Coordinate geometry is now a Next priority. Practise how methods connect: coordinates with algebra, vectors with area ratios, and data displays with cumulative frequency. Keep a deliberate block for probability diagrams and circle proofs with congruence.
These are useful practice combinations, not predictions of exact question structures. A topic tested in P1 can return in P2.
Choose a revision session
90-minute pass: graphs 20 min → quadratic modelling 20 min → matrices 10 min → trigonometry 20 min → one real-world question 20 min. Use this as a diagnostic; return to weak steps afterwards.
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Further trigonometry (Ch6-7), radians (Ch8), congruence (§9.2), similar figures/solids (Ch10) and circle properties (Ch11).
Book 4A
Combined probability (Ch2), cumulative frequency and SD (Ch3), and matrices (Ch4).
Book 4B
Vector geometry (Ch5), coordinate geometry (§7.5), mixed revision (Ch6-8) and real-world problems from p181.
Book 2B
Composite solids (§11.4), dot and stem-and-leaf diagrams (§13.1, §13.3), and grouped histograms (§13.4).
Book Secondary 1
Short refreshers: number patterns (Ch7), percentages/rates (Ch8-9), polygons and constructions (Ch11).
Your topic-by-topic checklist
Page numbers below are printed textbook pages, not PDF viewer positions. Section starts and review-exercise pages were checked against the supplied contents pages. Suggested problem selections are revision guidance, not invented exercise question numbers.
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First
1. Extended graphs
Suggested block: 30 min
P1 Q28 tested a quadratic minimum, but no plotting, tangent or extended graphical solution.
3A5.5 · Applications of graphs in real-world contexts Printed p139
4B6.5-6.6 · Functions and graphs; graphs in practical situations Printed pp83, 89
Textbook practice: 3A Review Exercise 5, p156. Select a graph-plotting problem and a tangent/application problem.
Your task: Complete one table and curve, draw a tangent, and solve an equation using a suitable line. Add a motion-graph check: a distance-time gradient gives speed; a speed-time gradient gives acceleration and the area under a speed-time graph gives distance travelled. Check axis units before calculating.
P1 used quadratic factorisation and vertex form, but Q22 reduced to a linear equation. Genuine quadratic solving remains a gap.
3A1.1 · Completing the square Printed p2
3A1.2 · Solving quadratic equations using formula Printed p9
3A1.3 · Fractional equations reducible to quadratic equations Printed p11
3A1.6 · Quadratic equations/functions in real-world contexts Printed p29
4B6.4 · Equations and inequalities Printed p78
Textbook practice: 3A Review Exercise 1, p37. Choose one formula question and one fractional or contextual equation. Also solve one quadratic by completing the square (CTS).
Your task: Write an equation from an area or journey-time situation, clear fractions, solve the resulting quadratic and explain any rejected root.
3BFinal section · Problems in Real-World Contexts Printed p229 onwards
Textbook practice: Choose one complete problem from the 4B real-world section, then check each numerical step and the final recommendation.
Your task: Select the relevant data, convert units, compare feasible options and finish with a justified decision. Include one financial comparison: tax/GST, profit and loss, or hire purchase (deposit plus all instalments). Use the rates and conditions given in the question. State an assumption if needed; the actual exam context is unknown.
P1 Q14(b)-(c) tested a line equation and distance (5 marks); Q14(a) added 1 vector mark. Intersections, division ratios and coordinate shapes remain useful practice. Our classification found 7, 9 and 6 coordinate-geometry marks in P2 in 2023, 2024 and 2025. This supports revision, not a guaranteed question.
3A4.1 · Length of a line segment Printed p92
3A4.2 · Gradient of a straight line Printed p98
3A4.3 · Equation of a straight line Printed p104
4B7.5 · Coordinate geometry revision Printed p137
Textbook practice: 3A Review Exercise 4, p112, then 4B §7.5, p137. Choose a longer question connecting an unknown coordinate, a length or area, and another line equation.
Your task: Find a line intersection using simultaneous equations. Use equal gradients for parallel lines and a known point to find the intercept. Find a point dividing a segment in a given ratio. Link triangle/trapezium area or a length condition to an equation and check which roots fit the geometry.
Past-year practice: 2023 P2 Q6(b); 2024 P2 Q3; 2025 P2 Q8 in full. Q8(a)(i)-(ii) adds quadratic modelling before the 6 coordinate marks in Q8(a)(iii)-(b).
Next
7. Vector geometry, proofs and area ratios
Suggested block: 25 min
Only one direct vector mark appeared in P1 Q14(a): a translation. Ratios, position vectors and proofs were not demanded.
