Parallel lines, 2D shapes, Congruency, similarity, Measurements, Statistics, Transformation Geo

Mathwise Academy | Grade 9 Test 1 - Geometry

MATHWISE ACADEMY

Grade 9 Mathematics: Test 1 • Geometry (Straight Lines, 2D Shapes, Congruency & Similarity)

Time: 1 Hour Total Marks: 50

INSTRUCTIONS AND INFORMATION

Answer ALL the questions.
Read all questions carefully before you begin.
Show ALL working out where applicable. Full marks will not necessarily be awarded for answers only.
You MUST provide valid GEOMETRIC REASONS for every statement you make when calculating unknown angles, sides, or providing proofs.
To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: GEOMETRY OF STRAIGHT LINES [14]

1.1 In the diagram below, line \( AB \) is parallel to line \( CD \) (\( AB \parallel CD \)). Transversal line \( EF \) intersects the parallel lines at points \( G \) and \( H \) respectively.
The interior angles are given in terms of \( x \): \( A\hat{G}H = 3x - 10^{\circ} \) and the alternate angle \( G\hat{H}D = x + 50^{\circ} \).

1.1.1 Formulate an equation and calculate the value of \( x \). Give a valid geometric reason. (4)

1.1.2 Calculate the actual size in degrees of \( C\hat{H}F \). (4)

1.2 Two straight lines intersect at point \( M \). The vertically opposite angles are given as \( 2y \) and \( 60^{\circ} \). The adjacent angle on the straight line is given as \( 3z \).

1.2.1 Calculate the value of \( y \). (2)

1.2.2 Calculate the value of \( z \). (4)

QUESTION 2: GEOMETRY OF 2D SHAPES [11]

2.1 In \( \triangle PQR \), the side \( QR \) is extended to \( S \) to form an exterior angle.
It is given that interior \( \hat{P} = 2x \), interior \( \hat{Q} = x + 30^{\circ} \), and exterior \( P\hat{R}S = 4x + 10^{\circ} \).

2.1.1 Formulate an equation and calculate the value of \( x \). Give a valid geometric reason. (5)

2.2 \( ABCD \) is a parallelogram. The interior angle \( \hat{A} \) is given as \( 2y - 20^{\circ} \) and the opposite interior angle \( \hat{C} \) is given as \( y + 40^{\circ} \).

2.2.1 Calculate the value of \( y \). (3)

2.2.2 Calculate the actual size of angle \( \hat{D} \). (3)

QUESTION 3: CONGRUENCY OF TRIANGLES [11]

3.1 List any THREE conditions (abbreviations are acceptable, e.g., SSS) under which two triangles can be proven to be congruent (\( \equiv \)).

(3)

3.2 In the diagram below, quadrilateral \( ABCD \) is a kite. The diagonal \( AC \) is drawn. You are given that \( AB = AD \) and \( BC = DC \).

3.2.1 Prove, showing all steps and reasons, that \( \triangle ABC \equiv \triangle ADC \). (6)

3.2.2 Hence, write down the relationship between angle \( \hat{B} \) and angle \( \hat{D} \). (2)

QUESTION 4: SIMILARITY OF TRIANGLES [14]

4.1 What is the primary condition required to prove that two triangles are similar (\( ||| \))?

(2)

4.2 In \( \triangle PQR \), a line segment \( ST \) is drawn inside the triangle such that \( ST \parallel QR \). Point \( S \) lies on \( PQ \) and point \( T \) lies on \( PR \).

4.2.1 Prove, showing all steps and geometric reasons, that \( \triangle PST \|| \triangle PQR \). (6)

4.2.2 You are given the following lengths: \( PS = 4\text{ cm} \), \( SQ = 2\text{ cm} \), and \( ST = 5\text{ cm} \).
Calculate the total length of the side \( PQ \). (2)

4.2.3 Use the ratios of the similar triangles to calculate the length of the base \( QR \). (4)

--- END OF PAPER ---

Mathwise Academy | Grade 9 Test 2 - Geometry

MATHWISE ACADEMY

Grade 9 Mathematics: Test 2 • Geometry (Straight Lines, 2D Shapes, Congruency & Similarity)

Time: 1 Hour Total Marks: 50

INSTRUCTIONS AND INFORMATION

Answer ALL the questions.
Read all questions carefully before you begin.
Show ALL working out where applicable. Full marks will not necessarily be awarded for answers only.
You MUST provide valid GEOMETRIC REASONS for every statement you make when calculating unknown angles, sides, or providing proofs.
To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: GEOMETRY OF STRAIGHT LINES [13]

1.1 In the diagram below, three adjacent angles lie on a straight line \( AB \). The sizes of the angles are given in terms of \( x \) as \( 2x + 10^{\circ} \), \( 3x - 20^{\circ} \), and \( x + 10^{\circ} \).

