Mathematics Revision Lists for Years 8, 9 and 10
- Bring all of your equipment on the day of the exam – pen, pencil, ruler, rubber, sharpener, compasses, protractor, scientific calculator – you are not giving yourself the best chance of success if you don’t!
- Answer all the questions – don’t leave any blank spaces!
- If you finish the paper before your time is up – go over the paper again…and again…and again…until you have run out of time! This may seem boring but you will spot mistakes you made the first time around and you will maximise your mark.
- When revising – use your notebook, workbook and textbook (and revision pack if you are in Year 9 or Year 10). The answers for the “Test Yourself” exercises are at the back of the book so you can do these and assess your own work. You can also re-do parts of exercises from the main body of the textbook (this is why we write in corrections!).
GET REVISING AND GOOD LUCK!
YEAR 8
TOPIC 1 NUMBER PATTERNS
You should | I can |
Be able to recognise number patterns and extend them | |
Be able to find multiples of a number | |
Be able to list the factors of a number | |
Be able to find the highest common factor of two numbers | |
Know and be able to find the prime numbers up to 100 | |
Be able to find the prime factors of a number | |
Be able to express a number as a product of primes | |
Be able to use function machines | |
Know and understand square and cube numbers | |
Know and be able to extend the triangular number pattern |
TOPIC 2
ARITHMETIC AND THE CALCULATOR
You should | I can |
Know the times tables up to 12×12 | |
Be able to round numbers to the nearest 10/100/1000etc | |
Be able to use mental Maths to work out answers in my head | |
Be able to estimate the answers to problems and can use this to check calculations | |
Be able to prioritise operations (BODMAS) | |
Be able to write powers using index notation | |
Be able to calculate powers written in index notation | |
Be able to use the bracket x² and memory keys on my calculator | |
Be able to use a calculator to find the answer to a problem |
TOPIC 3
ALGEBRA 1
You should | I can |
Be able to write one and two step formulae that represent real life problems | |
Be able to use these formulae to solve the problem by substituting values into them | |
Know the rules of algebra that are understood in any language | |
Be able to collect like terms to simplify | |
Be able to substitute numbers into formulae | |
Be able to use algebra to solve problems | |
Be able to generate a sequence using words or symbolic form |
TOPIC 4
ANGLES
You should | I can |
Know 1° is a unit used to measure angles | |
Know that the total angle about a point is equal to 360° | |
Know the properties of acute, obtuse and reflex angles and special angles | |
Be able to use a protractor to measure angles up to 360° | |
Be able to use a protractor to draw angles up to 360° |
TOPIC 5
STATISTICS
You should | I can |
Understand the importance of statistics and ways in which they are used in every day life | |
Be able to answer questions using information from a bar chart, pictogram or pie chart | |
Be able to collect information on a tally chart | |
Be able to use tallies to create a frequency table including grouped frequency | |
Be able to display information from these frequency tables, including grouped frequency, on a bar chart | |
Be able to display information on a pictogram | |
Be able to display information on a pie chart when the total frequency is a factor of 360° | |
Be able to plan and conduct a survey by collecting, displaying and interpreting data to find out information |
TOPIC 6
FRACTIONS
You should | I can |
Understand an use key language associated with fractions | |
Recognise the importance of fractions in every day life | |
Be able to write one number as a fraction of another | |
Be able to find a fraction of a quantity | |
Understand that fractions can be larger than 1 | |
Be able to change improper fractions into mixed numbers | |
Be able to change mixed numbers into improper fractions | |
Be able to find equivalent fractions | |
Be able to simplify fractions | |
Be able to add and subtract fractions by finding a common denominator | |
Be able to multiply a number by a fraction | |
Be able to multiply a fraction by a fraction | |
Understand the meaning of unit fraction | |
Be able to put fractions in order | |
Understand the effect of multiplying and dividing by a fraction greater than or less than 1 |
TOPIC 7
ALGEBRA 2
You should | I can |
Be able to perform inverse operations | |
Be able to solve equations using inverse function machines | |
Be able to form equations from words | |
Be able to solve equations with x on one side | |
Be able to solve equations using algebra | |
