H-Unit-12-Phase-1-MS - Mark scheme for similar shapes and scale factors

Sep 5, 2026

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Mark scheme content for a staged mathematics test, split into a non-calculator section (20 minutes) and a calculator section (30 minutes). It defines marking rules using codes such as B, M, A, C, P, FT, and OE, explaining how method, accuracy, communication, and process marks are awarded. The questions cover congruence and similarity using angle facts, scale factors for missing lengths, and problem solving for areas and volumes of similar shapes and solids.

LanguageEnglish

CategoryExam

FormatPDF

Pages7

Reading Time18 min

AccessFree to download

Non-Calculator

Marking scheme codes and guidance

Question-wise marking notes

Calculator

Question-wise marking notes

Similar shapes: scale factor, areas and volumes

This test is divided into non-calculator (20 minutes) and calculator (30 minutes) sections which can be delivered separately. The following marks are awarded for each question. | B | Unconditional accuracy mark | | --- | --- | | M | Method mark – the correct method must be shown but there may be an arithmetic error; the sight of the value given in brackets implies the award of the method mark | | A | Accuracy mark – unless the question specifies that working must be shown then the sight of the correct answer implies the award of full marks (unless the answer clearly comes from incorrect working) | | C | Communication mark | | P | Process mark to show correct process for problem solving. Any other process of a similar standard to achieve an accurate result is acceptable to achieve this mark | | FT | Incorrect values may be followed through from one step to the next provided that the correct method is seen in each step and the only errors are arithmetic. This is shown in mark schemes by putting a number in inverted commas. | | OE | Or equivalent answer mark | | Non-Calculator | | | | | --- | --- | --- | --- | | Q | Answer | Mark | Comment | | 1 | Explanation with appropriate angles and reasons | P1 | angle BCA = 30° and angle XYZ = 130° OE, e.g. angle BCA = 30 and angle YXZ = 35, so these are not equal or angle XYZ 130 and angle ABC = 135 so these are not equal
similar triangles must have identical angles, so the two triangles are not similar | | | | C1 | | | 3 | 14 (cm) | M1 | 21 ÷ 6 (= 3.5 OE) or 4 × 3.5 OE or uses ratio of width to length 2:3
14 | | | | A1 | | | 5a | Explanations | C1 | angle QPR = angle RTS alternate angles are equal and Angle PQR = angle RST alternate angles are equal; accept "same"instead of "equal" OE
angle PRQ = angle SRT vertically opposite angles are equal so PQR and RST are similar triangles; accept "same"instead of "equal" OE | | --- | --- | --- | --- | | | | C1 | | | 5b | a = 36(cm) and b = 5(cm) | M1 | 27 Scale factor = ~~ ~~ (= 4.5 OE)
6
a = 36 and b = 5 | | | | A1 | | | 7 | Full proof | C3 | e.g. XWM = MYZand WXM = MZY
because alternate angles are equal WX = YZ because opposite sides ofa parallelogram are equal and reference to ASA
C2 for identifying any two of XWM= MYZ, WXM = MZYor WX = YZ with correct reasons or all three with one correct reason
C1 for identifying any one of XWM= MYZ, WXM = MZYor WX = YZ with a correct reason or all three with no correct reason | | --- | --- | --- | --- | | Calculator | | | | | --- | --- | --- | --- | | 9 | No with comparison of two correct 2
figures, e.g. 1 ~~ ~~ and 2
3 | M1 | dimensions of WXYZ are
18 + 6 + 6 (= 30) and 12 + 6 + 6 (= 24)
2
length scale factor = 30 ÷ 18 (= 1~~ ~~3
OE)
and width scale factor = 24 ÷ 12 (= 2)
or for correct use of a scale factor to find a length eg width scale factor is 2, so for the length 18 × 2 = 36 | | | | M1 | | | | | C1 | | | 11a | 7 (cm) | M1 | scale factor = 10.5 ÷ 6 (= 1.75 OE) or 4 × 1.75 OE
7 | | | | A1 | | | 11b | 8.4 (cm) | M1 | 14.7 ÷ "1 .75" OE
8.4 | | | | A1 | | | 13 | 583.78 (cm2) | P1 | volume scale factor of
638.69
X to Y = = 4.913 OE
130
linear scale factor = 4.913 = 1.7 OE area scale factor = 1.72 = 2.89 OE or 202 × 2.89 | | --- | --- | --- | --- | | | | P1 | | | | | P1 | | | | | A1 | | | 15 | x2 􀀐 4
3(x 􀀐 2)
(x 􀀎 2)
3
􀂧 x 􀀎 2 􀂷 2
( A 􀀠)9 􀁵 􀂨 ~~ ~~ 􀂸 = x2 + 4x + 4
􀂩 3 􀂹 | C1 | for an expression of the length scale x2 􀀐 4
factor, e.g. ~~ ~~ OE
3(x 􀀐 2)
for simplifying the length scale factor, e.g. (x~~ ~~2x)􀀐(x2􀀎)~~ ~~2) or (x~~ ~~􀀎3~~ ~~2) OE
for an expression using the area scale
􀂧 x 􀀎 2 􀂷 2
factor, e.g. 9 􀁵 􀂨 ~~ ~~ 􀂸 = x2 + 4x + 4 OE
􀂩 3 􀂹
fully correct process | | | | C1 | | | | | C1 | | | | | C1 | | | Non-Calculator | | | | | --- | --- | --- | --- | | Question | Topic | Step | Marks | | 1 | Use the information given about the length

FAQs

How is each question marked in the non-calculator section?

Marks are awarded using codes like M for correct method with possible arithmetic error, A for accuracy (with conditions), C for communication, and P for correct process. FT and OE rules specify follow-through and equivalent answers when applicable.

What topics do the questions assess across the test?

The test assesses congruence and similarity using angle facts on parallel lines, using scale factors to find missing lengths, and solving problems involving areas and volumes of similar shapes and solids.

How are scale factors used to find missing lengths?

The mark scheme expects use of the correct linear scale factor (including fractional scale factors) to calculate missing lengths. For some items it also checks that the ratio approach and correct scale-factor reasoning are shown.

Sep 5, 2026

Upload by Patrick