CIE IAL · Mathematics · 9709 P3 · A Level

9709 P3 Algebra Topic Questions

Every 9709 P3 Algebra topic question from the 2020–2027 syllabus, drawn from 49 papers (2020–2026) and grouped by syllabus point. Each row opens a page listing the exact question numbers, marks and a direct link into the paper. These are questions by topic, not full papers, so you can revise one topic at a time.

9709 P3 5 subtopics 156 topic questions 49 papers 573 tagged marks

Back to Algebra All paper codes

Core finding

recall an appropriate form for expressing rational functions in… is the most frequently assessed subtopic in Algebra, with 36 topic questions and 178 marks across 34 papers. understand the meaning of …, sketch the graph of … and use… follows with 32 topic questions and 88 marks. The topic contains 5 subtopics, 156 topic questions and 573 marks in total. Rows count only the parts tagged to that subtopic, keep the same colour in both charts and repeat paper count, tagged marks and year range in the native table.

Topic question count and mark distribution

Subtopics are on the vertical axis and sorted from highest to lowest. Only the parts whose knowledge graph matches a subtopic are counted for it, and percentages are each row's share of the tagged total in that chart. A part tagged to several subtopics is counted in each bar, so the bars are not a partition of the topic total.

Questions by subtopic

question items

• recall an appropriate form for expressing rational functions in partial fractions, and carry out the decomposition, in cases where the denominator is no more complicated than –

(a x + b) (c x + d) (e x + f)

–

(a x + b) (c x + d)^{2}

–

(a x + b) (c x^{2} + d)

34 papers

3624.7%

• understand the meaning of

∣ x ∣

, sketch the graph of

y = ∣ a x + b ∣

and use relations such as

∣ a ∣ = ∣ b ∣ \Leftrightarrow a^{2} = b^{2}

and

∣ x - a ∣ < b \Leftrightarrow a - b < x < a + b

when solving equations and inequalities 23 papers

3221.9%

• use the expansion of

(1 + x)^{n}

, where

n

is a rational number and

∣ x ∣ < 1

22 papers

3221.9%

• divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero) 21 papers

2416.4%

• use the factor theorem and the remainder theorem 15 papers

2215.1%

Marks by subtopic

marks

• recall an appropriate form for expressing rational functions in partial fractions, and carry out the decomposition, in cases where the denominator is no more complicated than –

(a x + b) (c x + d) (e x + f)

–

(a x + b) (c x + d)^{2}

–

(a x + b) (c x^{2} + d)

34 papers

17833.1%

• use the expansion of

(1 + x)^{n}

, where

n

is a rational number and

∣ x ∣ < 1

22 papers

10719.9%

• understand the meaning of

∣ x ∣

, sketch the graph of

y = ∣ a x + b ∣

and use relations such as

∣ a ∣ = ∣ b ∣ \Leftrightarrow a^{2} = b^{2}

and

∣ x - a ∣ < b \Leftrightarrow a - b < x < a + b

when solving equations and inequalities 23 papers

8816.4%

• divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero) 21 papers

8215.3%

• use the factor theorem and the remainder theorem 15 papers

8215.3%

Subtopic comparison matrix

Curriculum order is by syllabus number, then alphabetically. Every row links to the matching past-paper question list.

Subtopic	Topic questions	Papers	Marks	Years
• divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero)	24	21	82	2020–2026	Open topic questions
• recall an appropriate form for expressing rational functions in partial fractions, and carry out the decomposition, in cases where the denominator is no more complicated than – $(a x + b) (c x + d) (e x + f)$ – $(a x + b) (c x + d)^{2}$ – $(a x + b) (c x^{2} + d)$	36	34	178	2020–2026	Open topic questions
• understand the meaning of $∣ x ∣$ , sketch the graph of $y = ∣ a x + b ∣$ and use relations such as $∣ a ∣ = ∣ b ∣ \Leftrightarrow a^{2} = b^{2}$ and $∣ x - a ∣ < b \Leftrightarrow a - b < x < a + b$ when solving equations and inequalities	32	23	88	2020–2026	Open topic questions
• use the expansion of $(1 + x)^{n}$ , where $n$ is a rational number and $∣ x ∣ < 1$	32	22	107	2020–2026	Open topic questions
• use the factor theorem and the remainder theorem	22	15	82	2021–2026	Open topic questions

Browse every topic question

• divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero) 24 question items · 21 papers 82 marks · 2020–2026 • recall an appropriate form for expressing rational functions in partial fractions, and carry out the decomposition, in cases where the denominator is no more complicated than – $(a x + b) (c x + d) (e x + f)$ – $(a x + b) (c x + d)^{2}$ – $(a x + b) (c x^{2} + d)$ 36 question items · 34 papers 178 marks · 2020–2026 • understand the meaning of $∣ x ∣$ , sketch the graph of $y = ∣ a x + b ∣$ and use relations such as $∣ a ∣ = ∣ b ∣ \Leftrightarrow a^{2} = b^{2}$ and $∣ x - a ∣ < b \Leftrightarrow a - b < x < a + b$ when solving equations and inequalities 32 question items · 23 papers 88 marks · 2020–2026 • use the expansion of $(1 + x)^{n}$ , where $n$ is a rational number and $∣ x ∣ < 1$ 32 question items · 22 papers 107 marks · 2020–2026 • use the factor theorem and the remainder theorem 22 question items · 15 papers 82 marks · 2021–2026

Topic question rules and edge cases

How many subtopics does Algebra contain?: This page lists 5 subtopics tagged to the current syllabus. They are ordered by syllabus number, then alphabetically, and each row opens a page of matching past-paper questions.
How are the subtopic question and mark totals calculated?: A multiple-choice question contributes one item and its marks to every subtopic it is tagged with. A structured question contributes one item per tagged part, and that part’s marks; untagged parts of the same question are not counted here. A part tagged to several subtopics therefore appears under each of them.
Why do some subtopics have no numbered prefix?: Practical-skills statements and some syllabus bullets are unnumbered. Numbered statements come first; unnumbered statements and ties are sorted alphabetically.
Is the LaTeX rendered without JavaScript?: Yes. Subtopics that contain formulas are converted to static KaTeX HTML during the build, and the KaTeX stylesheet is served from the same site.