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Maths Revision paper

1.Sets

1.1. Basic Set Notation

  • A set is a collection of distinct objects. We denote sets using curly brackets, for example, A={1,2,3,4}A = \{1, 2, 3, 4\}
  • A={1,2,3,4}.
  • The universal set UU
  • U contains all elements under consideration.

  • Union of sets AA
  • A and BB
  • B is written as A∪BA \cup B
  • A∪B and includes all elements from both sets.
  • Intersection of sets AA
  • A and BB
  • B is written as A∩BA \cap B
  • A∩B and includes elements that are common to both sets.
  • Complement of a set AA
  • A is the set of all elements in the universal set UU
  • U that are not in AA
  • A, denoted by A′A'
  • A′
  • .

Example Questions:

  1. Let A={1,2,3,4}A = \{1, 2, 3, 4\}
  2. A={1,2,3,4} and B={3,4,5,6}B = \{3, 4, 5, 6\}
  3. B={3,4,5,6}. Find A∪BA \cup B
  4. A∪B, A∩BA \cap B
  5. A∩B, and A′A'
  6. A′
  7. if the universal set is U={1,2,3,4,5,6,7}U = \{1, 2, 3, 4, 5, 6, 7\}
  8. U={1,2,3,4,5,6,7}.


2.Graphs

2.1. Types of Graphs

  • Bar Graphs: Used to display data with rectangular bars.
  • Line Graphs: Used to show changes over time, with points connected by straight lines.
  • Pie Charts: Show parts of a whole.

2.2. Plotting Coordinates

  • A coordinate grid is used to plot points on a graph. The x-coordinate tells you how far along the point is, and the y-coordinate tells you how far up or down it is.

Example Questions:

  1. Plot the points (2,3)(2, 3)
  2. (2,3), (−1,4)(-1, 4)
  3. (−1,4), and (4,−2)(4, -2)
  4. (4,−2) on a coordinate grid.
  5. A line graph shows the number of students in a school each month. If the number of students in January was 250, February 260, and March 240, plot this on a line graph.

3. Transformations

3.1. Types of Transformations

  • Translation: Moving a shape without rotating or flipping it.
  • Example: Translate point (2,3)(2, 3)
  • (2,3) by (3,−1)(3, -1)
  • (3,−1) to find the new point.
  • Reflection: Flipping a shape over a line (e.g., the x-axis, y-axis).
  • Rotation: Rotating a shape around a point, often the origin.
  • Enlargement: Making a shape bigger or smaller from a center point.

3.2. Rotation

  • To rotate a point, you need the angle of rotation (e.g., 90°) and the center of rotation (e.g., the origin).

Example Questions:

  1. Reflect the point (3,4)(3, 4)
  2. (3,4) over the x-axis.
  3. Rotate the point (2,1)(2, 1)
  4. (2,1) by 90° clockwise around the origin.
  5. Translate the triangle with vertices A(1,2)A(1, 2)
  6. A(1,2), B(4,2)B(4, 2)
  7. B(4,2), and C(2,5)C(2, 5)
  8. C(2,5) by (2,−3)(2, -3)
  9. (2,−3).

4. Angles

4.1. Types of Angles

  • Acute: Less than 90°.
  • Right Angle: Exactly 90°.
  • Obtuse: Greater than 90° but less than 180°.
  • Straight Angle: Exactly 180°.

4.2. Angle Relationships

  • Complementary Angles: Two angles that add up to 90°.
  • Supplementary Angles: Two angles that add up to 180°.
  • Vertically Opposite Angles: Angles opposite each other when two lines intersect. They are equal.

Example Questions:

  1. If two angles are complementary and one angle is 30°, what is the other angle?
  2. Two angles are supplementary. One angle is 120°. What is the other angle?

5. 2D Shapes

5.1. Properties of 2D Shapes

  • Triangle: Three sides, the sum of interior angles is 180°.
  • Equilateral Triangle: All sides and angles are equal.
  • Isosceles Triangle: Two sides are equal.
  • Scalene Triangle: No sides are equal.
  • Square: Four equal sides and four right angles.
  • Rectangle: Opposite sides are equal and four right angles.
  • Circle: All points are equidistant from the center.
  • Parallelogram: Opposite sides are equal and parallel.
  • Trapezium: One pair of parallel sides.

5.2. Perimeter and Area

  • Perimeter of a polygon is the sum of the lengths of its sides.
  • Area of a rectangle: Area=length×width\text{Area} = \text{length} \times \text{width}
  • Area=length×width
  • Area of a triangle: Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

  • Area=2
  • 1
  • ​×base×height
  • Area of a circle: Area=πr2\text{Area} = \pi r^2
  • Area=πr2

Example Questions:

  1. Find the perimeter and area of a rectangle with length 8 cm and width 5 cm.
  2. Find the area of a triangle with a base of 10 cm and height of 6 cm.
  3. A circle has a radius of 7 cm. Find its area.

6. Challenge Questions

  1. A set A={x∣x is an even number less than 10}A = \{x \mid x \text{ is an even number less than 10}\}
  2. A={x∣x is an even number less than 10} and set B={x∣x is a prime number less than 10}B = \{x \mid x \text{ is a prime number less than 10}\}
  3. B={x∣x is a prime number less than 10}. Find A∪BA \cup B
  4. A∪B and A∩BA \cap B
  5. A∩B.
  6. A triangle has angles of 35°, 65°, and xx
  7. x. Find the value of xx
  8. x.
  9. A rectangle has a diagonal length of 13 cm and one side length of 5 cm. Find the other side length.

