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Foundation Linear – Revision Guide (by topic)
Number
Add, subtract, multiply and divide any number up to 3 digits by 2 digits (F)
Understand and use number operations including inverse operations and the hierarchy of operations
(BODMAS/BIDMAS) (F)
Understand place value and use this to deal with large positive numbers (F)
Multiply and divide by powers of 10 (D)
Add, subtract, multiply and divide with negative numbers (F)
Know the concepts of multiple, factor, prime, square, cube and square/cube roots (E)
Recall square numbers 1-15 and cube numbers 1-5 and 10. Can find square/cube roots using a calculator (E)
Find the HCF and LCM of 2 numbers by listing factors and multiples (C)
Identify prime factors (C)
Rounding
Round numbers to the nearest 10 and 100 (G)
Round to one significant figure (E)
Round to a specific number of decimal places (F)
Make approximations to calculations by rounding (C)
Fractions
Can simplify fractions by cancelling and finding equivalent fractions (E)
Can convert between improper fractions and mixed numbers (F)
Find a fraction of a quantity (F)
Add, subtract and multiply fractions (E)
Divide a fraction by a fraction (C)
Write a quantity as a fraction of another quantity (D)
Use a calculator to add/subtract/times/divide fractions (D)
FDP
Convert between fractions, decimals and percentages (F)
Order rational numbers (E)
Find reciprocals of numbers or fractions (C)
Percentages
Calculate a percentage of a quantity using non calculator methods (eg find 50%, 25%, 10% etc and use these
to find other percentages) (E)
Calculate a percentage of a quantity using a calculator by converting a percentage to a decimal (E)
Solve percentage increase and decrease problems (D)
Work out one amount as a percentage of another amount (D)
Solve percentage change problems (eg percentage profit and loss) (C)
Polygon & Circle Properties
Name the different quadrilaterals & polygons and understand a regular shape has equal sides and angles (F)
Know the properties of different quadrilaterals and recognise quadrilaterals from their properties (D)
Name and draw different parts of a circle (E)
Basic Algebra
Understand the language of algebra e.g. term, expression, formulae, equation and inequality (F)
Simplify expressions by collecting like terms and by multiplying terms (E)
Expand a bracket and a single term (E)
Substitute into a formula and evaluate (D)
Expand more than one set of brackets and simplify the resulting expressions (C)
Factorise linear expressions by taking out a common factor (D/C)
Use index laws for multiplication and division of integer powers (C)
Collecting Data
Understand the Data Handling cycle (E)
Understand different types of data (eg qualitative, quantitative etc) (E)
Identify possible sources of bias (D)
Design data-collection sheets (tally charts) in order to carry out a survey or an experiment (D)
Extract data from printed tables and lists (D)
Design a questionnaire and criticise questions (C)
Representing Data
To draw diagrams for data including:
Frequency Table (E)
Pictogram (F)
Bar Chart (F)
Line Graph (D)
Stem and Leaf (D)
Pie Chart (E)
To draw conclusions from statistical diagrams mentioned above (G-D)
St Edwards – Department of Mathematics 2012-2013
Revised
Foundation Linear – Revision Guide (by topic)
Measures
Read and interpret scales and map scales (E)
Convert between metric measures (F)
Convert between metric and imperial units (F)
Convert between imperial measures (eg inches to feet) (E)
Make sensible estimates of everyday measures (F)
Choose appropriate units for estimating measures (G)
Angles
Know the sum of angles on a line and at a point (F)
Know the sum of angles in a triangle and a quadrilateral (E)
Find angles in parallel lines (D)
Find interior angles and exterior angles in regular polygons (D)
Use interior angles and exterior angles to find the number of sides in a regular polygon (C)
Name, measure and draw angles (F)
PAV
Calculate the perimeter and area of rectangles (F)
Calculate the areas of triangles, parallelograms, trapeziums and compound shapes (D)
Calculate the circumference and area of a circle (D)
Recall and calculate the surface area and volume of a cuboid (E)
Recall and calculate the surface area and volume of a prism (C)
Recall and calculate the volume of a cylinder (C)
Coordinates and Lines
Plot co-ordinates in all four quadrants (E)
Work out the coordinates of the midpoint of a line (E)
Recognise equations of vertical, horizontal and y=x lines (E)
Find the gradient of a straight line using the step method (C)
Drawing a line with a certain gradient (C)
Statistical Measures
Calculate the mean, median, mode and range from a list of data (F)
Work out mode, modal class, median and range from stem-and-leaf diagrams and other charts/diagrams i.e.
