Topic A revision of number work A revision of number work Indices Expressions: Expanding and Factorisation Form 4 Syllabus Scheme B Content 1. Directed Numbers 2. Factors and Multiples 3. Expressing a number as a product of prime factors 4. LCM and HCF (Handout) 1. 1.1. Standard form 1.2. Expressing numbers in standard form. 2. Changing from standard form to ordinary numbers 1. Finding the value of numbers in index form 2. Rules of indices 3. Common misconceptions 4. Summary of all the rules 1. Addition and subtraction of terms 2. Multiplication and division of terms 3. Expanding brackets 4. Factorisation using a common factor Core and Paper B Students will be able to: Understand and use positive and negative numbers in real life contexts. Multiply and divide negative numbers Recognise, understand and use a) Integers b) Factors, multiples, LCM, prime numbers and prime factors Write ordinary numbers in standard form and vice-versa. Learn to use the EXP key on the calculator Use and interpret positive and negative integral indices including zero. Use the index laws for multiplying and dividing integer power with the same number base. Solve simple exponential equations by inspection (KY Maths 3 Pg 34) 3 x = 81, 2 x = 1/16 Simplify algebraic expressions by collecting, cancelling, and multiplying terms of an expression. Factorise expressions completely by taking out a common factor (Pg. 127/8) Multiply a single term over a bracket (Pg. 123) Use letter symbols to represent unknown quantities in a formula Form 4 Syllabus Page 1 of 7
Solving linear equations simultaneously 1. Solve linear equations graphically 2. The Elimination method 3. Equations with different x and y coefficients 4. 4.1. Alternative Methods 4.2. Solving by equating equations 5. Solving by substitution 6. Applications of simultaneous equations to real life. 7. Rearranging formulae Solve two simultaneous linear equations algebraically. Solve problems leading to the solution of simultaneous linear equations. Solve two simultaneous linear equations graphically Equations and formulae Equations and Formulae Straight line graphs 1. Subject of a formula 2. One type operation 3. Two type operation 4. Forming formulae 1. 1.1. Solving linear equations with one variable (lsn 1) 1.2. Solving linear equations with one variable (lsn 1) 2. 2.1. Linear equations involving fractions (1) 2.2. Linear equations involving fractions (2) 1. Straight line graphs 2. The equation of a line 3. Types of straight lines 4. Vertical lines 5. Horizontal lines 6. Slant lines through the origin 7. Slant lines with intercept 8. The gradient of a line Derive a formula and change the subject of the formula Simplify algebraic expressions by collecting like terms Add/subtract algebraic fractions with numerical denominators Solve linear equations in one unknown that involve two or more operations (to include simple use of brackets) Generate and plot coordinate pairs that satisfy a linear rule. Use straight-line graphs to find the value of one coordinate given the other. Understand, interpret and calculate the gradient of a line from the coordinates of two points on the line. Use straight-line graphs to find the value of one coordinate given the other. Know and understand that parallel lines have equal gradient. Understand the relationship between the equation of a Form 4 Syllabus Page 2 of 7
Pythagoras Theorem and Trigonometric Ratios Area 1. Pythagoras theorem 2. Converse of Pythagoras theorem 3. Pythagorean triples 4. A summary of the three basic ratios. 5. Finding an angle given two sides. 6. Finding a side given one angle and a side 7. Applications of trigonometric ratios 1. 1.1. The triangle (lsn 1) 1.2. The triangle (lsn 2) 2. 