Problems on Sets

You will read and shade Venn diagrams for unions, intersections and complements, prove De Morgan's laws, and solve two-set and three-set problems in which some regions are unknown, including problems that need an equation and problems that ask for the largest or smallest possible number.

2

Quadratic Equations

You will recognise quadratic equations and solve them by factorising, by perfect squares and completing the square, by the quadratic formula and with synthetic division; use the discriminant to predict how many roots an equation has; and form and solve quadratic equations from real problems in Rwanda.

3

Number Bases

You will read and write numerals in bases other than ten, convert between base ten, bases 2, 5, 8, 12 and 16 and any other base, add, subtract, multiply and divide in other bases with the carries and borrows shown, and solve equations whose unknown is a digit or the base itself.

4

Algebraic Fractions

You will recognise algebraic fractions and state the values for which they do not exist; simplify, add, subtract, multiply and divide them by factorising; and solve equations and real problems that involve them, rejecting any solution that is an excluded value.

5

Simultaneous Linear Inequalities

You will solve simultaneous and compound inequalities in one unknown and show them on a number line; use a table of signs to solve product and quotient inequalities; graph linear inequalities in two unknowns with boundary lines and shaded regions; and solve simple linear-programming problems.

6

Linear and Quadratic Functions

You will find the gradient and intercepts of a straight line and move between its forms; find the equation of a line from a point and a gradient or from two points; use gradients to recognise parallel and perpendicular lines; and study quadratic functions through tables of values, the vertex, the axis of symmetry and the intercepts, sketching parabolas and solving equations graphically, including where a line meets a parabola.

7

Compound Interest, Reverse Percentage and Compound Proportional Change

You will use multipliers for percentage change, find an original amount by reverse percentages (including prices before VAT), work out compound interest year by year and with the formula A = P(1 + r)ⁿ, and apply compound growth and depreciation, and chains of multipliers, to savings, loans, prices, populations and the value of a moto.

8

Right-Angled Triangles

You will use Pythagoras' theorem and the median, altitude and leg theorems of a right-angled triangle; define the sine, cosine and tangent of an acute angle, find them with a calculator and from exact triangles; solve right-angled triangles; and apply trigonometry to heights and distances with angles of elevation and depression.

9

Circle and Related Theorems

You will name the parts of a circle and find circumference, area, arc length and sector area; use the properties of chords; and prove and apply the circle theorems on the angle at the centre, the angle in a semicircle, angles in the same segment, cyclic quadrilaterals and tangents, including the alternate segment theorem.

10

Collinear Points and Orthogonal Vectors in 2D

You will decide whether two vectors are collinear by using scalar multiples and the determinant, prove that three points lie on one line, decide whether two vectors are orthogonal by using the scalar (dot) product, and use both tests to solve problems on points, lines and shapes in the plane.

11

Enlargement and Similarity in 2D

You will decide when two figures are similar and find unknown lengths with similar triangles and Thales' theorem; enlarge shapes with positive, fractional and negative scale factors, on paper and in the Cartesian plane; locate the centre and scale factor of an enlargement; combine and invert enlargements; and use the scale factor to compare lengths, areas and volumes of similar figures.

12

Inverse and Composite Transformations in 2D

You will review translations, central symmetries, reflections and rotations with their coordinate rules; combine two or more of them and name the single transformation that results; and find and use inverse transformations, drawing every image on a grid with exact coordinates.

13

Interpretation of Statistical Graphs

You will tell ungrouped from grouped data and handle class boundaries, widths and frequency density; read exact values from bar charts, pie charts and line graphs; read histograms, frequency polygons and cumulative frequency curves to find medians, quartiles and percentages; and spot graphs that mislead.

14

Probability with Venn Diagrams

You will treat a sample space as a universal set and an event as a subset; count outcomes in two-set and three-set Venn diagrams; and use the addition rule, complements, mutually exclusive events and independent events to find the probabilities of real-life events.

Units