AS Level Math Syllabus Breakup (9709)
Pure Mathematics 1 (P1)
1. Simultaneous Equations (Pre-Requisite)
 Point of intersection using two Linear Equations
 Point of intersection using linear and Non-Linear Equations
2. Quadratics
 Completed Square form and its uses
 How to sketch a quadratic curve
 Finding and using the discriminant applied to:
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Curve and x- axis
(ii)
Straight line and a curve
 Solving quadratic equations and inequalities
 Solving disguised quadratic equations
3. Functions
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Introduction to functions
Types of functions (One-one, many-one, one-many)
Vertical Line Test
Domain (non-restricted and restricted)
Range of a one-one
Range of a many-one
Range of a quadratic function
Restricted domain and its effects on range
Restricted domain examples continued
Composite Functions domain and range
Inverse (intro)
Inverse of a one-one
Inverse of a many-one function
Horizontal line test
Describing and applying the following transformations to the given graphs:
(i) Translation in x and y
(ii) Reflection along x and y axis
(iii) Stretch along x and y axis
4. Coordinate Geometry
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Introduction to coordinate geometry
Distance between two points
Midpoint
Gradient
Parallel lines and collinear points
Perpendicular lines
Equation of a straight line
Finding the gradient and y-intercept from the equation
Equation of parallel and perpendicular lines
Equation of perpendicular bisector
Area and perimeter using the distance formula
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Intersection of a straight line and a curve or a circle
Area of any polygon on the xy-plane
Understanding equation of circles
Converting and using equation of circles to find radius and centre
Geometrical properties of circles e.g. tangent perpendicular to radius, angle
opposite to diameter, symmetry
5. Trigonometry
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3 main trigonometric ratios (Sin, Cos and Tan)
Understanding the 4 quadrants and its uses in finding the 3 trigonometric ratios
Understanding the difference between theta and basic angle
Calculating theta using alpha and vice versa
Expressing ratios as acute angles using alpha and quadrants
Sketching graphs of sin, cos and tan in degrees and radian
Use of two identities
Solving trigonometric equations involving the three main trigonometric functions
6. Circular Measure
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Introduction of formulas of arc length and area of sector from degrees to radian
(Note: Understanding the conversion is not important)
Arc length, perimeter of sector and perimeter of shaded region
Area of triangle and sector
Area of shaded region applied to multiple cases
7. Binomial Theorem
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Introduction to binomial theorem
Using the binomial theorem for expansion of (1 + 𝑏)𝑛 for positive integer n
Using the binomial theorem for expansion of (𝑎 + 𝑏)𝑛 for positive integer n
Finding the coefficient of a specific term if x is in the first term and if x is in the
second term
Finding the coefficient of a specific term if 𝑥 𝑛 is in the first/second term and if x is in
the second term
Finding the coefficient of a specific term if x is in both the first and the second term
Expansion of nCr without a calculator – intro
8. Arithmetic & Geometric Progression (AP-GP)
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Intro to AP-GP
Finding the nth term of an AP
Finding the sum of an AP
Alternate method: Finding the sum of an AP
Finding the nth term of GP
Finding the sum of n terms
Finding the number of terms
Sum to Infinity
Word Problems (Identifying whether AP or GP)
9. Differentiation
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Introduction to differentiation
Differentiation of 𝑎𝑥 𝑛 type functions
Differentiation of composite functions (𝑎𝑥 + 𝑏)𝑛
Differentiation to find the gradient at any point on the curve
Differentiation applied to find the stationary/maximum/minimum/turning point and
nature of turning point
Differentiation applied to find the equation of normal and tangent
Differentiation applied to rates of change
Differentiation applied to shapes to find stationary value of volume, area etc etc
10. Integration
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Introduction to integration
Integration of 𝑎𝑥 𝑛 type functions
Finding the equation of the curve using integration
Integration of composite functions (𝑎𝑥 + 𝑏)𝑛 type
Integration within limits to find area under the curve
Integration used to find area between a line and a curve and in between two curves
Improper integrals with infinity as one of the limits
Volumes of revolution