2.1. Quadrilateral (lsn 1) 2.2. Quadrilateral (lsn 2) straight line, its gradient and y-intercept. Rearrange linear equations into the form y = mx + c. Plot and interpret graphs of simple linear functions arising from real-life situations. Use Pythagoras theorem to find the side of a right angled triangle given the other two sides Identify Pythagorean triples. Use the converse of Pythagoras theorem. Understand the tangent function Understand the sine and cosine function Use the tangent ratio to find: the opposite side given an angle and its adjacent side, the adjacent side given an angle and its opposite side, the angle given two sides other than the hypotenuse side. Work out the area of a parallelogram & Work out the area and perimeter of composite shapes Derive and use the formula to find the area of the trapezium by dividing it into two s. Use the formula to find the area of a triangle to find the base and height. Volume 1. Finding the volume of solids with uniform crosssection (lsn 1) 2. Finding the volume of solids with uniform crosssection (lsn 2) 3. Finding a missing dimension (lsn 1) 4. Finding a missing dimension (lsn 2) Solve problems of volume of a prism Use V= Ah to find the volume/area and height of a prism Use appropriate units(area & volume) Use the formula V = r 2 h to find the volume, radius or height of a cylinder Form 4 Syllabus Page 3 of 7
Arithmetic in a Circle Percentages Money Ratios 1. Finding the radius from the circumference and area 2. Finding the circumference from the area 3. Finding the area from the circumference 4. Finding the radius and sector angle from the length of arc 5. Finding the radius and sector angle from sector area 1. Percentage increase and decrease 2. Reverse percentage increase and decrease 3. Percentage change 4. Percentage error 1. Simple interest 2. Using simple interest to find rate and time 3. Using the simple interest to find the principal 4. Using compound interest to find the principal, rate and time 5. Appreciation and depreciation 1. Ratios as comparisons 2. Using ratios to divide quantities 3. Finding unknown quantities in ratios Understand the terms arc, sector and segment of a circle. Use the formula C= d and C= 2 r to find the circumference of a circle and A = r 2 Use formula for the circumference and area to find the radius/diameter. Work out the length of an arc and the area of a sector as fractions of a circle. Work out the area of composite flat shapes Solve problems involving percentage increase and decrease Increase/decrease a quantity using a percentage multiplier Calculate the percentage increase/decrease of a quantity Successive percentage changes Carry out calculations involving reverse percentages Solve problems on personal and household finance (ex. VAT) Revise simple interest Use ratio notation in practical situations Recognise the connection between ratios and fractions Reduce ratios to their simplest form Divide a quantity in a given ratio Form 4 Syllabus Page 4 of 7
The quadratic equation Constructions and Loci Statistics Excel 1. Factorising a difference of two squares 2. The quadratic expression 3. Factorisation using the trinomial method 4. Factorising by grouping 5. 5.1. The either/or concept 5.2. A revision of factorization and the meaning of solutions 6. 6.1. Quadratic equations 6.2. Solve quadratic equations 7. 7.1. The quadratic formula 7.2. Forming quadratic equations from the roots 8. Problems leading to quadratic equations 1. Constructions (Handout) 2. Constructing Quadrilaterals 3. Loci 4. Circumscribed circle (lsn 1) 5. Circumscribed circle (lsn 2) 6. Inscribed Circle (lsn 1) 7. Inscribed Circle (lsn 2) 1. Discrete variables 2. Mean, median and mode 3. Representing data 4. Continuous variables 5. 5.1. Grouped data 5.2. Class boundaries Constructions (Handout) - Angles of 60, 45, 90, 30 - Bisecting an angle - Parallel lines - Perpendicular bisector of a line segment - Perpendicular from a point to a line Constructing Quadrilaterals Use ruler and compasses only to construct to locus of points which are: - At a fixed distance from a given point - Equidistant from a straight line Circumscribed Circle Inscribed Circle Construct and interpret information tables Understand, compute and interpret the mean, mode, median and range of a set of discrete/continuous and grouped data only. Draw a histogram (frequency diagram) with equal intervals from an un/grouped frequency table. 1. Spreadsheets Understand and use a spreadsheet to find the sum for a group of cells Understand and use a spreadsheet to find the mean, mode, median and range for ungrouped data Form 4 Syllabus Page 5 of 7