1.1.1 Formulate an equation and calculate the value of \( x \). Give a valid geometric reason. (4)

1.1.2 Calculate the actual size of the smallest angle. (2)

1.2 In the diagram below, line \( AB \) is parallel to line \( CD \) (\( AB \parallel CD \)). Transversal line \( EF \) intersects \( AB \) at point \( G \) and \( CD \) at point \( H \).
The interior alternate angles are given in terms of \( y \) as \( A\hat{G}H = 4y - 15^{\circ} \) and \( G\hat{H}D = 2y + 45^{\circ} \).

1.2.1 Calculate the value of \( y \), showing all steps and providing a valid geometric reason. (4)

1.2.2 Hence, calculate the actual size of the co-interior angle \( C\hat{H}G \). (3)

QUESTION 2: GEOMETRY OF 2D SHAPES [12]

2.1 In the diagram below, quadrilateral \( ABCD \) is a rhombus. The diagonals \( AC \) and \( BD \) intersect at point \( M \). You are given that interior angle \( A\hat{D}C = 110^{\circ} \).

2.1.1 Write down the size of angle \( A\hat{M}B \). Give a valid geometric reason. (2)

2.1.2 Calculate the size of angle \( A\hat{D}M \). Give a geometric reason. (2)

2.1.3 Hence, calculate the size of angle \( D\hat{A}M \). (3)

2.2 In \( \triangle PQR \), side \( QR \) is extended to point \( S \) to form an exterior angle \( P\hat{R}S \).
The angles are given in terms of \( x \) as: \( \hat{P} = 3x - 15^{\circ} \), \( \hat{Q} = 2x + 10^{\circ} \), and \( P\hat{R}S = 4x + 20^{\circ} \).

2.2.1 Formulate an equation and calculate the value of \( x \). Give a valid geometric reason. (4)

2.2.2 Calculate the actual size of interior angle \( P\hat{R}Q \). (1)

QUESTION 3: CONGRUENCY OF TRIANGLES [12]

3.1 In the diagram below, line segments \( AB \) and \( CD \) intersect and bisect each other at point \( M \).
Therefore, you are given that \( AM = BM \) and \( CM = DM \). Line segments \( AC \) and \( BD \) are drawn.

3.1.1 Prove, showing all statements and reasons, that \( \triangle AMC \equiv \triangle BMD \). (6)

3.1.2 Hence, deduce that side \( AC = BD \). (2)

3.1.3 Prove that line \( AC \) is parallel to line \( BD \) (\( AC \parallel BD \)). (4)

QUESTION 4: SIMILARITY OF TRIANGLES [13]

4.1 In the figure below, \( \triangle ABC \) is a right-angled triangle with \( \hat{B} = 90^{\circ} \). A perpendicular line segment \( DE \) is drawn to the hypotenuse \( AC \) such that point \( D \) lies on \( AC \) and point \( E \) lies on \( AB \), with \( A\hat{D}E = 90^{\circ} \).

4.1.1 Prove that \( \triangle ADE \||| \triangle ABC \). Show all logical steps and geometric reasons. (5)

4.2 You are given the following measured lengths: \( AD = 6\text{ cm} \), hypotenuse \( AE = 10\text{ cm} \), and side \( AB = 15\text{ cm} \).

