Instructions
This worksheet has two sections: English and Math. For each question, it's important not just to find the right answer, but to show how you got there. This means providing textual evidence in English and showing every step of your calculations in Math.
Part 1: English - Measuring Meaning
In English, "showing your workings" means using evidence from the text to support your ideas. Read the following passage from George Orwell's novel, Nineteen Eighty-Four. Then, answer the questions below, making sure to use specific quotes to back up your points.
It was a bright cold day in April, and the clocks were striking thirteen. Winston Smith, his chin nuzzled into his breast in an effort to escape the vile wind, slipped quickly through the glass doors of Victory Mansions, though not quickly enough to prevent a swirl of gritty dust from entering along with him.
The hallway smelt of boiled cabbage and old rag mats. At one end of it a coloured poster, too large for indoor display, had been tacked to the wall. It depicted simply an enormous face, more than a metre wide: the face of a man of about forty-five, with a heavy black moustache and ruggedly handsome features. Winston made for the stairs. It was no use trying the lift. Even at the best of times it was seldom working, and at present the electricity was cut off during daylight hours. It was part of the economy drive in preparation for Hate Week. The flat was seven flights up, and Winston, who was thirty-nine and had a varicose ulcer above his right ankle, went slowly, resting several times on the way. On each landing, opposite the lift-shaft, the poster with the enormous face gazed from the wall. It was one of those pictures which are so contrived that the eyes follow you about when you move. BIG BROTHER IS WATCHING YOU, the caption beneath it ran.
- The author uses sensory details to build the world. Identify one detail related to smell and one related to touch/feeling. Explain what each detail "measures" or suggests about the quality of life in this setting.
- The clocks strike "thirteen." This is an unusual measurement of time. What might this single detail imply about the society Winston lives in?
- Analyze the author's description of the poster. How does the measurement "more than a metre wide" combined with the verb "gazed" create a specific mood? Show your working by explaining the effect of these choices.
- Orwell states that the electricity was cut off as "part of the economy drive." How does this piece of information contrast with the fact that the poster is "too large for indoor display"? What does this contradiction reveal about the government's priorities?
Part 2: Math - Measurement in Practice
Solve the following problems. You must show all your workings, including the formulas you use and the steps you take to get your final answer. Use π ≈ 3.14 where necessary. Round final answers to two decimal places if needed.
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The Community Garden Plot
A local school has an L-shaped garden plot for its students. The dimensions are shown in the diagram below.20m 8m 12m 8m 12ma) What is the total area of the garden plot in square metres (m²)?
b) Students want to put a fence around the entire plot. What is the total length of the perimeter of the garden? -
The Paint Can
A can of paint is a cylinder with a radius of 8 cm and a height of 18 cm.a) What is the maximum volume of paint the can can hold in cubic centimetres (cm³)? (Formula for volume of a cylinder: V = πr²h)
b) What is the area of the paper label that wraps around the curved surface of the can? (Formula for curved surface area of a cylinder: A = 2πrh) -
The Bookshelf Support
You need to install a diagonal metal support brace on the back of a rectangular bookshelf. The bookshelf is 120 cm tall and 90 cm wide. The brace will run from one top corner to the opposite bottom corner. What is the length of the metal brace required? (Hint: Use the Pythagorean theorem a² + b² = c²).
Answer Key
Part 1: English - Sample Answers
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Smell: The text states the hallway "smelt of boiled cabbage and old rag mats." This suggests a place that is poor, not well-maintained, and perhaps unsanitary. The smell is unpleasant and institutional, indicating a low standard of living.
Touch/Feeling: The "vile wind" and "gritty dust" relate to feeling. The word "vile" suggests the wind is extremely unpleasant, not just cold. "Gritty" implies the air is full of dirt and pollution. Together, they measure the environment as harsh, dirty, and hostile. - Clocks normally go to twelve. A clock striking "thirteen" is a precise measurement, but it is outside of our normal system. This suggests that the society in the book operates on a different, perhaps illogical or controlling, set of rules. It immediately makes the setting feel unfamiliar and strange, hinting at military time or a system totally redefined by the state.
- The measurement "more than a metre wide" establishes that the poster is unnaturally large and imposing, especially for an indoor space. This size makes it impossible to ignore. The verb "gazed" personifies the poster, giving it a sense of consciousness and deliberate observation. Unlike "looked," "gazed" implies a steady, intense, and continuous stare. The combination creates a powerful mood of surveillance and intimidation, making Winston (and the reader) feel constantly watched.
- The contradiction lies in the government claiming to save resources ("economy drive") by cutting electricity, while simultaneously expending resources to create and display enormous, "too large" propaganda posters on every floor. This reveals that the government's priorities are not the comfort or well-being of its citizens, but rather control and psychological manipulation. The "economy drive" is likely just an excuse to enforce hardship while they pour resources into their own power.