Transformations Volume and surface area 1. 1.1. Translations 1.2. Reflections 2. 2.1. Horizontal and vertical mirror lines 2.2. Slant mirror lines 3. Rotations 4. 4.1. Enlargements 4.2. Enlargements with positive scale factors 5. 5.1. Describing a translation 5.2. Describing a reflection 6. 6.1. Describing a rotation 6.2. Describing an enlargements 1. Surface area of a cylinder (lsn 1) 2. Surface area of a cylinder (lsn 2) 3. Revision lesson 1. 1.1. Arithmetic sequences 1.2. Finding the general term of an arithmetic sequence 2. Using the general term to find a particular term Sequences 3. Using the general term to find the position 4. 4.1. The general term of a quadratic sequence 4.2. Finding the general term of a quadratic sequence 5. Using the general term of quadratic sequences Logo 1. Logo (Handout) 2. Exam Questions on Logo Transform points and shapes using translation, reflection, rotation and enlargements. Translation: Use a given column vector Reflection: Use y = c, x = c, y = x as mirror lines Rotation: Use angles of rotation in multiples of 90 o Enlargements: use positive integers or fractions as scale factor. Recognise that reflections, rotations and translations preserve length and angle so that any figure is congruent to its image under any of these transformations. Recognise that enlargements preserve angles and not length. Derive and use the formulae for the surface area of a cylinder Solve problems involving the volume and surface area of simple compound solid shapes (Handout) Extend patterns and sequences of numbers Generate terms of a sequence using term definitions of the sequences Use expressions to describe the nth term of a simple sequence Recognise geometric and number patterns Draw any regular polygon using logo and the commands PD, RT, FD, LT, BK, Home. Form 4 Syllabus Page 6 of 7
Polygons Circle Geometry Probability 1. 1.1. The sum of interior angles of a convex polygon 1.2. Finding an interior angle of a regular polygon 2. 2.1. Finding an interior angle of an irregular polygon 2.2. The sum of exterior angle of a convex polygon 3. 3.1. Finding an ext angle a convex regular polygon 3.2. Finding an ext angle of convex irregular polygon 4. 4.1. Finding the number of sides of a regular polygon given the exterior angle 4.2. Finding the number of sides of a regular polygon given the interior angle 1. An angle subtended by an arc, chord or segment 2. 2.1. Circle facts 2.2. Angle at centre and angle at circumference 3. 3.1. Angles in same segment 3.2. The cyclic quadrilateral 4. 4.1. Angles in a cyclic quadrilateral 5. 5.1. Exterior angle of a cyclic quadrilateral 5.2. Angles in a semicircle KY Maths 4 Ch 8 Pg 170 Circles and tangents 6. Using tangent properties to find unknown angles 1. Introduction 2. Finding the probability of an event 3. Probability with two events KY Maths 4 Ch 17:Possibility Spaces Understand a proof that the angle sum of a triangle is 180 o Understand a proof that the ext angle of a triangle is equal to the sum of the interior angles at the other two vertices Use the angle properties of equilateral, isosceles and rightangled triangles Understand a proof that the angle sum of a quadrilateral is 360 o Understand and use the properties of the square, rectangle, parallelogram, trapezium, rhombus and kite Classify quadrilaterals using their geometric properties Calculate and use the sums of the interior and ext angles of ir/regular polygons Use a formula, such as (2n 4) right angles or (n 2) 180, for the sum of the interior angles of a polygon with n sides Understand the meaning of terms related to the circle: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment Understand and use the angle properties: - Angle at the centre is twice the angles at the circumference - Angles in the same segment are equal - Angle in a semicircle is a right angle - Angles in opposite segments are supplementary - The exterior of a cyclic quadrilateral is equal to the interior opposite angle Understand the meaning of the term tangent to a circle Angle between the tangent and the radius is right angle. Understand and work out the probability of an event Work out the probability of an event by experiment. Work out the probability of an event from a frequency table. Compile a possibility space. Work out the combined probability outcomes of two independent events. Form 4 Syllabus Page 7 of 7