Assessment Pack — Mathematics 10

Term 1 · MATATAG Curriculum · Key Stage 3 · SY 2026–2027

⚠️ The weights are reported, and the Key Stage 3 attribution is an inference. See source-catalogue.md. The item content below is this repository's own work; confirm the weights before computing a real grade.

1. How assessment works this year

A summative may not exceed half the term examination's item count — 40 items, so 20 each. The Table of Specifications is this repository's, not DepEd's.

One marking rule specific to this term. Wherever a learner is asked to graph the region of an inequality, the test point must be written and circled. Half of all single-inequality questions can be shaded correctly by guessing, so an unsupported shading is not evidence of the competency. Every item below that asks for a graph says so in its own wording.

2. Table of Specifications — Term 1 Examination

40 items · Remembering · Understanding · Applying · Analysing

3. Summative Test 1 — Weeks 1–5

20 items · 40 minutes · end of Week 5

Part A · The laws of sines and cosines (items 1–7)

1. The law of sines says a ÷ sin A = ______ ÷ sin B.
2. Which law do you use when you are given two angles and one side? ______
3. Which law do you use when you are given three sides? ______
4. Which law do you use when you are given two sides and the angle between them? ______
5. In triangle ABC, A = 40°, B = 60°. Find C. ______
6. The law of cosines says a² = b² + c² − ______
7. What does the law of cosines become when A = 90°? ______

Part B · The ambiguous case (items 8–10)

8. In which of the four given-information cases can two different triangles exist? ______
9. If a construction gives two valid triangles, how many answers should you report? ______
10. Given two sides and a non-included angle, the case is called ______

Part C · The Cartesian plane and transformations (items 11–15)

11. In which quadrant is (−3, 5)? ______
12. In which quadrant is (4, −2)? ______
13. Translate (2, 3) by 4 units right and 1 unit down. ______
14. Reflect (5, 2) in the x-axis. ______
15. Reflect (5, 2) in the y-axis. ______

Part D · Quadratic inequalities in one variable (items 16–20)

16. Solve x² − 9 > 0. ______
17. Solve x² − 9 < 0. ______
18. Write the answer to item 17 in interval notation. ______
19. Solve (x − 1)(x − 5) ≤ 0. ______
20. On a number line, a strict inequality is drawn with what kind of circle? ______

Answer key — Summative Test 1

Marking notes.

• Item 7 is the item that shows whether the law of cosines was understood or memorised. cos 90° = 0, so the last term vanishes and Pythagoras falls out. A learner who cannot produce this has stored a formula, not a relationship.
• Items 16 and 17 are the same boundary, opposite regions — the one-variable rehearsal for Week 7. A learner giving the same answer twice has not separated them.
• Item 9 — "both" is the whole ambiguous case. Accept "two answers"; do not accept "the bigger one".
• Items 14 and 15 discriminate reliably. Reflecting in the x-axis changes the sign of y. Learners who change x instead have the axis and the coordinate swapped.

4. Summative Test 2 — Weeks 6–10

20 items · 40 minutes · end of Week 10

Part A · Boundaries (items 1–5)

1. To find the boundary of an inequality, you replace the inequality sign with ______
2. For y < 3x, is the boundary drawn broken or solid? ______
3. For y ≥ x² − 5, is the boundary drawn broken or solid? ______
4. What is the boundary of x² − y < 4? ______
5. Does a broken boundary include its own points as solutions? ______

Part B · Test points (items 6–11)

6. A test point must not lie on the ______
7. Is (0, 0) a legal test point for y > x² − 1? ______
8. Is (0, 0) a legal test point for y > 4x? ______
9. Test (0, 0) in y > x² − 1. True or false? ______
10. Test (0, 0) in x + y ≥ 5. True or false? ______
11. Your test point gives FALSE. Which side do you shade? ______

Part C · In, out, or on (items 12–16)

For y ≥ x² − 4, say whether each point is IN the region, OUT of it, or ON the boundary.