bar charts (E)
Understand the advantages and disadvantages of each type of average and decide which is the best to use (E)
Draw an ordered stem-and-leaf diagram (D)
Find the mode, median and mean from a frequency table (D)
Work out the estimated mean and the modal class from a grouped table (C)
Draw a frequency polygon for discrete and continuous data (C)
Probability
Understand and use the vocabulary of probability and the probability scale (F)
Calculate probabilities of single events (E)
List outcomes for single events and for two successive events and calculate probabilities (sample space
diagrams) (E)
Know that probabilities add up to 1 and calculate the probability of events not happening (D)
Understand relative frequency and realise that the more times an experiment is repeated, the more accurate
the results will be (C)
Predict the expected number of successes from a given number of trials if the probability of one success is
known (C)
Equations & Inequalities
Can solve simple two step linear equations (E)
Can solve equations with brackets with unknown on one side (E)
Can solve equations with unknowns on both sides (D)
Can solve equations with unknowns on both sides that require prior simplification (C)
You can solve two step linear inequalities and list integer solutions and show solutions on a number line (C)
You can set up and solve equations (C)
Can rearrange a formula/change the subject of a formula (C)
Can solve an equation using trial and improvement (C)
Real Graphs
Convert from one unit to another using a graph (E)
Interpret real-life graphs such as distance-time graphs (D)
Understand the relationship between speed, distance and time and work out one given the the other two (D)
Draw a graph without a table of values (C)
St Edwards – Department of Mathematics 2012-2013
Foundation Linear – Revision Guide (by topic)
Sequences
Can continue a sequence (F)
Can express the rule for a sequence in words (E)
Can generate a sequence given a start number and rule (E)
Work out terms in a linear sequence given the nth term rule (D)
Work out an expression in terms of n for the nth term of a linear sequence (C)
2D rep of 3D solid
Identify and name common solids, for example: Cube, Cuboid, Prism, Cylinder, Pyramid, Sphere and Cone (F)
Know the terms Face, Edge and Vertex (vertices) (F)
Draw nets of cuboids and other 3D shapes (E)
Can draw cuboids on an isometric grid (D)
Understand and draw front and side elevations and plans of shapes made from simple solids, for example a
solid made from small cubes (D)
Analyse 3D shapes through 2D projections and cross-sections, including plan and elevation (D)
Transformations
Can draw all the lines of symmetry on a 2-D shape (G)
Can find order of rotational symmetry for a 2-D shape (F)
Can recognise congruent shapes (G)
Can tessellate a 2-D shape (E)
Can reflect a shape in a named straight line (E/D/C)
Can translate a shape by a vector (C)
Can rotate a shape about a point (D/C)
Can enlarge a shape by a whole number scale factor from any point (C)
Fully describe a single transformation (C)
Construction
Can draw and interpret 3 figure bearings and use these to solve problems (D)
Measure and draw lines and angles (F)
Can accurately construct a triangle using compasses, ruler and protractor (D)
Can bisect a line and an angle using compasses and a ruler (C)
Can draw loci of points moving according to a rule (including practical problems) (C)
Ratio
Can simplify a ratio (E)
Divide quantities in a given ratio (C)
Can calculate with ratios when only part of the ratio is known (C)
Recognise and solve problems using direct proportion (unitary method) (D)
Compare prices of products to find the “best buy” (D)
Scatter Graphs
Can plot data on a scatter graph (E)
Recognise different types of correlation (E)
Draw a line of best fit and use it to make predictions (C)
Can interpret a scatter graph (C)
Algebraic Graphs
Can draw a linear graph given a table of values to complete (E)
Can solve a linear equation from it’s graph (D)
Can draw a quadratic graph given a table of values (D)
Can solve a quadratic equation from it’s graph (C)
Pythagoras
Can use Pythagoras’ Theorem to calculate the length of the hypotenuse in a right-angled triangle (C)
Can use Pythagoras’ Theorem to calculate the length of a shorter side in a right-angled triangle (C)
Can use Pythagoras’ Theorem to solve problems (C)
St Edwards – Department of Mathematics 2012-2013