Practice exercises

square and cube roots, roots of fractions, estimating roots, multiplying and dividing roots, taking a factor out of a root.

writing a situation as an expression, sums of consecutive numbers, perimeter as an expression, evaluating expressions, word problems about ages and price changes.

collecting like terms, adding and subtracting algebraic sums, multiplying a sum by a monomial, multiplying two binomials.

what percentage, percentage of a number, finding the whole, increases and discounts, percentage change, the price before a discount, two price changes in a row.

whether a number is a solution, solving linear equations, equations with brackets and fractions, rearranging formulas, word problems leading to equations.

proportions, directly proportional quantities, dividing in a given ratio, map and plan scale.

angles and parallel lines, angles in a parallelogram, angles in an isosceles triangle, the triangle inequality, angle sums in polygons, angles of regular polygons, triangle congruence, choosing the justification in a proof.

Pythagorean theorem, diagonal of a square and height of an equilateral triangle, areas of polygons, a length from the area, calculations in rhombi and trapezia, converting units of area.

sets of numbers on the number line, coordinates of points, quadrants of the coordinate plane, length of a segment, midpoint of a segment.

regular prisms and pyramids (edges), prisms and pyramids: surface area and volume, slant height of a pyramid, space diagonal of a cuboid, units of volume.

counting objects by listing them, simple random experiments (a die, a polyhedral die, drawing a ball), probability of an event.

bar charts, reading data from lists, what percentage of the whole and the whole from a percentage, pie charts (sector angle, reading), graphs, arithmetic mean.

circumference and area of a circle, expressions with π, radius from the circumference, radius and diameter from the area, part of a circle and disc (half, a quarter, three quarters), wheel turns.

reflecting a point in a line or in a point, axes of symmetry of figures, recognising symmetric points, perpendicular bisectors and angle bisectors, figures with point symmetry.

multiplying algebraic sums, special products, adding, subtracting and multiplying polynomials, factorising, domain, simplifying, multiplying and dividing rational expressions.

linear equations (including contradictions and identities), linear inequalities, quadratic equations and inequalities, factored polynomial equations, simple rational equations, word problems leading to equations.

systems of two linear equations (substitution and elimination), independent, dependent and inconsistent systems, word problems.

values and arguments of functions, reading from a graph, properties of functions read from a graph, piecewise functions, linear functions, quadratic functions in general, vertex and factored form, finding the formula of a quadratic, least and greatest values of a quadratic, inverse proportionality, shifting graphs, exponential and logarithmic functions, also in applications.

terms from explicit and recursive formulas, monotonicity of sequences, arithmetic and geometric sequences, sums of initial terms.

sine, cosine and tangent of acute and obtuse angles, values for 30°, 45° and 60°, the Pythagorean identity and tangent as sine over cosine, the law of cosines, area of a triangle from the sine of an angle, type of a triangle from its sides.

angles of an isosceles triangle, the Pythagorean theorem, similar triangles and the ratio of areas of similar figures, the intercept theorem, inscribed and central angles, tangents to a circle, the circumcircle of a right triangle, angles in quadrilaterals, regular polygons, areas of quadrilaterals, area and circumference of a circle, sectors, justifying steps of reasoning.

midpoint and distance between points, whether a point lies on a line, intersection and relative position of two lines, a parallel line through a point, equation of a circle, a circle and the axes, reflecting points and circles in the axes and the origin.

relative position of lines in a cube, diagonal of a cuboid and its angle with the base, volume of prisms and pyramids, surface area and volume of regular prisms and pyramids, angles in pyramids, surface area and volume of cylinders, cones and spheres, angles in cones and cylinders, similar solids.

the multiplication rule, arranging in order, codes, numbers whose digits meet conditions, the multiplication and addition rules together.

classical probability (balls, two dice, drawing several items, drawing twice with and without replacement), complementary events, arithmetic and weighted mean, median, mode.

optimisation problems described by a quadratic function: the largest product, the largest area, the largest revenue, the least sum of squares.