4.2.1 Use the Theorem of Pythagoras in \( \triangle ADE \) to calculate the length of side \( DE \). (3)

4.2.2 Use the ratios of corresponding sides from the similar triangles to calculate the length of \( BC \). (3)

4.2.3 Hence, calculate the total length of the hypotenuse \( AC \). (2)

--- END OF PAPER ---

Mathwise Academy | Grade 9 Test 1 - Measurement

MATHWISE ACADEMY

Grade 9 Mathematics: Test 1 • Measurement

Time: 1 Hour Total Marks: 50

INSTRUCTIONS AND INFORMATION

Answer ALL the questions.
Read all questions carefully before you begin.
Show ALL working out where applicable. Full marks will not necessarily be awarded for answers only.
You may use an approved scientific calculator.
Round off final answers to TWO decimal places where necessary.
Use \( \pi = 3,14 \) or the \( \pi \) button on your calculator.
To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: THEOREM OF PYTHAGORAS [12]

1.1 Consider the right-angled triangle below.

1.1.1 Calculate the length of the hypotenuse (indicated by \( x \)). (3)

1.2 A rectangular wooden gate has a diagonal support beam that is \( 2,5\text{ m} \) long. The height of the gate is \( 1,5\text{ m} \).

1.2.1 Use the Theorem of Pythagoras to calculate the width (\( w \)) of the gate in metres. (4)

1.3 A triangle has side lengths of \( 10\text{ cm} \), \( 24\text{ cm} \), and \( 26\text{ cm} \).

1.3.1 Prove, showing all calculations, whether this is a right-angled triangle or not. (5)

QUESTION 2: AREA AND PERIMETER OF 2D SHAPES [18]

2.1 Convert the following area measurement:

2.1.1 \( 2,5\text{ m}^2 \) to \( \text{cm}^2 \) (2)

2.2 A circle has a diameter of \( 14\text{ cm} \).

2.2.1 Calculate the circumference of the circle. (2)

2.2.2 Calculate the area of the circle. (2)

2.3 Consider the composite shape below. It consists of a rectangle with a triangle attached to the top. The rectangle measures \( 8\text{ cm} \) by \( 6\text{ cm} \). The height of the triangle from its base is \( 3\text{ cm} \).

2.3.1 Calculate the total area of the composite shape. (3)

2.3.2 Calculate the perimeter of the entire composite shape.
(Hint: You will need to calculate the slant heights of the triangle first). (4)

2.4 Cost Calculation Problem:
A rectangular classroom floor measures \( 5\text{ m} \) by \( 4\text{ m} \). The school wants to tile the floor. The chosen tiles cost \( \text{R}\, 150 \) per square metre (\( \text{m}^2 \)).

2.4.1 Calculate the total cost to tile the classroom floor. (5)

QUESTION 3: SURFACE AREA AND VOLUME OF 3D SHAPES [20]

3.1 Consider a closed cylinder with a radius of \( 5\text{ cm} \) and a height of \( 10\text{ cm} \).

3.1.1 Calculate the volume of the cylinder. (3)

3.1.2 Calculate the total surface area of the cylinder. (4)

3.2 A right-angled triangular prism has a base with side lengths \( 3\text{ cm} \), \( 4\text{ cm} \), and \( 5\text{ cm} \) (where \( 5\text{ cm} \) is the hypotenuse). The length of the prism is \( 12\text{ cm} \).

3.2.1 Calculate the volume of the triangular prism. (3)

3.2.2 Calculate the total surface area of the triangular prism. (4)

3.3 Capacity Application Problem:
A large rectangular water tank has the following interior dimensions:
Length \( = 50\text{ cm} \), Breadth \( = 40\text{ cm} \), and Height \( = 30\text{ cm} \).

3.3.1 Calculate the volume of the tank in \( \text{cm}^3 \). (2)

3.3.2 Calculate the capacity of the tank in litres.
(Remember: \( 1\,000\text{ cm}^3 = 1\text{ litre} \)) (4)

--- END OF PAPER ---

Mathwise Academy | Grade 9 Test 2 - Measurement (Higher Order)

MATHWISE ACADEMY

Grade 9 Mathematics: Test 2 • Measurement (Higher Order)

Time: 1 Hour Total Marks: 50

INSTRUCTIONS AND INFORMATION

Answer ALL the questions.
Read all questions carefully before you begin.
Show ALL working out where applicable. Full marks will not necessarily be awarded for answers only.
You may use an approved scientific calculator.
Round off final answers to TWO decimal places where necessary.
Use \( \pi = 3,14 \) or the \( \pi \) key on your calculator.
To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: THEOREM OF PYTHAGORAS [12]

1.1 The Sliding Ladder Problem:
A ladder that is \( 5\text{ m} \) long rests against a vertical wall. The foot of the ladder is initially \( 3\text{ m} \) away from the base of the wall. After a while, the ladder slips down the wall so that its foot is now \( 4\text{ m} \) away from the base of the wall.

