Mathwise Academy | Grade 10 Mathematics Paper 2 - Preparatory Paper 1
M

MATHWISE ACADEMY

Grade 10 Mathematics • Preparatory Paper 1 (Paper 2: Statistics, Analytical Geo, Trig, Euclidean Geo)

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 6 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • If necessary, round off answers to TWO decimal places, unless stated otherwise.
  • Diagrams are NOT necessarily drawn to scale.
  • Provide geometric reasons for all statements in Euclidean Geometry.

QUESTION 1: STATISTICS [15]

1.1 The marks of 11 learners out of 50 are given below:

12   ;   18   ;   25   ;   30   ;   32   ;   35   ;   40   ;   41   ;   45   ;   48   ;   49
  • 1.1.1 Determine the mean. (3)
  • 1.1.2 Determine the five-number summary (\(\text{Min}\), \(Q_1\), \(\text{Med}\), \(Q_3\), \(\text{Max}\)). (5)
  • 1.1.3 Calculate the Interquartile Range (\(\text{IQR}\)). (2)
  • 1.1.4 Draw a box and whisker plot for this data on the number line below. (3)
10 20 30 40 50
  • 1.1.5 Comment on the skewness of the data. (2)

QUESTION 2: ANALYTICAL GEOMETRY [15]

2.1 In a Cartesian plane, points \( A(-2 ; 1) \), \( B(3 ; 4) \), and \( C(1 ; -2) \) are given.

x y A(-2; 1) B(3; 4) C(1; -2) M
  • 2.1.1 Calculate the length of \( AB \). (Leave in surd form). (3)
  • 2.1.2 Determine the coordinates of \( M \), the midpoint of \( AC \). (2)
  • 2.1.3 Calculate the gradient of \( BC \). (2)
  • 2.1.4 Determine the equation of the line passing through \( A \) and \( B \). (4)
  • 2.1.5 Prove whether \( \triangle ABC \) is a right-angled triangle at \( A \). (4)

QUESTION 3: TRIGONOMETRY [20]

3.1 Evaluate with a calculator (correct to 2 decimal places):

  • 3.1.1 \( \sin 42^\circ + \cos 18^\circ \) (2)
  • 3.1.2 \( \dfrac{\tan 55^\circ}{\sin 20^\circ} \) (2)

3.2 Given \( \sin \theta = \dfrac{3}{5} \) and \( 0^\circ \le \theta \le 90^\circ \). Without a calculator, use a sketch to find:

  • 3.2.1 \( \cos \theta \) (3)
  • 3.2.2 \( \tan \theta \) (2)
  • 3.2.3 \( \cos^2 \theta + \sin^2 \theta \) (3)

3.3 Solve for \( x \) if \( x \in [0^\circ ; 90^\circ] \):

  • 3.3.1 \( 2\cos x = 1 \) (2)
  • 3.3.2 \( \tan x - 2,5 = 0 \) (3)
  • 3.3.3 \( \sin(x + 10^\circ) = 0,5 \) (3)

QUESTION 4: TRIGONOMETRY (2D PROBLEMS & GRAPHS) [20]

4.1 In \( \triangle PQR \), \( \hat{Q} = 90^\circ \), \( PQ = 8\text{ cm} \), and \( QR = 6\text{ cm} \).

  • 4.1.1 Calculate the length of \( PR \). (2)
  • 4.1.2 Calculate the size of \( \hat{R} \) (correct to 1 decimal place). (3)

4.2 A surveyor stands at point \( A \) and measures the angle of elevation to the top of a building (\( T \)) to be \( 35^\circ \). The distance from \( A \) to the base of the building (\( B \)) is \( 50\text{ m} \).