12. (0, 0) ______
13. (2, 0) ______
14. (1, −5) ______
15. (−3, 5) ______
16. (0, −9) ______

Part D · Reasoning (items 17–20)

17. Are y > x² − 4 and x² − y < 4 the same region or different? ______
18. Are y > x² − 4 and y < x² − 4 the same region or different? ______
19. Why can the origin not be used as a test point for y ≤ 3x? ______
20. The solution of an inequality in two variables is what kind of thing? ______

Answer key — Summative Test 2

Marking notes.

• Items 17 and 18 are adjacent on purpose and are the most diagnostic pair on the paper. Same, then different. A learner who answers by comparing the inequality signs gets both wrong: 17 has > against <, and so does 18. Only testing separates them.
• Item 15 catches more learners than any other item here. (−3, 5): (−3)² = 9, and 9 − 4 = 5, so the point is exactly ON. A learner who writes −3² = −9 gets OUT.
• Item 8 is the origin trap and it is worth double weight in your reading of the paper even though it scores one mark. A learner who says "yes" will produce clean, wrong working all year.
• Item 11 — the single most useful line on the paper. Accept any wording that names the opposite side.
• Item 14 — −5 ≥ 1 − 4 = −3 is false, so OUT. Learners who answer IN have compared the magnitudes and ignored the signs.

5. Term 1 Examination — Weeks 1–11

40 items · 60 minutes · end-of-term block

Part A · The laws of sines and cosines (items 1–6)

1. State the law of sines. ______
2. In triangle ABC, A = 35°, B = 75°, a = 10. Which law finds b? ______
3. In triangle ABC, b = 7, c = 9, A = 50°. Which law finds a? ______
4. In triangle ABC, A = 50°, C = 60°. Find B. ______
5. Write the law of cosines for side c. ______
6. Setting C = 90° in item 5 gives what well-known result? ______

Part B · Problems, including bearings (items 7–9)

7. A bearing is measured clockwise from which direction? ______
8. Two boats leave the same port. Which law would you use to find the distance between them, given both distances travelled and the angle between their courses? ______
9. A surveyor has two angles and the side between them and needs the third side. Name the law and say why the other one will not do. ______

Part C · Points and transformations (items 10–13)

10. Give the coordinates of a point on the y-axis, 4 units below the origin. ______
11. Reflect (−2, 6) in the x-axis. ______
12. Translate (−2, 6) by 3 right and 5 down. ______
13. Rotate (3, 0) by 90° counter-clockwise about the origin. ______

Part D · Quadratic inequalities in one variable (items 14–19)

14. Solve x² − 16 ≥ 0. ______
15. Solve x² − 16 ≤ 0. ______
16. Write the answer to item 15 in interval notation. ______
17. Solve (x + 2)(x − 6) < 0. ______
18. A rectangle has length x and width x − 3, and its area must be at most 40 m². Write the inequality. ______
19. Using item 18, what is the largest whole-number length possible? ______

Part E · Inequalities in two variables (items 20–28)

20. To graph an inequality in two variables, what are the two steps? ______
21. For y ≤ 2x − 5, is the boundary broken or solid? ______
22. What is the boundary of x² − y ≥ 9? ______
23. Is (0, 0) a legal test point for y < 5x? Say why. ______
24. Test (0, 0) in y > x² − 7, and say which side is shaded. ______
25. Is (4, 9) a solution of y ≥ x² − 7? Show your substitution. ______
26. Is (4, 9) a solution of y > x² − 7? Show your substitution. ______
27. Graph y ≥ x² − 4. Mark and circle your test point. ______
28. Are y > x² − 4 and x² − y < 4 the same region? Justify with a test point, not by comparing their signs. ______

Part F · Measures of position (items 29–34 continue below; items 35–40)