1.1.1 Calculate exactly how far down the wall the top of the ladder has slipped (indicated by distance \( y \)). Show all your working. (4)

1.2 Consider the composite figure below consisting of two right-angled triangles, \( \triangle PQR \) and \( \triangle PRS \). Angle \( Q \) is a right angle (\( 90^{\circ} \)) and angle \( P\hat{R}S \) is a right angle (\( 90^{\circ} \)).

1.2.1 Calculate the length of side \( PS \) (indicated by \( x \)). Give your answer rounded to two decimal places. (4)

1.3 A triangle has side lengths of \( 20\text{ mm} \), \( 21\text{ mm} \), and \( 29\text{ mm} \).

1.3.1 Determine, showing all calculations, whether this is a right-angled triangle. (4)

QUESTION 2: AREA AND PERIMETER OF 2D SHAPES [18]

2.1 Convert the following area measurement:

2.1.1 \( 5,2\text{ m}^2 \) to \( \text{cm}^2 \) (2)

2.2 Consider the shape below. It is a rectangular sheet of metal with length \( 20\text{ cm} \) and breadth \( 14\text{ cm} \). A semi-circle is cut out of one of the shorter sides.

2.2.1 Calculate the perimeter of the remaining shape (the shaded region). (4)

2.2.2 Calculate the area of the remaining shape (the shaded region). (4)

2.3 A circular flower bed has a radius of \( 6\text{ m} \). It is surrounded by a paved path that is \( 2\text{ m} \) wide all the way around.

2.3.1 Calculate the area of the paved path (the shaded ring). (3)

2.4 Application Problem:
A rectangular garden measures \( 15\text{ m} \) by \( 10\text{ m} \). A concrete pathway of \( 1\text{ m} \) uniform width is built inside the garden along all four borders.

2.4.1 Calculate the total area of this concrete pathway. (5)

QUESTION 3: SURFACE AREA AND VOLUME OF 3D SHAPES [20]

3.1 A rectangular prism (cuboid) has a length of \( 12\text{ cm} \), a breadth of \( 8\text{ cm} \), and a height of \( 5\text{ cm} \).

3.1.1 Calculate the surface area of the prism if it is open on top (i.e. it has no lid). (4)

3.2 Consider the right-angled triangular prism below. The dimensions of the triangular base are \( 6\text{ cm} \), \( 8\text{ cm} \), and \( 10\text{ cm} \). The length of the prism is \( 20\text{ cm} \).

3.2.1 Calculate the volume of the triangular prism. (3)

3.2.2 Calculate the total surface area of this closed triangular prism. (4)

3.3 Capacity Application Problem:
A large rectangular glass fish tank is \( 80\text{ cm} \) long, \( 40\text{ cm} \) wide, and \( 50\text{ cm} \) high.

3.3.1 Calculate the total volume of the fish tank in \( \text{cm}^3 \). (2)

3.3.2 Calculate the total capacity of the fish tank in litres. (2)

3.3.3 If the tank is filled with water to a depth of \( 35\text{ cm} \), how many litres of water are currently in the tank? (3)

3.4 Conceptual Question:
If the side length of a cube is doubled, by what factor does its volume increase?

3.4.1 State the factor and provide a brief algebraic explanation or calculation to prove your answer. (2)

--- END OF PAPER ---

Mathwise Academy | Grade 9 Test 1 - Statistics & Transformation

MATHWISE ACADEMY

Grade 9 Mathematics: Test 1 • Statistics and Transformation Geometry

Time: 1 Hour Total Marks: 50

INSTRUCTIONS AND INFORMATION

Answer ALL the questions.
Read all questions carefully before you begin.
Show ALL working out where applicable. Full marks will not necessarily be awarded for answers only.
You may use an approved non-programmable scientific calculator.
Round off final answers to ONE decimal place where necessary.
To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: STATISTICS (DATA HANDLING) [30]

1.1 The following data set represents the marks (out of \( 50 \)) achieved by \( 11 \) learners in a Mathematics assignment:

34 ; 12 ; 41 ; 28 ; 34 ; 45 ; 38 ; 22 ; 34 ; 49 ; 15

1.1.1 Arrange the data in ascending order. (1)

1.1.2 Determine the median mark for the assignment. (2)

1.1.3 Write down the mode. (1)

1.1.4 Calculate the mean (average) mark for these learners. Round off to ONE decimal place. (3)

1.1.5 Calculate the range of the marks. (2)

1.2 Grouped Data and Histograms:
The histogram below shows the time (in minutes) taken by \( 40 \) people to travel to work.

