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SM Remainder and Factor Theorem
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Functions (Ext1), F2 Polynomials (Y11)
Remainder and Factor Theorems (Ext1)
Teacher: Gary Macaulay
Exam Equivalent Time: 61 minutes (based on allocation of 1 minutes per mark)
HISTORICAL CONTRIBUTION
Polynomials has contributed a solid 7%, on average, to new syllabus Ext1 exams since being introduced
in 2020.
This topic has been split into two categories for analysis purposes which are: 1-Remainder and Factor
Theorems (2%) and 2-Sum, Products and Multiplicity of Roots (4%).
This analysis looks at Remainder and Factor Theorems.
HSC ANALYSIS - What to expect and common pitfalls
Remainder and Factor Theorems (2%) has been examined in every new syllabus Ext1 exam to date, twice
in the longer answer section (2023 and 2020) and twice in the multiple choice (2022 and 2021).
2022 Ext1 3 MC represents the upper difficulty level of this topic area, producing a 51% mean mark.
Review carefully.
Notwithstanding the above point, this topic area is typically examined around a band 3-4 level of difficulty
and represents a great opportunity to score highly. Revise this area carefully to eliminate silly errors and
get ahead of the exam clock, in that order.
EXTENSION 1
Stage 6
1. Functions, EXT1 F2 2013 HSC 1 MC
2. Functions, EXT1 F2 2017 HSC 1 MC
3. Functions, EXT1 F2 2016 HSC 2 MC
4. Functions, EXT1 F2 2019 MET2-N 3 MC
Questions
The polynomial has a factor.
What is the value of?
A.
B.
C.
D.
Which polynomial is a factor of?
A.
B.
C.
D.
What is the remainder when is divided by?
A.
B.
C.
D.
If is a factor of , where , then the value of is
A. 7
B. 4
C. 1
D. –
5. Functions, EXT1 F2 2021 HSC 3 MC
6. Functions, EXT1 F2 SM-Bank 2 MC
7. Functions, EXT1 F2 2015 HSC 1 MC
8. Functions, EXT1 F2 2012 HSC 8 MC
What is the remainder when is divided by?
A.
B.
C.
D.
Let. When is divided by , the remainder is 5.
The value of is
A.
B.
C.
D.
RAP Data (vs state mean) - Bottom 11%: School result (77%) was 9% below state average (86%)
What is the remainder when is divided by?
A.
B.
C.
D.
RAP Data (vs state mean) - Bottom 21%: School result (66%) was 2% below state average (68%)
When the polynomial is divided by , the remainder is.
What is the remainder when is divided by?
A.
B.
C.
D.
9. Functions, EXT1 F2 2014 HSC 9 MC
10. Functions, EXT1 F2 2022 HSC 3 MC
11. Functions, EXT1 F2 2018 HSC 11a
12. Functions, EXT1 F2 2020 HSC 11a
13. Functions, EXT1 F2 2015 HSC 11f
RAP Data (vs state mean) - Bottom 1%: School result (53%) was 26% below state average (79%)
The remainder when the polynomial is divided by is.
What is the value of?
A.
B.
C.
D.
Let be a polynomial of degree 5. When is divided by the polynomial , the remainder is
.
Which of the following is true about the degree of?
A. The degree must be 1.
B. The degree could be 1.
C. The degree must be 2.
D. The degree could be 2.
Part ii: RAP Data (vs state mean) - Bottom 5%: School result (75%) was 13% below state average (88%)
Consider the polynomial.
i. Show that is a zero of. (1 mark)
ii. Find the other zeros. (2 marks)
Let.
i. Show that. (1 mark)
ii. Hence, factor the polynomial as , where is a quadratic polynomial. (2 marks)
Consider the polynomials and.
i. Given that is divisible by , show that. (1 mark)
ii. Find all the zeros of when. (2 marks)
1. Functions, EXT1 F2 2013 HSC 1 MC
2. Functions, EXT1 F2 2017 HSC 1 MC
3. Functions, EXT1 F2 2016 HSC 2 MC
4. Functions, EXT1 F2 2019 MET2-N 3 MC
Worked Solutions 5. Functions, EXT1 F2 2021 HSC 3 MC
6. Functions, EXT1 F2 SM-Bank 2 MC
7. Functions, EXT1 F2 2015 HSC 1 MC
8. Functions, EXT1 F2 2012 HSC 8 MC
9. Functions, EXT1 F2 2014 HSC 9 MC
♦ Mean mark 51%.
10. Functions, EXT1 F2 2022 HSC 3 MC
11. Functions, EXT1 F2 2018 HSC 11a
i.
ii.
12. Functions, EXT1 F2 2020 HSC 11a
i.
ii.
16. Functions, EXT1 F2 2007 HSC 2c
17. Functions, EXT1 F2 2009 HSC 2a
18. Functions, EXT1 F2 2011 HSC 2a
MARKER’S
COMMENT: “Grave
concern” that many who
found
stated the remainder was
27.
19. Functions, EXT1 F2 2008 HSC 1a
20. Functions, EXT1 F2 2004 HSC 3b
i.
(ii)
ii. COMMENT: This
question requires a
fundamental
understanding of the
remainder theorem.
21. Functions, EXT1 F2 2010 HSC 2c
i.
Copyright © 2016-2024 M2 Mathematics Pty Ltd (SmarterMaths.com)
Was this document helpful?
SM Remainder and Factor Theorem
Subject: math advanced
513 Documents
Students shared 513 documents in this course
Was this document helpful?
Functions (Ext1), F2 Polynomials (Y11)
Remainder and Factor Theorems (Ext1)
Teacher: Gary Macaulay
Exam Equivalent Time: 61.5 minutes (based on allocation of 1.5 minutes per mark)
HISTORICAL CONTRIBUTION
Polynomials has contributed a solid 7.2%, on average, to new syllabus Ext1 exams since being introduced
in 2020.
This topic has been split into two categories for analysis purposes which are: 1-Remainder and Factor
Theorems (2.9%) and 2-Sum, Products and Multiplicity of Roots (4.3%).
This analysis looks at Remainder and Factor Theorems.
HSC ANALYSIS - What to expect and common pitfalls
Remainder and Factor Theorems (2.9%) has been examined in every new syllabus Ext1 exam to date, twice
in the longer answer section (2023 and 2020) and twice in the multiple choice (2022 and 2021).
2022 Ext1 3 MC represents the upper difficulty level of this topic area, producing a 51% mean mark.
Review carefully.
Notwithstanding the above point, this topic area is typically examined around a band 3-4 level of difficulty
and represents a great opportunity to score highly. Revise this area carefully to eliminate silly errors and
get ahead of the exam clock, in that order.
EXTENSION 1
Stage 6
1.Functions, EXT1 F2 2013 HSC 1 MC
2.Functions, EXT1 F2 2017 HSC 1 MC
3.Functions, EXT1 F2 2016 HSC 2 MC
4.Functions, EXT1 F2 2019 MET2-N 3 MC
Questions
The polynomial has a factor .
What is the value of ?
A.
B.
C.
D.
Which polynomial is a factor of ?
A.
B.
C.
D.
What is the remainder when is divided by ?
A.
B.
C.
D.
If is a factor of , where , then the value of is
A. 7
B. 4
C. 1
D. –2
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