  • 4.2.1 Sketch a diagram in the space provided to represent this information. (3)
  • 4.2.2 Calculate the height of the building (\( TB \)). (3)
  • 4.2.3 Calculate the distance from the surveyor to the top of the building (\( AT \)). (4)

4.3 Given \( f(x) = \sin x \) and \( g(x) = 2\cos x \) for \( x \in [0^\circ ; 360^\circ] \).

  • 4.3.1 State the amplitude of \( g \). (1)
  • 4.3.2 Sketch both graphs on the same set of axes provided on the grid below. (3)
0° 90° 180° 270° 360° 3 2 1 -1 -2

QUESTION 5: EUCLIDEAN GEOMETRY [15]

  • 5.1 State two properties of a parallelogram. (2)
  • 5.2 In quadrilateral \( ABCD \), \( AB \parallel DC \) and \( AD \parallel BC \). Prove that \( \triangle ABD \equiv \triangle CDB \). (6)

5.3 In parallelogram \( PQRS \), \( \hat{P} = 2x + 10^\circ \) and \( \hat{S} = 3x - 20^\circ \).

  • 5.3.1 Calculate the value of \( x \). (5)
  • 5.3.2 Calculate the size of \( \hat{Q} \). (2)

QUESTION 6: EUCLIDEAN GEOMETRY [15]

  • 6.1 State the Midpoint Theorem in words. (2)

6.2 In \( \triangle DEF \), \( M \) is the midpoint of \( DE \) and \( N \) is the midpoint of \( DF \). \( MN = 2x - 4 \) and \( EF = 3x + 2 \).

  • 6.2.1 Write down the relationship between \( MN \) and \( EF \). (2)
  • 6.2.2 Calculate the value of \( x \). (4)
  • 6.2.3 Calculate the length of \( EF \). (2)

6.3 In a rhombus \( ABCD \), the diagonals intersect at \( O \). \( AC = 16\text{ cm} \) and \( BD = 12\text{ cm} \).

  • 6.3.1 Write down the length of \( AO \) and \( BO \). (2)
  • 6.3.2 Calculate the length of side \( AB \). (3)
Mathwise Academy | Grade 10 Mathematics Paper 2 - Preparatory Paper 3
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 3 • Paper 2

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 6 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • If necessary, round off answers to TWO decimal places, unless stated otherwise.
  • Diagrams are NOT necessarily drawn to scale.
  • You must provide geometric reasons for all statements in Euclidean Geometry.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: STATISTICS [15]

1.1 A frequency table shows the marks of \( 40 \) students:

Interval Frequency
\( 0 < x \le 20 \) 4
\( 20 < x \le 40 \) 10
\( 40 < x \le 60 \) 15
\( 60 < x \le 80 \) 8
\( 80 < x \le 100 \) 3
  • 1.1.1 Write down the modal class. (1)
  • 1.1.2 Estimate the mean mark. (4)

1.2 A set of \( 5 \) numbers has a mean of \( 12 \). Four of the numbers are \( 8 \), \( 10 \), \( 15 \), and \( 12 \).

  • 1.2.1 Calculate the fifth number. (3)
  • 1.2.2 Calculate the median of the 5 numbers. (2)
  • 1.2.3 Write down a 5-number summary. (5)

QUESTION 2: ANALYTICAL GEOMETRY [15]

2.1 The line passing through \( A(-1 ; 2) \) and \( B(x ; 6) \) has a gradient of \( 2 \).

  • 2.1.1 Calculate the value of \( x \). (3)
  • 2.1.2 Determine the equation of line \( AB \). (3)
  • 2.1.3 Calculate the coordinates of the midpoint of \( AB \). (3)
  • 2.1.4 Calculate the length of \( AB \). (3)
  • 2.1.5 Determine the equation of a line parallel to \( AB \) passing through the origin. (3)

QUESTION 3: TRIGONOMETRY [20]

3.1 Use a calculator to find the value of \( x \), where \( x \in [0^\circ ; 90^\circ] \):

  • 3.1.1 \( \cos x = 0,4 \) (2)
  • 3.1.2 \( \sin(x - 20^\circ) = 0,8 \) (3)

3.2 Given \( \tan \alpha = \frac{5}{12} \) and \( \cos \alpha > 0 \). Use a sketch to evaluate:

  • 3.2.1 \( \sin \alpha \) (4)
  • 3.2.2 \( \cos \alpha \) (2)
  • 3.2.3 \( \sin^2 \alpha + \cos^2 \alpha \) (3)

3.3 Without a calculator, evaluate:

\( \dfrac{\sin 30^\circ \cdot \cos 60^\circ}{\tan 45^\circ} \)
[6]

QUESTION 4: TRIGONOMETRY (2D PROBLEMS) [20]

4.1 An aeroplane takes off at an angle of \( 15^\circ \) to the horizontal. It flies in a straight line for \( 5\text{ km} \).