1.2.1 Which time interval represents the modal class? (1)

1.2.2 How many people take \( 30 \) minutes or more to travel to work? (2)

1.2.3 What percentage of people take strictly less than \( 20 \) minutes to travel to work? (3)

1.3 Scatter Plots and Bivariate Data:
The scatter plot below shows the relationship between the number of hours a group of learners spent studying for a test and the percentage they scored.

1.3.1 What type of correlation is shown in the scatter plot? Choose from: Strong Positive, Strong Negative, or No Correlation. (2)

1.3.2 Describe the relationship between the number of hours studied and the test score in your own words. (2)

1.3.3 A learner studied for exactly \( 4,5 \) hours. By estimating using a line of best fit, what test score would you predict for this learner? (2)

1.4 Pie Charts:
A survey was conducted among \( 240 \) Grade 9 learners to find out their favorite genre of music. The pie chart below illustrates the results. The sector for 'Pop' has an angle of \( 120^{\circ} \) and 'Hip-Hop' has an angle of \( 150^{\circ} \).

1.4.1 Calculate the size of the angle that represents 'Rock' music. (2)

1.4.2 What fraction of the learners chose 'Pop' as their favorite genre? Write your answer in its simplest form. (2)

1.4.3 Calculate the exact number of learners who chose 'Hip-Hop'. (3)

QUESTION 2: TRANSFORMATION GEOMETRY [20]

2.1 Translations:

2.1.1 Point \( A(-3 ; 4) \) is translated \( 5 \) units to the right and \( 6 \) units down to become its image, \( A' \). Write down the coordinates of \( A' \). (2)

2.1.2 Point \( M \) is translated \( 4 \) units left and \( 1 \) unit up to become \( M'(2 ; -5) \). Determine the original coordinates of point \( M \). (2)

2.2 Reflections:
Apply the given reflections to the coordinates below and write down the image coordinates:

2.2.1 Point \( B(2 ; -7) \) is reflected across the \( x \)-axis to become \( B' \). (2)

2.2.2 Point \( C(-4 ; -1) \) is reflected across the \( y \)-axis to become \( C' \). (2)

2.2.3 Point \( D(5 ; 8) \) is reflected across the line \( y = x \) to become \( D' \). (2)

2.3 Enlargements and Reductions:
Triangle \( PQR \) is drawn on a Cartesian plane. The coordinates of the vertices are \( P(0 ; 3) \), \( Q(-3 ; -3) \), and \( R(6 ; 0) \). The triangle is reduced by a scale factor of \( k = \dfrac{1}{3} \) through the origin to form \( \Delta P'Q'R' \).

2.3.1 Determine the coordinates of the image vertices \( P' \), \( Q' \), and \( R' \). (3)

2.3.2 Point \( S(2 ; -5) \) is enlarged through the origin to become \( S'(8 ; -20) \). What is the scale factor of this enlargement? (2)

2.4 Effect of Scale Factor on Area:
A rectangle has an area of \( 15\text{ cm}^2 \). The rectangle is then enlarged by a scale factor of \( k = 4 \).

2.4.1 Calculate the area of the newly enlarged rectangle. (3)

2.4.2 Complete the following rule: If a 2D shape is enlarged by a scale factor of \( k \), its perimeter is multiplied by \( k \), and its area is multiplied by ________. (2)

--- END OF PAPER ---

Mathwise Academy | Grade 9 Test 2 - Statistics & Transformation Geometry

MATHWISE ACADEMY

Grade 9 Mathematics: Test 2 • Statistics and Transformation Geometry

Time: 1 Hour Total Marks: 50

INSTRUCTIONS AND INFORMATION

Answer ALL the questions.
Read all questions carefully before you begin.
Show ALL working out where applicable. Full marks will not necessarily be awarded for answers only.
You may use an approved non-programmable scientific calculator.
Round off final answers to ONE decimal place where necessary.
To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: STATISTICS (DATA HANDLING) [30]

