Rational Numbers and Operations Quiz

Study Notes

Rational Numbers:
- A rational number is a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
- Examples: 3/4, 22/7, 1/2
Operations on Rational Numbers:
- Addition and subtraction: follow the same rules as fractions
- Multiplication: multiply the numerators and denominators separately
- Division: invert the second number and multiply

Linear Equations:
- A linear equation is an equation in which the highest power of the variable is 1.
- Examples: 2x + 3 = 5, x - 2 = -3
- Solving linear equations: use the inverse operation to isolate the variable
Quadratic Equations:
- A quadratic equation is an equation in which the highest power of the variable is 2.
- Examples: x^2 + 4x + 4 = 0, x^2 - 7x + 12 = 0
- Solving quadratic equations: use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a

Understanding Shapes:
- Types of angles: acute, obtuse, right, straight, reflex
- Properties of angles: sum of angles in a triangle is 180°
Properties of 2D Shapes:
- Properties of quadrilaterals: opposite sides are equal, opposite angles are equal
- Properties of triangles: sum of angles is 180°, exterior angle is equal to the sum of the two remote interior angles
Properties of 3D Shapes:
- Properties of cubes: all faces are squares, all edges are equal
- Properties of cuboids: opposite faces are rectangles, opposite edges are equal

Area and Perimeter of 2D Shapes:
- Area of triangle: (base × height) / 2
- Area of quadrilateral: sum of areas of triangles formed by dividing the quadrilateral
- Perimeter of triangle: sum of all sides
Volume and Surface Area of 3D Shapes:
- Volume of cube: side^3
- Volume of cuboid: length × width × height
- Surface area of cube: 6 × side^2
- Surface area of cuboid: 2 × (length × width + width × height + height × length)

Rational numbers can be expressed in the form p/q, where p and q are integers and q ≠ 0.
Examples of rational numbers include 3/4, 22/7, and 1/2.
To perform addition and subtraction on rational numbers, follow the same rules as fractions.
To multiply rational numbers, multiply the numerators and denominators separately.
To divide rational numbers, invert the second number and multiply.

Linear equations are equations in which the highest power of the variable is 1.
Examples of linear equations include 2x + 3 = 5 and x - 2 = -3.
To solve linear equations, use the inverse operation to isolate the variable.
Quadratic equations are equations in which the highest power of the variable is 2.
Examples of quadratic equations include x^2 + 4x + 4 = 0 and x^2 - 7x + 12 = 0.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.

Angles can be classified as acute, obtuse, right, straight, or reflex.
The sum of angles in a triangle is 180°.
Opposite sides of quadrilaterals are equal, and opposite angles are equal.
The sum of angles in a triangle is 180°, and the exterior angle is equal to the sum of the two remote interior angles.
All faces of a cube are squares, and all edges are equal.
Opposite faces of a cuboid are rectangles, and opposite edges are equal.

The area of a triangle is (base × height) / 2.
The area of a quadrilateral is the sum of the areas of triangles formed by dividing the quadrilateral.
The perimeter of a triangle is the sum of all sides.
The volume of a cube is side^3.
The volume of a cuboid is length × width × height.
The surface area of a cube is 6 × side^2.
The surface area of a cuboid is 2 × (length × width + width × height + height × length).