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Activities for pupils

Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

• Plotting Graphs Complete a table of values then plot the corresponding points to create a graph.
• Factorising Video A reminder of how to factorise an algebraic expression. This video is to help you do the online, self-marking exercise.
• New Way to Solve Quadratics A computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations.
• Quadratic Equations Video Learn the common methods of solving quadratic equations by factorising and by using the quadratic formula.
• Quadratic Formula Song A song from Math Upgrade dot com.
• Quadratic Equations Solve these quadratic equations algebraically in this seven-level, self-marking online exercise.
• Completing the Square Practise this technique for solving quadratic equations and analysing graphs.
• Graph Equation Pairs Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.
• Graph Patterns Find the equations which will produce the given patterns of graphs.
• Graph Match Match the equations with the images of the corresponding graphs. A drag-and-drop activity.
• Name that Graph Choose from the given functions the one that best describes the shape of the graph.
• Graph Plotter An online tool to draw, display and investigate graphs of many different kinds.
• Problems Leading To Quadratics Situations from 1885 which can be described using algebra and explained by solving quadratic equations

Here are some exam-style questions on this topic:

• "The diagram below is a sketch of \(y = f(x)\) where \(f(x)\) is a quadratic function." ... more
• "Write down the coordinates of the turning point on the graph of \(y = 9 - (x - 5)^2\)" ... more
• "The volume of the larger red cube is 386cm³ greater than the volume of the smaller blue cube." ... more
• "(a) Write \(x^2 - 6x + 5\) in the form \((x-a)^2 + b\)." ... more
• "The graph of the curve A with equation \(y=f(x)\) is transformed to give the graph of the curve B with equation \(y=5-f(x)\)." ... more
• "The graph of y = f(x) is drawn accurately on the grid." ... more
• "(a) Show that the equation \(\frac{3}{x+1}+\frac{3x-9}{2}=1\) can be simplified to \(3x^2-8x-5=0\)." ... more
• "(a) By completing the square, solve \(x^2+8x+13=0\) giving your answer to three significant figures." ... more
• "In this question all measurements are in centimetres." ... more
• "A red rug has a width of \(x-3\) cm and a length of \(4x\) cm." ... more
• "The graph of the following equation is drawn and then reflected in the x-axis" ... more
• "The diagram below is a sketch of a curve, a parabola, which is not drawn to scale." ... more
• "In the diagram below, which is not drawn to scale, all dimensions are in centimetres and all angles are multiples of 90^o. If the shaded area is 698cm², work out the value of \(x\)." ... more
• "Given that:" ... more
• "The area of triangle ABC (not drawn to scale) is " ... more
• "(a) Find the interval for which \(x^2 - 9x + 18 \le 0\)" ... more
• "(a) Write \(2x^2+8x+27\) in the form \(a(x+b)^2+c\) where \(a\), \(b\), and \(c\) are integers, by 'completing the square'" ... more
• "Consider the function \(f(x)=\frac{1}{2}\left(2x-3\right)\left(x+5\right)\) for \(x \in \mathbb R\). The following diagram shows part of the graph of \(f\)." ... more
• "A function is defined as \(f(x) = 2{(x - 3)^2} - 5\) ." ... more
• "\(f\) and \(g\) are two functions such that \(g(x)=3f(x+2)+7\)." ... more
• "Let \(f(x)=5x^2-20x+k\). The equation \(f(x)=0\) has two equal roots." ... more
• "The functions \( f \) and \( g \) are defined for \( x \in \mathbb{R} \) by \( f(x) = 3 + 5x - 2x^2 \) and \( g(x) = x + k \), where \( k \in \mathbb{R} \)." ... more
• "The graphs of the functions \(f(x)\), a parabola, and \(g(x)\), a straight line, meet at exactly one point." ... more

See all these questions

Here is an Advanced Starter on this statement:

• Venn Graphs
  Type the equation of a graph into each section of the Venn diagram. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

• Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
• Functions A relationship between two sets can be called a mapping. Elements of the first set (domain) are mapped to elements of the second set (range). A function is a special type of mapping for which one value in the domain maps to one, and only one value in the range.Pupils in Primary school will use the concept of function machines to perform calculations. They will then learn to ‘work backwards’ to find the inverse function. The study of functions becomes more formal as pupils become more proficient and able to cope with more complex mathematical ideas.
• Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.