Be able to change the subject of a formula |
TOPIC 8
DECIMALS(Decimals Percentages and Fractions)
You should | I can |
Know and understand place value for whole numbers | |
I understand decimals and the place values of numbers that appear after the decimal point. | |
Be able to write numbers in words and vice versa. | |
Be able to put decimals in order of size. | |
Be able to add and subtract decimals. | |
Be able to multiply and divide a decimal by a whole number | |
Be able to multiply a decimal by a decimal | |
Be able to solve problems involving decimals. | |
Be able to round decimals. | |
Know that all fractions are either exact or recurring when written as decimals and understand why this is. | |
Be able to write fractions as decimals and percentages | |
Be able to write decimals as fractions and percentages | |
Be able to write percentages as fractions and decimals | |
Be able to order fractions in ascending or descending order | |
Be able to use decimals in context |
TOPIC 9
STATISTICS
You should | I can |
Be able to find the mean of a list of values and understand what it tells me | |
Be able to find the median of a list of values and understand what it tells me | |
Be able to find the mode of a list of values and understand what it tells me | |
Be able to find the range of a list of values and understand what it tells me |
YEAR 9
TOPIC 1
ESTIMATING YOUR MENTAL POWERS
You should | I can |
Understand powers and roots | |
Be able to use your calculator to find the square of a number | |
Be able to use your calculator to find the square root of a number | |
Be able to use your calculator to find a number to any power | |
Be able to use your calculator to find any root of a number | |
Be able to use the rules of mental maths to work out answers in your head | |
Be able to round to a given number of significant figures | |
Be able to estimate solutions to a problem using rounded numbers | |
Be able to estimate the square root of a number | |
Be able to appreciate the importance of showing method when using a calculator. |
TOPIC 2
ALGEBRA
You should | I can |
Be able to find rules for extending simple number patterns | |
Be able to find the formula for the general term of a simple number pattern using algebra. | |
Be able to find two step rules for extending patterns | |
Be able to solve an equation which has an unknown on both sides of the equal sign | |
Remember the rules of BODMAS when substituting values into formulae | |
Know and understand what the nth term of a sequence is. | |
Be able to find the formula for the nth term of a two step number sequence using algebra | |
Be able to use a formula to find a particular term | |
Be able to find the inverse of a formula |
TOPIC 3
POLYGONS
You should | I can |
Know and be able to name polygons with 3, 4 5, 6, 8 and 10 sides. | |
Know that a polygon has the same number of vertices as sides. | |
Understand that a diagonal joins two vertices of a shape an be able to count the number of diagonals in any polygon | |
Know the difference between regular and irregular polygons. | |
Be able to draw and count the lines of symmetry on a regular polygon. | |
Know that a regular polygon has rotational symmetry and be able to work out the order for each polygon. | |
Recognise the difference between convex and concave polygons. | |
Be able to identify particular sides of a shape by using letters. | |
Be able to use a compass to construct triangles and polygons. | |
Understand congruence. | |
Be able to draw tessellations of regular polygons. | |
Know what is meant by “exterior angle” and “interior angle” in the context of polygons | |
Know the interior angles of a triangle add up to 180° | |
Know the interior angles of a quadrilateral add up to 360° | |
Know that the exterior angles of any polygon add up to 360° | |
Know that the sum of the exterior and interior angles is 180° |
TOPIC 4
STATISTICS
You should | I can |
Be able to use a compass to draw a circle of specific radius and diameter | |
Be able to draw a pie chart and use it to analyse data when the total frequency is a factor of 360° | |
Be able to find the mode from a frequency table, pie chart or bar chart | |
Be able to find the median from a frequency table | |
Be able to find the mean from a frequency table | |
Be able to understand how questionnaires and statistical diagrams can mislead | |
Be able to design a questionnaire |
TOPIC 5
NEGATIVE NUMBERS
You should | I can |
Know that the number line extends below zero to negative numbers | |
Be able to put a range of directed numbers in ascending/descending order | |
Be able to use “>” and “<” signs between numbers efficiently | |
Be able to find the difference between two given temperatures | |
