Basic Mathematics Topics - Form Four

 

TOPIC 1: Coordinate Geometry

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1. Equation of a Line

   • Derive the general equation of a straight line

2. Midpoint of a Line Segment

   • Determine the coordinates of the midpoint of a line segment

3. Distance Between Two Points on a Plane

   • Calculate the distance between two points on a plane

4. Parallel and Perpendicular Lines

   • Compute gradients in order to determine the conditions for any two lines to be parallel

   • Compute gradients in order to determine the conditions for any two lines to be perpendicular

   • Solve problems on parallel and perpendicular lines

 

TOPIC 2: Area of Any Triangle

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1. Area of any Triangle

   • Derive the formula for the area of any triangle

   • Apply the formula to find the area of any triangle

2. Area of a Rhombus

   • Derive the formula for finding the area of rhombi in terms of the diagonals.

   • Apply the formula to find the areas of quadrilaterals

3. Perimeter of a Regular Polygon

   • Derive the formula for finding the length of a side of a regular polygon

   • The formula to determine the perimeter of a regular polygon

4. Area of a Regular Polygon

   • Derive the formula for finding the area of a regular polygon

   • Apply the formula to calculate the area of a regular polygon

5. Area of Similar Polygons

   • Find the ratio of areas of similar polygons

   • Solve problems related to ratio for areas of similar polygons

 

TOPIC 3: Three Dimensional Figures

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1. Three Dimensional Figures

   • Classify three dimensional figures

   • List the characteristics of each class

2. Construction of Three Dimensional Figures

   • Construct three dimensional figures

3. Sketching Three Dimensional Figures

   • Sketch three dimensional figures

   • Identify properties of three dimensional figures

   • Find the angle between a line and a plane

   • Calculate the angle between two planes

4. Surface Area of Three Dimensional Objects

   • Derive the formulae for calculating the surface area of prisms, cylinder and pyramids and cone

   • Apply the formulae to calculate the surface area of spheres

5. Volume of Three Dimensional Objects

   • Derive the formulae for calculating volume of prisms, cylinders and pyramids

   • Apply the formulae to calculate the volume of cylinders, pyramids and cones

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TOPIC 4: Probability

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1. Probability of an Events

   • Determine the probability of an event through experiments

   • Interpret experimental results in relation to real life occurrences

   • Write the formula for finding the probability of an event

   • Apply the formula to calculate the probability of an event

2. Combined Events

   • Perform experiments of two combined events

   • Draw a tree diagram of combined events

   • Find the probability of two combined events using the formula

   • Apply the knowledge of probability to determine the occurrence of events in real life situation

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TOPIC 5: Trignometry

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1. Trigonometric Ratios

   • Determine the sine, cosine and tangent of an angle measured in the clockwise and anticlockwise directions

   • Apply trigonometric ratios to solve problems in daily life

2. Sine and Cosine Functions

   • Find sines and cosines of angles 0 such that -720°≤ᶿ≥ 720°

   • Draw the graphs of sine and cosine

   • Interpret the graphs of sine and cosine functions

3. Sine and Cosine Rules

   • Derive the sine and cosine rules

   • Apply the sine and cosine rules in solving problems on triangles

4. Compound Angles

   • Apply the compound of angle formulae or sine, cosine and tangent in solving trigonometric problems

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TOPIC 6: Vectors

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1. Displacement and Positions of Vectors

   • Explain the concept of a vector quantity

   • Distinguish between displacement and position vectors

   • Resolving any vector into I and J components

2. Magnitude and Direction of a Vector

   • Calculate the magnitude and direction of a vector

3. Sum and Difference of Vectors

   • Find the sum of two or more vectors

   • Find the difference of vectors

4. Multiplication of a Vector by a Scalar

   • Multiply a vector by a scalar

5. Application of Vectors

   • Apply vectors in solving simple problems on velocities, displacements and forces

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TOPIC 7: Matrices and Transformations

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1. Operations on Matrices

   • Explain the concept of a matrix

   • Add matrices of order up to 2 X 2

   • Subtract matrices of order up to 2 X 2

   • Multiply a matrix of order 2 X 2 by a scalar

   • Multiply two matrices of order up to 2 X 2

2. Inverse of a Matrix

   • Calculate the determinant of a 2 X 2 matrix

   • Find the inverse of a 2 X 2 matrix

   • Apply 2 X 2 matrix to solve simultaneous equations

3. Matrices and Transformations

   • Transform any point P(X, Y) into P¹(X¹,Y¹) by pre-multiplying (ᵡᵧ) with a transformation matrix T

   • Apply the matrix to reflect a point P(X, Y ) in the x-axis

   • Apply the matrix to reflect a point P(X, Y) in the Y-Axis

   • Use a matrix operator to rotate any point P( X, Y ) through 90° 180°, 270° and 360° about the Origin

   • Use the enlargement matrix E in enlarging figures

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TOPIC 8: Liner Programming

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1. Simultaneous Equations

   • Form simultaneous equation from word problems

   • Solve simultaneous equations graphically

2. Inequalities

   • Form linear inequalities in two unknowns from word problems

   • Find the solution set of simultaneous linear inequalities graphically

3. The Objective Function

   • Form an objective function from word problems

4. Maximum and Minimum Values

   • Locate corner points on the feasible region

   • Find the minimum and maximum values using the objective function

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