  • 4.1.1 Calculate its horizontal distance from the start. (3)
  • 4.1.2 Calculate its vertical height above the ground. (3)

4.2 In \( \triangle DEF \), \( \angle E = 90^\circ \), \( DE = 12 \) and \( EF = 5 \).

  • 4.2.1 Calculate \( DF \). (2)
  • 4.2.2 Calculate \( \angle D \). (3)
  • 4.2.3 Calculate \( \angle F \). (2)

4.3 Given \( f(x) = \sin x + 1 \) for \( x \in [0^\circ ; 360^\circ] \).

  • 4.3.1 Write down the amplitude. (1)
  • 4.3.2 Write down the range. (2)
  • 4.3.3 Sketch the graph of \( f(x) \). (4)
3 2 1 -1 -2 -3 y 90° 180° 270° 360° x

QUESTION 5: EUCLIDEAN GEOMETRY [15]

5.1 In parallelogram \( ABCD \), diagonal \( BD \) is drawn. Prove that \( \triangle ABD \equiv \triangle CDB \).

A B C D
[6]

5.2 In a rhombus, the diagonals are \( 10\text{ cm} \) and \( 24\text{ cm} \).

12 12 5 5
  • 5.2.1 Calculate the length of a side of the rhombus. (4)
  • 5.2.2 Calculate the perimeter of the rhombus. (2)
  • 5.3 State the properties of the diagonals of a kite. (3)

QUESTION 6: EUCLIDEAN GEOMETRY [15]

6.1 In \( \triangle ABC \), \( D \) is the midpoint of \( AB \) and \( E \) is the midpoint of \( AC \). \( DE = 3x - 1 \) and \( BC = 5x + 4 \).

A B C D E 3x - 1 5x + 4
  • 6.1.1 Write down the equation connecting \( DE \) and \( BC \). (2)
  • 6.1.2 Calculate the value of \( x \). (4)
  • 6.1.3 Find the length of \( DE \). (2)

6.2 \( PQRS \) is a rectangle. \( PR \) and \( QS \) intersect at \( T \). \( \angle PTQ = 120^\circ \).

120° P Q R S T
  • 6.2.1 Calculate \( \angle PTR \). (2)
  • 6.2.2 Prove that \( \triangle PQT \) is equilateral if it is given that \( PQ = PT \). (5)
--- END OF PAPER ---
Mathwise Academy | Grade 10 Mathematics Paper 2 - Preparatory Paper 3
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 3 • Paper 2

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 6 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • If necessary, round off answers to TWO decimal places, unless stated otherwise.
  • Diagrams are NOT necessarily drawn to scale.
  • You must provide geometric reasons for all statements in Euclidean Geometry.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: STATISTICS [15]

1.1 A frequency table shows the marks of 40 students:

Interval Frequency
\(0 < x \le 20\) 4
\(20 < x \le 40\) 10
\(40 < x \le 60\) 15
\(60 < x \le 80\) 8
\(80 < x \le 100\) 3
  • 1.1.1 Write down the modal class. (1)
  • 1.1.2 Estimate the mean mark. (4)

1.2 A set of 5 numbers has a mean of 12. Four of the numbers are 8, 10, 15, and 12.

  • 1.2.1 Calculate the fifth number. (3)
  • 1.2.2 Calculate the median of the 5 numbers. (2)
  • 1.2.3 Write down a 5-number summary. (5)

QUESTION 2: ANALYTICAL GEOMETRY [15]

2.1 The line passing through \(A(-1;2)\) and \(B(x;6)\) has a gradient of 2.

  • 2.1.1 Calculate the value of \(x\). (3)
  • 2.1.2 Determine the equation of line AB. (3)
  • 2.1.3 Calculate the coordinates of the midpoint of AB. (3)
  • 2.1.4 Calculate the length of AB. Leave your answer in simplest surd form. (3)
  • 2.1.5 Determine the equation of a line parallel to AB passing through the origin. (3)

QUESTION 3: TRIGONOMETRY [20]