Understand that position can be shown by drawing two number lines perpendicular to each other and calling the horizontal line the x axis and the vertical line the y axis | |
Be able to describe positions of points within these quadrants using co-ordinates which describe how far across the horizontal and how far up/down the vertical line the point lies from the origin | |
Be able to draw x and y axes with negative and positive numbers to produce four quadrants | |
Be able to plot points in all four quadrants | |
Be able to read a bank statement | |
Understand how an overdraft works | |
Be able to add and subtract directed numbers | |
Be able to multiply and divide directed numbers | |
Be able to use your calculator to carry out operations involving directed numbers | |
Be able to substitute negative values into a given formula |
TOPIC 6
PERCENTAGES AND FRACTIONS
You should | I can |
Recall what the word percentage means and that the symbol % represents it | |
Be able to use equivalent fractions to convert 21/30 to a percentage | |
Be able to change any fraction (e.g. exam result 57/63) to a percentage | |
Know that to write one quantity as a percentage of another it should first be written as either a fraction or a decimal | |
Be able to find simple discounts of 50%, 25% and 10% | |
Be able to find a percentage of a quantity by finding 1% first | |
Be able to calculate fractions of quantities by a variety of methods | |
Be able to calculate a percentage of a quantity by multiplying the equivalent fraction or decimal by the quantity | |
Know and understand what VAT is | |
Be able to find the VAT on an item with and without a calculator | |
Know and understand simple and compound interest | |
Be able to find the simple interest on a bank account | |
Be able to find the compound interest on a bank account | |
Understand what the term APR means | |
Be able to make an informed choice when choosing a savings account |
TOPIC 7
AREA
You should | I can |
Know the difference between perimeter and area | |
Be able to find the perimeter of a shape | |
Be able to find or estimate the area of a shape by counting squares | |
Be able to find the area of a rectangle | |
Be able to draw or identify the base and corresponding perpendicular height of any triangle | |
Be able to find the area of a triangle | |
Be able to find the area of a parallelogram | |
Be able to find the area of a trapezium | |
Be able to find the area of a kite | |
Be able to find the area of a rhombus | |
Know the formulae required for all of the shapes listed above | |
Be able to find the compound area of any shape | |
Be able to convert metric units of length and area |
TOPIC 8
ANGLES AND BEARINGS
You should | I can |
Be able to calculate missing angles on a straight line or at a point using algebra | |
Be able to calculate missing angles on a triangle using algebra | |
Be able to identify corresponding, alternate and interior angles on parallel lines | |
Be able to use corresponding, alternate and interior angle properties to calculate missing angles | |
Be able to find missing angles on a parallelogram | |
Know and understand the properties of a quadrilateral. | |
Be able to identify parallel lines and know which shapes have these. | |
Know the eight points of a compass | |
Be able to measure or calculate a bearing between two points | |
Be able to write a given scale in ration notation | |
Be able to calculate a distance using a given scale | |
Be able to draw an accurate diagram using bearings and scaled distances |
YEAR 10
TOPIC 1
PYTHAGORAS’ THEOREM
You should | I can |
Be able to identify the hypotenuse on a right angle triangle | |
Know what Pythagoras’ theorem tells you about a right angled triangle | |
Be able to use Pythagoras’ theorem to find the hypotenuse of a right angle triangle | |
Be able to use Pythagoras’ theorem to find a shorter side of a right angle triangle | |
I can use Pythagoras’ Theorem with co-ordinates to find the length of a line |
TOPIC 2
ALGEBRA 1
You should | I can |
Be able to substitute values into a wide variety of formulae | |
Recognise how algebraic formulas can be used in every day life | |
Be able to write a formula for a real life situation | |
Be able to write two step formula for real life situations | |
Be able to find the nth term of a linear sequence (revision) | |
Be able to find the nth term for simple quadratic sequences e.g. n², 2n², n²+1 | |
Be able to solve equations by trial and improvement | |
Be able to solve real life problems using trial and improvement |
TOPIC 3
LINEAR GRAPHS AND SIMULTANEOUS EQUATIONS
You should | I can |
Be able to draw a linear graph from a table of values | |
Be able to relate the term linear to previous knowledge of linear equations and sequences | |
