Syllabus Form 3. Objectives Students will be able to: Mathematics Department. Revision of numbers. Form 3 Syllabus Page 1 of 7

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1 Syllabus Form 3 Topic Revision of numbers Content 1. Rounding 2. Estimation 3. Directed numbers 4. Working with decimals 5. Changing fractions to 6. decimals and vice versa The reciprocal of a number 7.2. Fraction of a quantity Add & Subtract Fractions 8.2. Multiplication and Division of Fractions 9. Using BIDMAS in fractions(lsn 1) 10. Using BIDMAS in fractions(lsn 2) 11. Working with mixed numbers Factors and multiples 12.2 Expressing a number as a product of its prime factors Square numbers Determining if a number is a perfect square Cubic Numbers Standard Form Numbers in Standard Form Changing from Standard form to ordinary Numbers Working with numbers in standard form Objectives Students will be able to: Add and subtract fractions/mixed numbers. Multiply and divide fractions/mixed numbers. Round numbers to a given number of significant figures. Choose reasonable approximations. Carry out rough estimates to check accuracy Write ordinary numbers in standard form and vice versa. Form 3 Syllabus Page 1 of 7

2 Indices Percentages Money Sequences Ratios Finding the value of numbers in index form 1.2. Rules of indices Rule Rules of indices Rule Rules of indices Rule Rules of indices Rule Rules of indices Rule Rules of indices Rule Rules of indices Rule 7 4. Revision of Indices Expressing percentages as decimals and fractions 1.2. Expressing decimals and fractions as percentages 2. Percentage of a quantity 3. Expressing a quantity as a percentage of another 4. Percentage increase and decrease 5. Reverse percentage increase and decrease Percentage Change 6.2. Percentage Error 1. Simple interest 2. Using simple interest to find the rate and time 3. Using simple interest to find the principal 4. Using simple interest to find the rate and time given the amount 1. Arithmetic Sequences 2. Geometric Sequences 3. Other Sequences 1. Ratios as a comparison 2. Using ratios to divide quantities 3. Finding unknown quantities in ratios 4. Direct and Inverse Proportion 5. Speed/ distance / time Use and interpret positive integral indices and zero Use the index laws in simple instances Understand that a negative power will give the reciprocal of the number Work out the percentage increase/ decrease using a multiplying factor. Solve problems involving percentages. Carry out reverse percentage calculations. Use percentages to calculate the simple interest on a sum of money. Use the formula, or a variation of it, to find the simple interest, the principal sum, the rate, the time or the amount. Use a calculator and/or a spread sheet to investigate the effect of changing the principal, rate or time on simple interest. Generate terms of a sequence, given the formula, for the nth term and the value of n. Use algebraic expressions to describe the nth term of a linear sequence. Divide quantities in a given ratio. Find missing quantities in a given ratio. Understand and use the elementary ideas of direct and inverse proportion. Use direct and inverse proportion to calculate speed/average speed/ distance/time Form 3 Syllabus Page 2 of 7

3 Expanding and Factorising Algebraic Terms 1.2. Addition and Multiplication of terms 2. Multiplication and division of terms 3. Expanding brackets Perfect Squares 4.2. Product of two brackets 5. Harder Expansions Factorization 6.2. Factorisation using common factor Factorise fully expressions by taking out the highest common factor. Use and interpret positive integral indices and zero Multiply a bracket by a single term. Expand two brackets Simplify and/or factorise more complicated non-linear expressions. Solve two simultaneous equations graphically and linearly. Solve problems leading to the solution of simultaneous linear equations. Equations and Formula Solving linear equations simultaneously 1. Solving linear equations with one variable 2. Solving linear equations with one variable (brackets) 3. Linear equations involving fractions (2 lessons) 4. Solve problems by forming linear equations in one unknown Subject of the formula 5.2. One type operation 6. Two type operation 7. Two occurrences of the same unknown Substitution 8.2. Forming formulae 1. The elimination method 2. Equations with different x and y coefficients (lesson 1) 3. Equations with different x and y coefficients (lesson 2) 4. Solving by using substitution 5. Applications of simultaneous equations to real life Solve linear equations in one unknown. Solve problems by forming linear equations in one unknown. Introduce the use of trial and improvement method to solve equations correct to 1 d.p. Evaluate practical formulae by substituting variables with numbers. Students are encouraged to interpret the results. Change the subject of the formula involving more than one operation. Solve two simultaneous equations graphically. Solve two linear equations simultaneously. Solve problems leading to the solution of simultaneous linear equations. Form 3 Syllabus Page 3 of 7