29. Solve |x| = 7. ______

30. Solve |x − 3| = 5. ______

31. Solve |x| < 4. ______

32. Write the answer to item 31 in interval notation. ______

33. Solve |x| > 4. ______

34. Why does item 33 give two intervals and item 31 only one? ______

35. What percentage of the data lies below Q1? ______

36. In an ordered list of 19 values, which position is the median? ______

37. The IQR is which two quartiles subtracted? ______

38. Q1 = 12 and Q3 = 20. Find the IQR. ______

39. Using item 38, find the upper outlier fence, 1.5 × IQR above Q3. ______

40. A box-and-whisker plot displays how many summary values? Name them. ______

Answer key — Term 1 Examination

Marking notes — Term 1 Examination

• Items 25 and 26 are the highest-value pair on the paper. Same point, same boundary, one strict sign and one not. (4, 9) sits exactly ON the parabola, so ≥ admits it and > does not. A learner who answers the same way twice has not understood what the boundary line style is for. Two marks each, one for the answer and one for the substitution.
• Item 28 is the three-mark item. Award 1 for "yes", 2 for a correct substitution in one of the two forms, 3 for substituting in both and stating that the shared result is what makes them the same region. A learner who argues from the signs earns nothing here, even if the answer is "yes" — the item explicitly forbids it.
• Item 27 carries two marks and one of them is the circled test point. Say so on the paper when you hand it back; it is the term's marking rule made visible.
• Item 23 is the origin trap. One mark, and it predicts more about next term than any other single item.
• Items 14 and 15 are the same boundary, opposite regions, and items 31 and 33 do it again with absolute value. A learner consistent across both pairs has the idea; a learner right on one pair and wrong on the other is pattern-matching.
• Item 19 — x(x − 3) ≤ 40 with x a whole number. x = 8 gives 40, which is allowed by "at most"; x = 9 gives 54. Learners who answer 9 have read ≤ as <.
• Item 34 requires a sentence. Accept any wording that contrasts between with outside.
• Item 9 requires the reason, not just the name. One mark for "sines", one for saying that the law of cosines needs two sides.

Suggested mark allocation. One mark each for items 1–8, 10–18, 21, 22, 24, 29–33, 35–38 and 40. Two marks each for items 9, 19, 20, 23, 25, 26, 27, 34 and 39. Three marks for item 28. That is 30 one-mark items, 9 two-mark items and one three-mark item — 51 marks over 40 items; scale to whatever your school records.

6. Week 7 weekly check

10 items · 15 minutes · Day 5 · Written Works Covers only competencies Q1 · 9–10 — inequalities in two variables and the region of solutions.

1. What is the boundary of y > x² − 6? ______
2. Is that boundary broken or solid? ______
3. Is the boundary of y ≤ 4x + 1 broken or solid? ______
4. Is (0, 0) a legal test point for y > x² − 6? ______
5. Is (0, 0) a legal test point for y > 6x? Say why. ______
6. Test (0, 0) in y > x² − 6. True or false? Which side is shaded? ______
7. Is (3, 3) IN, OUT, or ON for y ≥ x² − 6? ______
8. Is (3, 3) IN, OUT, or ON for y > x² − 6? ______
9. Are y < x² − 6 and x² − y > 6 the same region? Test a point. ______
10. In one sentence: why is testing a point better than reading the inequality sign? ______

Answer key — Week 7 weekly check

Items 5, 7, 8 and 9 are the whole check. A learner who gets 1–4, 6 and 10 right and misses those four can recite the routine and cannot apply it — which looks identical on any test that asks only for the routine.

Items 7 and 8 are one point asked twice. (3, 3) is ON the boundary in both. It is a solution of the first and not of the second. If a learner gives different positions rather than different verdicts, they have not separated where a point is from whether it counts.

7. Performance task rubrics

All four use 4 criteria × 4 levels = 16 points. Convert with score ÷ 16 × 100.

7.1 Where Is It Allowed? — Term 1 task

7.2 The Middle Half — Term 2 task

7.3 Check the Claim — Term 3 task

7.4 What It Really Costs — Term 3 task

7.5 Group activity rubrics

The two group activities in offline-activities.md carry their own 12-point rubrics. They are scored separately and also feed the Performance Tasks component.

8. What is deliberately not in this pack

Part of the E-turo MATATAG artifact set. Companion files: syllabus.md · lesson-plan.md · lesson-plan-ilaw.md · offline-activities.md · class-record.html · worksheet.html