Math for Secondary 1 to Secondary 4 Students

At the secondary level, Math mastery requires a deeper understanding of subject knowledge and problem-solving skills to achieve consistent academic excellence. This sets the foundation for success in junior colleges, where critical thinking, strong learning habits, and exam-ready skills are essential.

The PaceUP programme is thoughtfully designed to bridge the transition from Primary to Secondary Math, laying a strong foundation for success in junior college—where critical thinking, effective learning habits, and exam-readiness are essential for long-term academic achievement.

Why Sign Your Teen Up for the PaceUP Programme?

01

Strong foundations. Emphasis on building a solid base in core topics such as Algebra, Geometry, Trigonometry, and Calculus.

02

Strategy-led practice. Customised worksheets guide students through problem-solving strategies and provide ample practice to reinforce learning.

03

MOE-aligned. Lessons are aligned with the latest MOE syllabus to ensure relevance and exam readiness.

04

Tracked progress. Termly reviews and mock tests help track progress, boost exam preparedness, and build students' confidence.

05

Real-world application. Exposure to real-world context and application-based problems helps students apply concepts effectively.

06

Room to stretch. Higher-order questions available for students seeking to stretch their abilities and deepen their understanding.

Guided Thought Process

A clear path through simultaneous equations

Two equations can feel like two problems at once. This is the exact sequence you follow to work through them.

Elimination Method

Guided Thought Process
LEARNit! (2)

Solve the following pair of simultaneous equations by elimination method.

8x + 3y = 39

17x − 9y = 6

Tip Look at the coefficients to determine which one is easier to eliminate.

Answer

Step 1

Label the equations.

8x + 3y = 39  ...(1)

17x − 9y = 6  ...(2)

Step 2

Multiply the equation(s) with a suitable constant so that the coefficient of one variable is the same.

In this example, we multiply equation (1) by 3 to make the coefficients of y the same, i.e. 9.

Step 3

Add or subtract the equations from Step 2 to eliminate the variable. Here, we add equation (2) into equation (3).

(1) × 3 :   24x + 9y = 117  ...(3)

Same coefficient as equation (2).

We guide the thinking, one step at a time

Every PaceUP technique comes with the reasoning behind it, not just the steps. Here is how your teen is guided through completing the square, a core method for solving quadratic equations at secondary level.

LEARNit! (2)

Solve x² + 9x + 18 = 0

Answer

x² + 9x + 18 = 0

x² + 9x = −18

x² + 9x + ( 92)2  =  −18 + ( 92)2

(x + 92)2  =  −18 + 814

(x + 92)2  =  94

x + 92  =  ± √ 94  =  ± 32

x = −3, −6

Step by step guide

1
Rearrange the equation such that it is in the form ax² + bx + c = 0.
2
Ensure a = 1. Otherwise, divide throughout. (Refer to LEARNit! [3])
3
Rewrite the coefficient of x into multiple of 2.
4
Add (b/2)² − (b/2)² after the x-term. Notice that the first 3 terms follow the identity (a+b)² = a² + 2ab + b².
5
Simplify and bring the constant term to the right.
6
Apply square root on both sides and solve for x.

Note: should the constant term on the right-hand side be negative at Step 5, the equation has no root.

Topics Covered

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Secondary 1

Topics covered

  • Integers, Rational Numbers and Real Numbers
  • Primes, HCF and LCM
  • Approximation and Estimation
  • Basic Algebra and Algebraic Manipulation
  • Linear Equations
  • Linear Functions and Graphs I
  • Linear Functions and Graphs II
  • Number Patterns
  • Percentage
  • Ratio and Rate
  • Basic Geometry
  • Polygons and Geometrical Constructions
  • Perimeter and Area of Plane Figures
  • Volume and Surface Area of Prisms and Cylinders
  • Statistical Data Handling

Topics covered

  • Linear Functions and Graphs
  • Simultaneous Linear Equations
  • Linear Expressions, Linear Equations and Simple Inequalities
  • Expansion and Factorisation of Algebraic Expressions
  • Expansion and Factorisation using Special Algebraic Identities
  • Direct and Inverse Proportion
  • Algebraic Fractions
  • Congruence and Similarity
  • Pythagoras’ Theorem
  • Trigonometric Ratio
  • Volume and Surface Area of Pyramids, Cones and Spheres
  • Probability of Single Events
  • Statistical Diagrams
  • Averages of Statistical Diagrams
ADDITIONAL MATHEMATICS

Topics covered

  • Quadratic Equations
  • Equations and Inequalities
  • Surds
  • Polynomials, Cubic Equations and Partial Fractions
  • Exponential and Logarithm Functions I
  • Exponential and Logarithm Functions II
  • Binomial Theorem and its Applications
  • Coordinate Geometry
  • Linear Law
  • Trigonometric Functions and Graphs
  • Trigonometric Equations and Identities
ELEMENTARY MATHEMATICS

Topics covered

  • Indices and Standard Form
  • Quadratic Equations and Functions
  • Linear Inequalities
  • Coordinate Geometry
  • Graphs of Functions and Graphical Solutions I
  • Graphs of Functions and Graphical Solutions II
  • Further Trigonometry
  • Application of Trigonometry
  • Arc Length, Area of Sector and Radian Measure
  • Congruence and Similarity Tests I
  • Congruence and Similarity Tests II
  • Area and Volume of Similar Figures and Solids
  • Geometrical Properties of Circles
ADDITIONAL MATHEMATICS

Topics covered

  • Gradients, Derivatives and Differentiation Techniques
  • Application of Differentiation
  • Differentiation of Trigonometric, Exponential and Logarithmic Functions and their Applications
  • Integration
  • Application of Integration
  • Kinematics
  • Proofs of Plane Geometry
ELEMENTARY MATHEMATICS

Topics covered

  • Sets
  • Probability of Combined Events
  • Statistical Data Analysis
  • Matrices
  • Vectors I
  • Vectors II
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