End of Revision Paper


Maths Revision paper

1.Sets

1.1. Basic Set Notation

  • A set is a collection of distinct objects. We denote sets using curly brackets, for example, A={1,2,3,4}A = \{1, 2, 3, 4\}
  • A={1,2,3,4}.
  • The universal set UU
  • U contains all elements under consideration.

  • Union of sets AA
  • A and BB
  • B is written as A∪BA \cup B
  • A∪B and includes all elements from both sets.
  • Intersection of sets AA
  • A and BB
  • B is written as A∩BA \cap B
  • A∩B and includes elements that are common to both sets.
  • Complement of a set AA
  • A is the set of all elements in the universal set UU
  • U that are not in AA
  • A, denoted by A′A'
  • A′
  • .

Example Questions:

  1. Let A={1,2,3,4}A = \{1, 2, 3, 4\}
  2. A={1,2,3,4} and B={3,4,5,6}B = \{3, 4, 5, 6\}
  3. B={3,4,5,6}. Find A∪BA \cup B
  4. A∪B, A∩BA \cap B
  5. A∩B, and A′A'
  6. A′
  7. if the universal set is U={1,2,3,4,5,6,7}U = \{1, 2, 3, 4, 5, 6, 7\}
  8. U={1,2,3,4,5,6,7}.


2.Graphs

2.1. Types of Graphs

  • Bar Graphs: Used to display data with rectangular bars.
  • Line Graphs: Used to show changes over time, with points connected by straight lines.
  • Pie Charts: Show parts of a whole.

2.2. Plotting Coordinates

  • A coordinate grid is used to plot points on a graph. The x-coordinate tells you how far along the point is, and the y-coordinate tells you how far up or down it is.

Example Questions:

  1. Plot the points (2,3)(2, 3)
  2. (2,3), (−1,4)(-1, 4)
  3. (−1,4), and (4,−2)(4, -2)
  4. (4,−2) on a coordinate grid.
  5. A line graph shows the number of students in a school each month. If the number of students in January was 250, February 260, and March 240, plot this on a line graph.

3. Transformations

3.1. Types of Transformations

  • Translation: Moving a shape without rotating or flipping it.
  • Example: Translate point (2,3)(2, 3)
  • (2,3) by (3,−1)(3, -1)
  • (3,−1) to find the new point.
  • Reflection: Flipping a shape over a line (e.g., the x-axis, y-axis).
  • Rotation: Rotating a shape around a point, often the origin.
  • Enlargement: Making a shape bigger or smaller from a center point.

3.2. Rotation

  • To rotate a point, you need the angle of rotation (e.g., 90°) and the center of rotation (e.g., the origin).

Example Questions:

  1. Reflect the point (3,4)(3, 4)
  2. (3,4) over the x-axis.
  3. Rotate the point (2,1)(2, 1)
  4. (2,1) by 90° clockwise around the origin.
  5. Translate the triangle with vertices A(1,2)A(1, 2)
  6. A(1,2), B(4,2)B(4, 2)
  7. B(4,2), and C(2,5)C(2, 5)
  8. C(2,5) by (2,−3)(2, -3)
  9. (2,−3).

4. Angles

4.1. Types of Angles

  • Acute: Less than 90°.
  • Right Angle: Exactly 90°.
  • Obtuse: Greater than 90° but less than 180°.
  • Straight Angle: Exactly 180°.

4.2. Angle Relationships

  • Complementary Angles: Two angles that add up to 90°.
  • Supplementary Angles: Two angles that add up to 180°.
  • Vertically Opposite Angles: Angles opposite each other when two lines intersect. They are equal.

Example Questions:

  1. If two angles are complementary and one angle is 30°, what is the other angle?
  2. Two angles are supplementary. One angle is 120°. What is the other angle?

5. 2D Shapes

5.1. Properties of 2D Shapes

  • Triangle: Three sides, the sum of interior angles is 180°.
  • Equilateral Triangle: All sides and angles are equal.
  • Isosceles Triangle: Two sides are equal.
  • Scalene Triangle: No sides are equal.
  • Square: Four equal sides and four right angles.
  • Rectangle: Opposite sides are equal and four right angles.
  • Circle: All points are equidistant from the center.
  • Parallelogram: Opposite sides are equal and parallel.
  • Trapezium: One pair of parallel sides.

5.2. Perimeter and Area

  • Perimeter of a polygon is the sum of the lengths of its sides.
  • Area of a rectangle: Area=length×width\text{Area} = \text{length} \times \text{width}
  • Area=length×width
  • Area of a triangle: Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

  • Area=2
  • 1
  • ​×base×height
  • Area of a circle: Area=πr2\text{Area} = \pi r^2
  • Area=πr2

Example Questions:

  1. Find the perimeter and area of a rectangle with length 8 cm and width 5 cm.
  2. Find the area of a triangle with a base of 10 cm and height of 6 cm.
  3. A circle has a radius of 7 cm. Find its area.

6. Challenge Questions

  1. A set A={x∣x is an even number less than 10}A = \{x \mid x \text{ is an even number less than 10}\}
  2. A={x∣x is an even number less than 10} and set B={x∣x is a prime number less than 10}B = \{x \mid x \text{ is a prime number less than 10}\}
  3. B={x∣x is a prime number less than 10}. Find A∪BA \cup B
  4. A∪B and A∩BA \cap B
  5. A∩B.
  6. A triangle has angles of 35°, 65°, and xx
  7. x. Find the value of xx
  8. x.
  9. A rectangle has a diagonal length of 13 cm and one side length of 5 cm. Find the other side length.

End of Revision Paper

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