Be able to draw a linear graph by using x values to find corresponding y values to complete a table | |
Be able to draw a linear graph using the cover up method to complete a table | |
Be able to name lines parallel to the x and y axes | |
Be able to draw a line parallel to an axis given its name | |
Know that the equations of linear graphs take the form y=mx + c | |
Know that the value of m effects the gradientKnow that the value of c shows where the line crosses the y axis | |
Recognise that parallel lines have the same gradient (m) as each other | |
Be able to write down the equations of a straight line given the equation of a line parallel to it and the point where it crosses the y axis | |
Show that a point lies on a line by substitution | |
Be able to solve linear simultaneous equations graphically | |
Be able to solve linear simultaneous equations algebraically |
TOPIC 4
STATISTICS
You should | I can |
Be able to draw a scatter graph for two variables | |
Be able to use positive, negative or no correlation to describe the link between the two variables | |
Know when/if it is appropriate it is appropriate to draw a line of best fit | |
Be able to draw a line of best fit | |
Be able to use it to predict results | |
Be able to draw pie charts using the fraction of total method | |
Be able to use percentages with pie charts | |
Be able to recognise misleading diagrams |
TOPIC 5
CIRCLES
You should | I can |
Know and understand the key vocabulary used for circles | |
Be able to locate the “pi” key on my calculator | |
Be able to find the circumference of a circle given the diameter/radius | |
Be able to find the diameter/radius of a circle given the circumference | |
Be able to find the area of a circle given the diameter/radius | |
Be able to find the radius/diameter of a circle given the area | |
Be able to find the area/perimeter of compound shapes which involve circles | |
Know that a cylinder is a prism | |
Be able to find the volume of a cylinder |
TOPIC 6
VOLUME
You should | I can |
Understand what volume is | |
Be able to put containers in order of volume | |
Be able to estimate the volume of containers in cm³, ml, and litres | |
Be able to find the number of containers in a stack | |
Be able to find the volume of simple cuboids by counting blocks | |
Understand what a prism is | |
Be able to find the volume of a prism | |
Be able to convert between metric units of volume | |
Be familiar with the term capacity |
TOPIC 7
NUMBER AND FINANCIAL CAPABILITY
You should | I can |
Be able to increase and decrease quantities by a given percentage | |
Be able to find the original quantity with and without a calculator | |
Know and understand the terms used in bank statements, salaries, bills etc | |
Be able to use my mathematical knowledge to check or complete bank statements and bills (financial capability) |
TOPIC 8
RATES OF CHANGE AND PROPORTION
You should | I can |
Be able to write a ratio in figures | |
Be able to simplify ratios | |
Be able to share a quantity in a given ratio (two or more parts) | |
Be able to use ratio with scales on a map to find distances | |
Be able to write map scales as ratios | |
Understand the term “direct proportion” | |
Be able to change the amounts of quantities which are in a given direct proportion (e.g. for a recipe) | |
Understand the term “inverse proportion” | |
Be able to change the amounts of quantities which are in a given inverse proportion (e.g. no. of men to build a wall and the time taken working at the same rate) | |
Know the relationship between speed, distance and time | |
Know the units for speed | |
Be able to use direct proportion to find distance travelled at a fixed speed as time changes and vice versa | |
Be able to use inverse proportion to find time taken as speed changes over a fixed distance and vice versa | |
Be able to use formulae to find speed, distance or time | |
Know the relationship between mass, density and volume | |
Know the units for density | |
Be able to use direct proportion to find mass as volume changes and vice versa | |
Be able to use formulae to find mass, density and volume |
TOPIC 9
ALGEBRA 2
You should | I can |
Be able to collect terms in order to simplify algebraic expressions | |
Be able to multiply algebraic expressions | |
Be able to square a single term expression | |
Recognise the importance of order of operations when using algebra (BODMAS) | |
Be able to multiply out brackets by a number and a letter | |
Be able to multiply out two brackets and simplify | |
Be able to square a bracket | |
Be able to recognise a quadratic expression | |
Be able to factorise algebraic expressions with a common factor | |
Be able to solve linear equations involving brackets |
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