4 Trigonometry Bearings 1. Finding the Hypotenuse 2. Finding one of the shorter sides 3. Converse of Pythagoras Theorem 4. Pythagorean Triples 5. Applications of Pythagoras Theorem Trigonometric Ratios 6.2. Summary of three basic ratios 7. Finding an angle given two sides 8. Finding a side given one angle and a side 9. Angles of Elevation and Depression 10. Applications of trigonometric ratios 1. Finding bearings and other angles (lesson 1) 2. Finding bearings and other angles (lesson 2) 3. Scale drawings Understand the rule of Pythagoras through drawing and measurement. Use Pythagoras rule to find the side of a right- angled triangle given the other two sides. Use Pythagoras rule to solve practical problems. Understand sine, cosine and tangent as the ratio between pairs of sides of a right-angled triangle. Use trigonometric ratios to find the length of a side given a side and an angle. Use three-figure bearings to describe direction and the position of one point from another. Use scale drawings to solve problems involving angles of elevation and depression. Use scale drawings to solve problems involving bearings Form 3 Syllabus Page 4 of 7

5 Polygons 1. Sum of interior angles of a polygon 2. Finding an interior angle of a regular polygon 3. Finding an interior angle of an irregular polygon The sum of exterior angles of a convex polygon 4.2. Finding an exterior angle of a convex regular polygon Finding an exterior angle of a convex irregular polygon 5.2. Finding the number of sides of a regular polygon given the exterior angle 6. Finding the number of sides of a regular polygon given the interior angle 7. Draw the inscribed regular hexagon in a given circle using ruler and compasses only Tessellations 8.2. Types of tessellations Solve problems involving the angles of triangle and quadrilaterals. Derive the sum of the exterior/interior angles of a polygon. Draw the inscribed regular hexagon in a given circle using ruler and compasses only. Inscribe a regular polygon in a circle with given radius for integral values of 360 /n. Solve problems involving angles of polygons Arithmetic in Circle 1. The circumference 2. Arc of a circle and length of arc 3. Perimeter of compound shapes with circular parts Area of a circle 4.2. Area of a sector 5. Area of compound shapes with circular parts Finding the radius from the circumference and area 6.2. Finding the circumference from the area 6.3. Finding the area from the circumference Understand the notion of π as a ratio of circumference to diameter. Deduce and use the formulae of C= πd and C=2 πr Deduce and use the formula for the area of a circle A= πr 2 by dividing into sectors. Find the length of arc and area of sector as fractions of a circle Form 3 Syllabus Page 5 of 7

6 Circle Geometry Area Volume Straight line graphs 1. Definitions related to circles (arc, sector, segment, diameter, ) Circle facts 2.2. Angles at the centre is twice angle at the circumference 3. Angles in the same segment 4. Angles in a semicircle 1. Area of a Triangle The Quadrilateral 2.2. Rectangle and Square Parallelogram 3.2. Trapezium 4. Curved Surface Area 5. Total Surface Area Introduction 1.2. Finding the volume of solids with uniform crosssection 2. Finding the missing dimension Coordinates 1.2. Straight line graphs 2. How many points? The equation of a line 3.2. Vertical and horizontal lines 3.3. Slant lines through the origin 4. Slant lines with intercepts 5. The gradient of a line Gradient of horizontal lines 6.2. Gradient of vertical lines 6.3. Parallel and perpendicular lines The x- and y- intercepts 7.2. Disguised equations of lines Coordinate geometry 8.2. Points on a line Prove the following circle theorems: the angle at the centre is twice the angle at the circumference; angles in the same segment are equal; the angle in a semicircle = 90. Use the formula of the volume of a cylinder to find the volume. Derive and use the formulae of the surface area of a cylinder. Generate and plot coordinate pairs that satisfy a linear rule. Understand, interpret and calculate the gradient of a line from the coordinates of two points on the line. Understand how the gradient and the y-intercept are connected to y = mx + c. Draw quadratic graphs and identify maxima/minima. Use quadratic graphs to solve equations of the form f(x) = c. Form 3 Syllabus Page 6 of 7

7 Probability Statistics Logo 8.3. Finding the gradient of a line segment Finding the equation of a line segment 9.2. Finding the equation of a slant line given the gradient and one point 10. Quadratic graphs (lesson 1) 11. Quadratic graphs (lesson 2) Finding the probability of an event (lesson 1) 1.2. Finding the probability of an event (lesson 2) Probability with two events (lesson 1) 2.2. Probability with two events (lesson 2) Discrete variables 1.2. Mean 1.3. Median 1.4. Mode Representing data 2.2. Continuous variables 3. Grouped data Pie charts 4.2. Interpreting pie charts Understand and work out the probability of an event. Understand that the probabilities of all mutually exclusive outcomes add up to 1. Compile and use a possibility space. Work out the probability from a frequency table. Understand, compute and interpret the mean, median, mode and range of a set of ungrouped data from a frequency table. Interpret bar charts and pie charts. Draw bar charts with equal intervals from frequency tables. 1. LOGO provides an ideal environment for students to experience angle as a measure of turn, in both clockwise and anti-clockwise direction. Besides, turtle geometry gives students an opportunity to manipulate angles of different sizes. Form 3 Syllabus Page 7 of 7