PLAN · PRACTISE · REVISE

Year 7 and Year 8: lower-volume chapter core practice

11 textbook chapters, 25 classroom packs and 400 fixed original questions.

Use after the corresponding textbook lessons and for chapter review. Year 7 has 49 textbook lessons and Year 8 has 42; this plan preserves their teaching sequence.

All 53 Year 7–8 upper- and lower-volume packs in Traditional Chinese and English. Includes teacher answers; student core, further practice and teacher papers are in separate folders.

Use the same bank in two ways

Ordinary classes: prerequisites 4 min, short inquiry 5, worked and guided attempts 8, independent practice 15, correction 5, exit 3. Advanced classes: inquiry 18, organise 4, selected practice 13, exit 5.

Every pack has one worked example, one guided attempt, eight core tasks, four follow-ups and two extensions. Student core worksheets contain two A4 pages; supplements and teacher references are separate.

Year 7 lower volume

Chapter5 · text pp.1–28

Intersecting and parallel lines

Consolidate after the referenced textbook lessons · Textbook lessons 1–14

  1. Intersections, perpendiculars and distance

    Distinguish angle position from angle size, and perpendicular distance from an oblique segment.

    Referenced lessons 1, 2, 3, 4
  2. Parallel lines: conditions and reasoning

    Use angle relations in the correct direction and distinguish a hypothesis from a conclusion.

    Referenced lessons 5, 6, 7, 8, 9, 10, 11, 12
  3. Translation: matching points and invariant lengths

    Move a whole figure in one direction by one distance; distinguish translation from rotation or reflection.

    Referenced lessons 13, 14

Chapter6 · text pp.29–38

Real numbers

Consolidate after the referenced textbook lessons · Textbook lessons 15–19

  1. Square roots and cube roots: meanings and signs

    Distinguish two square roots from one principal square root, and allow negative cube roots.

    Referenced lessons 15, 16, 17
  2. Real numbers: classification, bounds and approximation

    Use exact definitions and square comparisons; keep an approximation distinct from an equality.

    Referenced lessons 18, 19

Chapter7 · text pp.39–50

Cartesian coordinates

Consolidate after the referenced textbook lessons · Textbook lessons 20–25

  1. Coordinates: location and translation

    Use ordered pairs, quadrants, map scales and one common coordinate change.

    Referenced lessons 20, 21, 22, 23, 24, 25

Chapter8 · text pp.51–70

Systems of linear equations

Consolidate after the referenced textbook lessons · Textbook lessons 26–35

  1. Two-variable systems: substitution and elimination

    Reduce two unknowns to one, then recover the complete solution and check both equations.

    Referenced lessons 26, 27, 28, 29, 30
  2. Two-variable systems: quantities and models

    Name unknowns, keep units consistent, build independent conditions and check contextual feasibility.

    Referenced lessons 31, 32, 33
  3. Three-variable systems: eliminate, solve and check

    Eliminate the same unknown to obtain a two-variable system, then back-substitute all three values.

    Referenced lessons 34, 35

Chapter9 · text pp.71–88

Inequalities and systems of inequalities

Consolidate after the referenced textbook lessons · Textbook lessons 36–44

  1. Linear inequalities: direction and endpoints

    Keep equivalent conditions, reverse for negative division and show the complete solution set.

    Referenced lessons 36, 37, 38, 39
  2. Inequality systems: overlap and feasible choices

    Translate every restriction, take the overlap and then apply meaningful integer conditions.

    Referenced lessons 40, 41, 42, 43, 44

Chapter10 · text pp.89–98

Collecting, organising and representing data

Consolidate after the referenced textbook lessons · Textbook lessons 45–49

  1. Statistical surveys: samples, proportions and claims

    Choose a defensible survey method, read proportions and state the limits of sample-based estimates.

    Referenced lessons 45, 46, 47
  2. Grouped data and histograms: frequency and area

    Count boundary values once, label the vertical measure, and use frequency per class width for unequal classes.

    Referenced lessons 48, 49

Year 8 lower volume

Chapter16 · text pp.1–12

Square-root expressions

Consolidate after the referenced textbook lessons · Textbook lessons 1–6

  1. Square roots: meaning, simplification and domain

    Distinguish a square root from the solutions of a squared equation, and retain every real-domain condition.

    Referenced lessons 1, 2
  2. Square-root operations: factor, multiply and combine

    Simplify square factors, apply real-domain product and quotient laws, then combine like radicals.

    Referenced lessons 3, 4, 5, 6

Chapter17 · text pp.13–26

Pythagoras’ theorem

Consolidate after the referenced textbook lessons · Textbook lessons 7–13

  1. Pythagoras: identify the sides and calculate lengths

    Model right triangles, choose addition or subtraction of squares, and retain positive exact lengths.

    Referenced lessons 7, 8, 9
  2. Pythagoras converse: conditions and combined problems

    Test actual side data and combine the converse with length, midpoint and perpendicularity reasoning.

    Referenced lessons 10, 11, 12, 13

Chapter18 · text pp.27–48

Parallelograms

Consolidate after the referenced textbook lessons · Textbook lessons 14–24

  1. Parallelograms: properties, criteria and midsegments

    Separate given facts from conclusions, use diagonals carefully, and prove the triangle midsegment theorem.

    Referenced lessons 14, 15, 16, 17, 18
  2. Rectangles and rhombi: diagonal conditions and converses

    Keep the parallelogram premise, distinguish equal from perpendicular diagonals, and use the right-triangle median theorem.

    Referenced lessons 19, 20, 21, 22
  3. Squares and inclusive quadrilateral classification

    Combine rectangle and rhombus conditions, compare diagonals and reject unsupported converse statements.

    Referenced lessons 23, 24

Chapter19 · text pp.49–74

Linear functions

Consolidate after the referenced textbook lessons · Textbook lessons 25–37

  1. Functions: inputs, domains, tables and graphs

    Decide whether a relation is a function, use three representations and check mathematical and contextual domains.

    Referenced lessons 25, 26, 27, 28, 29
  2. Linear functions: coefficients, graphs and determination

    Relate slope and intercept to the graph, distinguish constant functions, and determine a line from two distinct inputs.

    Referenced lessons 30, 31, 32, 33
  3. Linear models: equations, inequalities and intersections

    Translate contextual conditions and connect graphical solutions with exact algebra.

    Referenced lessons 34, 35, 36, 37

Chapter20 · text pp.75–84

Analysing data

Consolidate after the referenced textbook lessons · Textbook lessons 38–42

  1. Data centres: weights, ordering and choosing a summary

    Calculate weighted means, medians and all tied modes; distinguish grouped estimates from raw-data answers.

    Referenced lessons 38, 39, 40, 41
  2. Variance: calculation, stability and transformations

    Use the textbook’s n-denominator definition, compare data with the same centre and reason about shifts and scales.

    Referenced lessons 42

Collect classroom evidence, then deepen the set

Record completion of the core tasks, both exit questions and two common errors. If many students cannot finish, add guidance or split a step before increasing the question count. After the chapter core set, add lesson-by-lesson variants using this evidence, then deepen the sets in both volumes.

The questions and explanations are original. Textbook and foundation page references identify the skills; the source PDFs and answer books are not reproduced. Paper answers do not create automatic scores or browser learning records.

Lower-volume questions were independently checked. Only the source textbooks were supplied; no separate lower-volume foundation or answer books were checked.