Part 2: Math - Answers and Workings
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The Community Garden Plot
a) Area:- Split the L-shape into two rectangles.
- Rectangle A (left): 8m × 20m = 160 m²
- Rectangle B (right, top): The width is (8m + 12m) - 8m = 12m. The height is 12m. So, 12m × 12m = 144m². Wait, the diagram gives the dimensions. Let's use the given ones.
- Rectangle A (left section): 8m × 20m = 160 m²
- Rectangle B (bottom section): We can see the full length is 20m and the top section is 12m high, so the bottom section height is 20m - 12m = 8m. The full width is 8m + 12m = 20m. Let's use the dimensions given to avoid confusion: Rectangle 1 (tall part): 8m wide × 20m high = 160 m² Rectangle 2 (short part): 12m wide × 12m high = 144 m² Total Area = Area 1 + Area 2 = 160 m² + 144 m² = 304 m²
- Add up all the outside edge lengths.
- Perimeter = 20m (left) + (8m + 12m) (top) + 12m (right-top side) + 12m (right-bottom side) + 8m (bottom-left side) + 8m (left-inner side). Let's trace it:
- Perimeter = 20m + 8m + 12m + 8m + 12m + (20m - 8m) = Let's use the dimensions on the diagram. Left side: 20m. Top side: 8m. Inner right side: 8m. Bottom right side: 12m. Bottom side: 12m. Inner left side: 12m. Let's trace from the top left corner clockwise: 8m + 12m + 8m + 12m + 20m + (20m - 12m) + (12m+8m). This is confusing. Let's use the outer edges from the diagram: 20m (far left) + 8m (top left) + 12m (top right) + 12m (side, top right) + 8m (side, bottom right) + 12m (bottom). No, that's not right. Let's list the sides: Far left = 20m. Top = 8m + 12m = 20m. Far right = 12m + 8m = 20m. Bottom = 12m + 8m = 20m. No, this isn't a square. Correct side lengths: 20m (left), 8m (top-left), 12m (inner-vertical), 12m (bottom-right), (8m+12m)=20m (bottom), (20m-12m)=8m (far-right). Perimeter = 20 + 8 + 12 + 12 + 20 + 8 = 80 m (Let's check: 20 + (8+12) + 12 + ( (8+12)-8) + (20-12) = 20 + 20 + 12 + 12 + 8 = 72m. Let's re-read the diagram. Left: 20m. Top: 8m. Vertical indent: (20m-12m) = 8m. Horizontal indent: 12m. Bottom: (8m+12m) = 20m. Right side: 12m. Perimeter = 20 + 8 + 8 + 12 + 20 + 12 = 80m. Ah, the labels are confusing. Let's assume the labels apply to the segment they are near. Left side=20m. Top side=8m. Right side, upper=12m. Horizontal indent=12m. Vertical indent=(20-12)=8m. Bottom side=(12+8)=20m. No, this is wrong. Let's use the provided diagram numbers: Left=20m. Top=8m. Right side upper=12m. Right side lower=8m. Bottom=12m. Indent horizontal=12m. That can't be. Final attempt based on standard L-shape interpretation: Left side = 20m. Top side = 8m. Right side = 12m. Bottom side = (8m+12m) = 20m. Inner vertical side = (20m-12m) = 8m. Inner horizontal side = 12m. Perimeter = 20 + 8 + 8 + 12 + 20 + 12 = 80m. This seems wrong. Let's re-read the diagram one more time. The shape is composed of a 8x20 rectangle and a 12x12 rectangle. Perimeter = 20 + 8 + (20-12) + 12 + 12 + (8+12) = 20 + 8 + 8 + 12 + 12 + 20 = 80m. Correct.
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The Paint Can
a) Volume:- Formula: V = πr²h
- Substitute values: V = 3.14 × (8 cm)² × 18 cm
- Calculate radius squared: V = 3.14 × 64 cm² × 18 cm
- Calculate final volume: V = 200.96 cm² × 18 cm = 3617.28 cm³
- Formula: A = 2πrh
- Substitute values: A = 2 × 3.14 × 8 cm × 18 cm
- Calculate: A = 6.28 × 8 cm × 18 cm
- Calculate final area: A = 50.24 cm × 18 cm = 904.32 cm²
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The Bookshelf Support
- The height and width of the rectangle form the two shorter sides of a right-angled triangle (a and b). The diagonal brace is the hypotenuse (c).
- Formula: a² + b² = c²
- Substitute values: (120 cm)² + (90 cm)² = c²
- Calculate squares: 14400 cm² + 8100 cm² = c²
- Add them: 22500 cm² = c²
- Find the square root: c = √22500 cm²
- Final length: c = 150 cm