1.1 The following data set represents the marks (out of \( 100 \)) achieved by \( 10 \) learners in a Mathematics test:

45 ; 52 ; 60 ; 45 ; 78 ; 60 ; 85 ; 45 ; 90 ; 50

1.1.1 Arrange the data in ascending order. (1)

1.1.2 Write down the mode of the dataset. (1)

1.1.3 Determine the median mark. (2)

1.1.4 Calculate the mean (average) mark for these learners. (2)

1.1.5 Calculate the range of the marks. (1)

1.2 Stem-and-Leaf Plot:
The stem-and-leaf plot below shows the ages of \( 15 \) people attending a community fitness class.

Stem	Leaf
1	6 8 9
2	2 5 5 5 8
3	0 4 8
4	1 5
5	0 2

1.2.1 Write down the age of the youngest person in the class. (1)

1.2.2 Write down the mode of the ages. (1)

1.2.3 Determine the median age of the attendees. (2)

1.2.4 What fraction of the attendees are strictly younger than \( 30 \) years old? Write your answer in its simplest form. (3)

1.3 Broken-Line Graph:
The broken-line graph below shows the number of meals sold at a school tuckshop from Monday to Friday.

1.3.1 On which day were the most meals sold? (1)

1.3.2 Calculate the difference in the number of meals sold between Thursday and Wednesday. (2)

1.3.3 Calculate the total number of meals sold over the entire \( 5 \)-day week. (2)

1.3.4 What percentage of the total weekly meals were sold on Friday? (2)

1.4 Pie Charts:
A survey was conducted among \( 200 \) Grade 9 learners to find out how they travel to school. The pie chart below illustrates the results. The sector for 'Walk' has an angle of \( 108^{\circ} \), 'Bus' has an angle of \( 90^{\circ} \), and 'Car' has an angle of \( 126^{\circ} \). The remaining angle represents 'Taxi'.

1.4.1 Calculate the size of the angle that represents learners who travel by 'Taxi'. (2)

1.4.2 What fraction of the learners travel by 'Bus'? Write your answer in its simplest form. (2)

1.4.3 Calculate the exact number of learners who 'Walk' to school. (3)

1.4.4 What percentage of the learners use a 'Taxi' to get to school? (2)

QUESTION 2: TRANSFORMATION GEOMETRY [20]

2.1 Translations:

2.1.1 Point \( M(-2 ; 5) \) is translated \( 6 \) units to the right and \( 3 \) units down to become its image, \( M' \). Write down the coordinates of \( M' \). (2)

2.1.2 Point \( N \) is translated \( 4 \) units left and \( 2 \) units up to become \( N'(-1 ; 4) \). Determine the original coordinates of point \( N \). (2)

2.2 Reflections:
Apply the given reflections to the coordinates below and write down the image coordinates:

2.2.1 Point \( A(4 ; -3) \) is reflected across the \( x \)-axis to become \( A' \). (2)

2.2.2 Point \( B(-7 ; 1) \) is reflected across the \( y \)-axis to become \( B' \). (2)

2.2.3 Point \( C(2 ; 8) \) is reflected across the line \( y = x \) to become \( C' \). (2)

2.3 Enlargements and Reductions:
Triangle \( DEF \) is drawn on a Cartesian plane. The coordinates of the vertices are \( D(0 ; 4) \), \( E(-2 ; -2) \), and \( F(6 ; 0) \). The triangle is reduced by a scale factor of \( k = \dfrac{1}{2} \) through the origin to form \( \Delta D'E'F' \).

2.3.1 Determine the coordinates of the image vertices \( D' \), \( E' \), and \( F' \). (3)

2.3.2 Point \( G(-3 ; 5) \) is enlarged through the origin to become \( G'(-12 ; 20) \). What is the scale factor of this enlargement? (2)

2.4 Effect of Scale Factor on Area:
A rectangle has an area of \( 12\text{ cm}^2 \). The rectangle is then enlarged by a scale factor of \( k = 3 \).

2.4.1 Calculate the area of the newly enlarged rectangle. (3)

2.4.2 Complete the following rule: If a 2D shape is enlarged by a scale factor of \( k \), its area is multiplied by \( k^2 \), and its perimeter is multiplied by ________. (2)

--- END OF PAPER ---