3.1 Use a calculator to find the value of \(x \in [0^{\circ};90^{\circ}]\):

  • 3.1.1 \(\cos x = 0,4\) (2)
  • 3.1.2 \(\sin(x-20^{\circ}) = 0,8\) (3)

3.2 Given \(\tan \alpha = \frac{5}{12}\) and \(\cos \alpha > 0\). Use a sketch to evaluate:

  • 3.2.1 \(\sin \alpha\) (4)
  • 3.2.2 \(\cos \alpha\) (2)
  • 3.2.3 \(\sin^{2}\alpha + \cos^{2}\alpha\) (3)

3.3 Without a calculator, evaluate:

\( \frac{\sin 30^{\circ} \cdot \cos 60^{\circ}}{\tan 45^{\circ}} \)
[6]

QUESTION 4: TRIGONOMETRY (2D PROBLEMS) [20]

4.1 An aeroplane takes off at an angle of \(15^{\circ}\) to the horizontal. It flies in a straight line for 5 km.

  • 4.1.1 Calculate its horizontal distance from the start. (3)
  • 4.1.2 Calculate its vertical height above the ground. (3)

4.2 In \(\triangle DEF\), \(\angle E = 90^{\circ}\), \(DE = 12\) and \(EF = 5\).

  • 4.2.1 Calculate DF. (2)
  • 4.2.2 Calculate \(\angle D\). (3)
  • 4.2.3 Calculate \(\angle F\). (2)

4.3 Given \(f(x) = \sin x + 1\) for \(x \in [0^{\circ};360^{\circ}]\).

  • 4.3.1 Write down the amplitude. (1)
  • 4.3.2 Write down the range. (2)
  • 4.3.3 Sketch the graph of \(f(x)\). Use the grid below. (4)
3 2 1 -1 -2 -3 y 90° 180° 270° 360° x

QUESTION 5: EUCLIDEAN GEOMETRY [15]

  • 5.1 In parallelogram ABCD, diagonal BD is drawn. Prove that \(\triangle ABD \equiv \triangle CDB\). (6)

5.2 In a rhombus, the diagonals are 10 cm and 24 cm.

  • 5.2.1 Calculate the length of a side of the rhombus. (4)
  • 5.2.2 Calculate the perimeter of the rhombus. (2)
  • 5.3 State the properties of the diagonals of a kite. (3)

QUESTION 6: EUCLIDEAN GEOMETRY [15]

6.1 In \(\triangle ABC\), D is the midpoint of AB and E is the midpoint of AC. \(DE = 3x - 1\) and \(BC = 5x + 4\).

A B C D E
  • 6.1.1 Write down the equation connecting DE and BC. (2)
  • 6.1.2 Calculate the value of \(x\). (4)
  • 6.1.3 Find the length of DE. (2)

6.2 PQRS is a rectangle. PR and QS intersect at T. \(\angle PTQ = 120^{\circ}\).

120° P Q R S T
  • 6.2.1 Calculate \(\angle PTR\). (2)
  • 6.2.2 Prove that \(\triangle PQT\) is equilateral if \(PQ = PT\). (5)
--- END OF PAPER ---
Mathwise Academy | Grade 10 Mathematics Paper 2 - Preparatory Paper 4
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 4 • Paper 2

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 6 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • If necessary, round off answers to TWO decimal places, unless stated otherwise.
  • Diagrams are NOT necessarily drawn to scale.
  • You must provide geometric reasons for all statements in Euclidean Geometry.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: STATISTICS [15]

1.1 Given the dataset:

10   ;   12   ;   14   ;   14   ;   16   ;   18   ;   20   ;   22
  • 1.1.1 Determine the mean. (2)
  • 1.1.2 Determine the median. (2)
  • 1.1.3 Determine the mode. (1)
  • 1.1.4 Determine the five-number summary. (5)
  • 1.1.5 Draw a box and whisker plot on the number line provided below. (3)
8 10 12 14 16 18 20 22 24
  • 1.1.6 What percentage of the data lies between the lower and upper quartile? (2)

QUESTION 2: ANALYTICAL GEOMETRY [15]