4B5.4 · Scalar multiples of a vector Printed p30
4B5.5 · A vector in terms of two other vectors Printed p34
4B5.6 · Position vectors Printed p36
4B5.7 · Applications of vectors Printed p41
3B10.1 · Area of similar figures Printed p160
Textbook practice: 4B Review Exercise 5, p55. Choose a ratio question and a parallelism or collinearity proof. Further revision: §7.6, p143.
Your task: Write two routes to a point, use the given segment ratios, then show one vector is a scalar multiple of another. State the geometric conclusion. Extend this to areas: triangles with the same perpendicular height have area ratio equal to base ratio; similar triangles have area ratio equal to the square of the corresponding length ratio. Establish the condition before choosing a rule.
P1 tested grouped mean, box plots and transformation of SD. It did not test cumulative-frequency reading or numerical SD calculation.
4A3.1 · Cumulative frequency table and curve Printed p76
4A3.2 · Median, quartiles, percentiles, range and IQR Printed p89
4A3.4 · Standard deviation Printed p115
2B13.1 · Dot diagrams Printed p143
2B13.3-13.4 · Stem-and-leaf diagrams; histograms for grouped data Printed pp151, 155
4B8.2 · Statistics revision Printed p167
Textbook practice: 4A Review Exercise 3, p133. Select a cumulative-frequency question and a numerical SD question.
Your task: Read a percentile from a curve, find the number above a threshold, and calculate or compare numerical SD in context. Practise taking data from a stem-and-leaf or dot diagram into a frequency/CF table; grouping changes what can be recovered exactly. Check a misleading graph: explain the effect of a truncated or inconsistent scale, distorted bar widths, or pictogram size. For histogram practice, use equal class intervals as specified in this syllabus.
P1 Q18/Q25 covered annulus area and a sector folded into a cone. Composite exposed surfaces and similar-solid scaling remain useful gaps.
2B11.1-11.3 · Pyramids, cones and spheres Printed pp86, 98, 105
2B11.4 · Volume and surface area of composite solids Printed p111
3B10.1-10.3 · Similar figures/solids: area, volume and applications Printed pp160, 168, 174
3B8.3-8.4 · Radian measure; arc length and sector area in radians Printed pp82, 89
4B7.4 · Mensuration revision Printed p129
Textbook practice: 2B Review Exercise 11, p116; 3B Review Exercise 10, p179. Add a radian/sector or segment item from Review Exercise 8, p99.
Your task: Mark exposed surfaces before adding areas. Write a volume-conservation equation. Use squared/cubed scale factors. For a minor segment, subtract the triangle area from the sector area. The formulas s = rθ and sector area = ½r²θ require θ in radians; set the calculator to match the angle unit whenever using trigonometric functions.
4B7.1 · Angles, triangles and polygons revision Printed p108
Textbook practice: Do one compass-bisector construction and one polygon-angle or scale-drawing problem from these sections.
Your task: Keep construction arcs visible. Distinguish interior and exterior angles and give reasons involving parallel lines, triangles or quadrilaterals. For map scales, put both lengths in the same units before using the ratio; use the square of the linear scale factor for areas.
Past-year practice: Extra cross-paper method drills: 2024 P1 Q6 and Q16
Maintain
12. Probability diagrams, circle proofs and algebra
Suggested block: 25 min
P1 already tested probability (Q8(c), Q19), circles (Q3), algebra and percentages. Their methods can return in longer P2 questions. Maintain means a deliberate practice block, especially if one of these is a weakness.
4B6.3 · Algebraic manipulation and formulae Printed p71
3B9.2 · Congruent figures and congruent triangles Printed p120
3B11.1-11.2 · Symmetry and angle properties of circles Printed pp184, 202
Sec 1Chapters 8-9 · Percentage; Ratio & Rate Use chapter headings
Textbook practice: 4A Review Exercise 2, p70: choose a tree/possibility-diagram problem. Use 3B Review Exercise 9, p153, and Review Exercise 11, p223, to practise congruence and circle reasons. Add one change-of-subject and one simple/compound-interest calculation from the listed algebra/percentage sections.
Your task: Draw a probability tree or possibility diagram; update probabilities without replacement, multiply along each path and add mutually exclusive successful paths. For circle proofs, identify a valid congruence test and use corresponding parts with named circle properties. A diagram that looks symmetric is not proof. Finish with a formula rearrangement and an interest calculation using the correct base and period.
Past-year practice: Foundation checks: actual 2026 P1 Q3, Q8(c), Q16, Q17, Q19 and Q21. The combined question types above are practice suggestions, not a claim that all appeared together in these questions.