c,d, 13a,b,c, 14a,b,c

Exercise 7.2: 4a, 6, 8, 11, 13, 17, 18,1a,c,h, 4a, 5a, 6a, 7a, 8a, 9a,d, 11a,e, 20

Exercise 7.3: 3a,b,c,d,e, 5a, 7a,b,c, 9a,b, 16, 17

Exercise 7.4: 1a,b,c, 4a, 6a,b, 8a,b, 10, 15a,b, 16a,b,c,d

Chapter 8 Advanced periodic and exponential functions I

Exercise8.1; 1, 3, 6, 15, 16, 18, 20

Exercise 8.2: 1a, 3a, 4a, 5,9, 11,13, 16, 19, 21, 24, 26

Exercise 8.3: 1a(i),(ii),b(i),(ii), 3, 7, 8, 12, 14, 17a,b,c, 19, 20

Chapter 9 Introductory modelling with probability I

Exercise 9.1: 2e,g,h, 4, 5a, 6a, 7, 9

Exercise 9.2: 1, 2, 4, 5, 6, 10a,b, 11a(i),(ii),b, 13

Exercise 9.3: 2a,b,c, 4, 6, 8, 9a,b,c,d,e,f, 11, 13

Chapter 10 Introduction to number theory I

Exercise 10.1: 1, 3, 5, 9, 11, 13, 16, 18, 20, 22, 24

Exercise 10.2: 4, 5, 6, 8a, 9a, 11, 13a,b, 15, 19, 21a,b

Exercise 10.3: 2a, 3a,b, 11, 12, 14

Chapter 11 Advanced differential calculus

Exercise 11.1: 1, 7, 8, 10, 12, 13, 15

Exercise 11.2: 1a, 2, 4, 6, 8, 9, 13, 16a,b

Exercise 11.3: 1a, 2, 4, 6, 8, 11

Chapter 12 Matrices and determinants

Exercise 12.1: 1a,e,i

Exercise 12.2: 1e,i, 2a,c

Exercise 12.3: 1a, 2a,e

Chapter 13 Approximation methods in calculus

Exercise 13.1: 1, 3a, 7a,b,c,d,e, 9, 11a, 13

Exercise 13.2: 1a, 2a(i), 4, 5a

Exercise 13.3: 1, 2, 6

Exercise 13.4: 1, 4a,b, 9

Exercise 13.5: 2a,b, 4, 6a,b, 8

Chapter 14 Linear programming II

Exercise 14.1: 1a,e, 2

Exercise 14.2: 1a,b, 3a, 8a,b

Exercise 14.3: 1, 3

Exercise 14.4: 1, 3, 7, 8

Chapter 15 Conics II

Exercise 15.1: 3a,c,e,f, 4a,b,d,e, 6a,c, 7

Exercise 15.2: 1a, 2a, 3a,c, 6, 7

Exercise 15.3: 1a, 3a, 4, 5a,b, 7, 9, 11, 13, 16, 17

Exercise 15.4: 1a, 3a, 5a, 6a, 9, 11, 12

Exercise 15.5: 1a, 3, 5a, 10, 11, 15a,b

Chapter 16 Dynamics II

Exercise 16.1: 2, 3a,b,c, 7a,b,c,d,e, 10a,b, 11a,b,c

Exercise 16.2: 1a,b,d, 2a, 3a,c, 4a,c, 5, 6, 7, 8, 11, 12a,b, 12, 13

Exercise 16.3: 1a,b(i), 3a, 4, 5, 6a,b,c, 9a,b,c,d, 12a,b

Exercise 16.4: 1a,b, 2, 4, 5, 7, 10, 13a,b, 16, 19

Chapter 17 Advanced periodic and exponential functions II

Exercise 17.1: 1a, 2, 5, 7a,b,c, 9

Exercise 17.2: 1a,b, 3a, 4a,b,d, 5a,b,c

Exercise 17.3: 1, 3, 5a,b, 7

Chapter 18 Introductory modelling with probability II

Exercise 18.1: 1a,b,f, 4a,b,c,d, 6a,b,c, 7

Exercise 18.2: 1, 2, 3a, b(i), 5, 6, 7a, 9, 11, 12

Exercise 18.3: 2a,b, 4a, 5, 6, 7a, 9, 12a, 15a,b,c

Chapter 19 Introduction to number theory II

Exercise 19.1: 1a,b,c,d, 4a,c, 7, 9, 11, 13, 15, 17, 19, 20

Exercise 19.2: 1a,c, 2a, 4, 6, 8, 10, 11, 12

Exercise 19.3: 1a,b, 2a, 3, 5, 6, 7, 9

Selected from middle difficulty and most difficult questions in each set, chosen to help students progress in each topic

Plenty of modelling and problem-solving questions included

Solutions are in the same style as the examples in the textbooks, with “thinking” explanations on the left and mathematical working on the right

Questions are included with the solutions.

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