2.1 Given the points \( A(-4 ; 2) \) and \( B(2 ; -6) \).

  • 2.1.1 Calculate the length of \( AB \). (3)
  • 2.1.2 Calculate the gradient of \( AB \). (2)
  • 2.1.3 Find the midpoint \( M \) of \( AB \). (2)
  • 2.1.4 Find the equation of the line passing through \( A \) and \( B \). (4)
  • 2.1.5 A line perpendicular to \( AB \) passes through \( M \). Find its gradient. (4)

QUESTION 3: TRIGONOMETRY [20]

3.1 Without a calculator, evaluate:

\( \tan 45^\circ + \cos 60^\circ - \sin 30^\circ \)
[5]

3.2 Given \( 5 \sin \theta - 4 = 0 \) and \( 90^\circ \le \theta \le 360^\circ \).

  • 3.2.1 Find \( \sin \theta \). (1)
  • 3.2.2 Use a sketch to find \( \cos \theta \). (4)
  • 3.2.3 Evaluate \( \tan \theta \). (2)

3.3 Solve for \( x \ (0^\circ \le x \le 90^\circ) \):

  • 3.3.1 \( 4 \cos x - 1 = 0 \) (3)
  • 3.3.2 \( \sin 2x = 0,5 \) (3)
  • 3.3.3 \( \tan(x + 15^\circ) = 1 \) (2)

QUESTION 4: TRIGONOMETRY (2D PROBLEMS) [20]

4.1 A person stands \( 20\text{ m} \) away from a tree. The angle of elevation to the top of the tree is \( 40^\circ \). The person's eye level is \( 1,5\text{ m} \) above the ground.

  • 4.1.1 Draw a sketch of the situation in the space below. (3)
    • [ SKETCH SPACE ]
  • 4.1.2 Calculate the height of the tree. (5)

4.2 In \( \triangle XYZ \), \( \angle Y = 90^\circ \), \( XY = 7 \) and \( YZ = 24 \).

  • 4.2.1 Calculate \( XZ \). (2)
  • 4.2.2 Calculate \( \sin X \). (2)
  • 4.2.3 Calculate \( \angle Z \). (3)

4.3 Sketch \( f(x) = \cos x - 1 \) for \( x \in [0^\circ ; 360^\circ] \) on the grid provided.

[5]
3 2 1 -1 -2 -3 y 90° 180° 270° 360° x

QUESTION 5: EUCLIDEAN GEOMETRY [15]

  • 5.1 Prove that the diagonals of a rectangle are equal in length. (6)
    • A B C D

5.2 In a kite \( KLMN \), \( KL = KN \) and \( ML = MN \). Diagonals intersect at \( O \).

K L M N O
  • 5.2.1 Write down the size of \( \angle LOM \). (1)
  • 5.2.2 Prove that \( \triangle KLM \equiv \triangle KNM \). (5)
  • 5.2.3 If \( \angle LKN = 80^\circ \), calculate \( \angle OKL \). (3)

QUESTION 6: EUCLIDEAN GEOMETRY [15]

6.1 In \( \triangle ABC \), \( D \) is the midpoint of \( AB \) and \( E \) is on \( AC \) such that \( DE \parallel BC \).

A B C D E

  • 6.2 In parallelogram \( WXYZ \), \( \angle W = 50^\circ \).

    50° W X Y Z
    • 6.2.2 Calculate \( \angle Y \). (2)
    • 6.2.3 Prove that interior angles on the same side of transversal \( WX \) are supplementary. (4)
--- END OF PAPER ---
Mathwise Academy | Grade 10 Mathematics Paper 2 - Preparatory Paper 5
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 5 • Paper 2

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 6 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers.
  • You may use an approved scientific calculator (non-programmable and non-graphical).
  • Round off answers to TWO decimal places where applicable.
  • Diagrams are NOT necessarily drawn to scale.

QUESTION 1: STATISTICS [15]

1.1 Two classes wrote a test. The results were as follows:

Class A: 40 ; 45 ; 50 ; 50 ; 55 ; 60 ; 65 ; 70 ; 80

Class B: 10 ; 30 ; 50 ; 55 ; 60 ; 60 ; 65 ; 85 ; 90

  • 1.1.1 Calculate the mean for both classes. (4)
  • 1.1.2 Find the median for both classes. (2)
  • 1.1.3 Calculate the range for both classes. (2)
  • 1.1.4 Draw side-by-side box and whisker plots for the two classes using the scale below. (5)
0 10 20 30 40 50 60 70 80 90 100
  • 1.1.5 Which class performed better consistently? Motivate your answer using the range. (2)

QUESTION 2: ANALYTICAL GEOMETRY [15]

2.1 A quadrilateral has vertices \( A(0;4) \), \( B(4;6) \), \( C(6;2) \), and \( D(2;0) \).

  • 2.1.1 Calculate the lengths of \( AB \) and \( CD \). (4)
  • 2.1.2 Calculate the gradients of \( AB \) and \( CD \). (4)
  • 2.1.3 Calculate the gradients of \( AD \) and \( BC \). (4)
  • 2.1.4 Based on your calculations, what type of quadrilateral is \( ABCD \)? Give a reason. (3)

QUESTION 3: TRIGONOMETRY [20]

3.1 Evaluate without a calculator:

  • 3.1.1 \( \sin 30^\circ + \cos 60^\circ \) (3)
  • 3.1.2 \( \dfrac{\tan 45^\circ}{\sin 90^\circ} \) (3)

3.2 If \( 17\sin \beta = 8 \) and \( \cos \beta < 0 \), find without a calculator:

  • 3.2.1 \( \cos \beta \) (4)
  • 3.2.2 \( \tan \beta \) (2)

3.3 Solve for \( x \) correct to 2 decimal places \( (x \in [0^\circ ; 90^\circ]) \):

  • 3.3.1 \( \cos x = 0,75 \) (2)
  • 3.3.2 \( 3\tan x = 5 \) (3)
  • 3.3.3 \( \sin 3x = 0,5 \) (3)

QUESTION 4: TRIGONOMETRY (2D PROBLEMS) [20]

4.1 A guy wire is attached to a pole. The wire is \( 15\text{ m} \) long and makes an angle of \( 55^\circ \) with the ground.

55° 15 m Pole
  • 4.1.1 Calculate the height of the pole where the wire is attached. (3)
  • 4.1.2 Calculate the distance from the base of the pole to where the wire is staked. (3)

4.2 In \( \triangle PQR \), \( \angle Q = 90^\circ \), \( PR = 20 \), and \( \angle P = 60^\circ \).

60° P Q R 20
  • 4.2.1 Calculate \( PQ \). (3)
  • 4.2.2 Calculate \( QR \). (3)

4.3 Given \( f(x) = 2\sin x \) for \( x \in [0^\circ ; 360^\circ] \).

  • 4.3.1 Write down the amplitude. (1)
  • 4.3.2 Write down the range. (2)
  • 4.3.3 Sketch the graph of \( f(x) \) on the grid below. (5)
3 2 1 -1 -2 -3 y 90° 180° 270° 360° x

QUESTION 5: EUCLIDEAN GEOMETRY [15]

  • 5.1 Prove that the diagonals of a parallelogram bisect each other. (6)
O A B C D

5.2 In rectangle \( ABCD \), diagonals intersect at \( O \). \( \angle OAB = 30^\circ \).

30° O A B C D
  • 5.2.1 Calculate \( \angle OBA \). (3)
  • 5.2.2 Calculate \( \angle AOB \). (2)
  • 5.2.3 Calculate \( \angle OAD \). (4)

QUESTION 6: EUCLIDEAN GEOMETRY [15]

6.1 In \( \triangle KLM \), \( S \) is the midpoint of \( KL \) and \( T \) is the midpoint of \( KM \). \( ST = 10\text{ cm} \).

K L M S T 10 cm
  • 6.1.1 Write down the length of \( LM \). (2)
  • 6.1.2 State the theorem used. (2)

6.2 In a rhombus \( PQRS \), \( \angle P = 100^\circ \).

100° P Q R S
  • 6.2.1 Calculate \( \angle Q \). (2)
  • 6.2.2 Calculate \( \angle R \). (2)
  • 6.2.3 Diagonal \( PR \) is drawn. Calculate \( \angle SPR \). (3)
  • 6.2.4 Diagonal \( QS \) is drawn. Calculate \( \angle PQS \). (4)
--- END OF PAPER ---