line graphs Primes time. This time series graph shows median incomes in the UK from 1980 to The factors of a number are any whole numbers

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1 PROBABILITY NUMBER Factors, multiples and primes Line graphs Median income ( s) A time series graph is a line graph that shows how a variable changes over a period Factors and multiples Primes time. This time series graph shows median incomes in the UK from 9 to. factors a number are any whole numbers A prime number has exactly two factors. It graph should have a title. graph shows upward UK median that divide into it exactly. canincomes only be divided by and byanitself. trend. This means that in general, and the number itself are both factors first ten prime numbers are any as time passes, the median number.,,, 7,,, 7, 9,, 9. vertical axis shows the income increases. factors are,,,, and. variable which changes over time. Factors come in pairs. Each pair is a multiplication with the number as its answer. factor pairs are, and. is not a prime number. It has only factor. Factor trees You can use a factor tree to find prime A common factor is a number that is a factor horizontal axis always shows 9 99factors. two or more numbers. units time.. Choose a factor pair the number. is a common factor and.. Circle the prime factors as you go multiples a number are all the numbers in along. Vertical line graphs its times table.. Continue until every branch ends with multiples 7 are 7,,,,, A vertical line graph is sometimes a prime number. Acalled common multiplegraph. is a number thatinis a multiple This vertical line graph shows the number pairs It works a bar-line. At the end write down all the circled the twosame or more trainers owned by the in members a class. way numbers. as a bar chart but numbers, putting multiplication signs. is a common multiple and. the bars are straight, vertical lines.! Here is a list numbers. the 7 mean from this This is like finding From this list write down frequency table: (a) a prime number Number pairs 7 trainers (b) a multiple 7 Work out the total number pairs trainers (c) then two factors the which have a sum owned, divide by total number. ( marks) members the class. how to find the mean from a You canand revise frequency table on page. ber. (a) is also a prime num s. are all factor You will need use problem-solving skills toand,, (c) throughout your exam be prepared! e a sum. hav and Only 7 Write 9 as the product prime factors. Give your in index form. ( marks) answer Number pairs 9 9 trainers You can revise bar charts on page 7. What was the mean number pairs trainers owned? ( marks) Total number pairs trainers owned = Use a factor tree to find all the Total number members class appears twice e factors. prim inthe + + e, =so you have tor tre fac+ =. to write. mean is. ck it! trainers. Chepairs 9 9 Here a list numbers. Write as the product its prime tableison the right gives factors. information about the percentage Percentage (%) Give youranswer in index form. 7 From the list, write down students who passed a pressional (a) each the number that is a to multiple ( marks) exam year from 7. 7 (b) the number that is a factor ( mark) in eak (a) Draw a time series graph to You can use a br (c) the number that is a multiple and a can. you axis e represent this data. ( marks) l sur tica recognise all ke ver Ma your factor ( mark) (b) Describe the trend. the prime numbers below. (d) two prime numbers. ( marks)

2 PROBABILITY Line graphs A time series graph is a line graph that shows how a variable changes over a period time. This time series graph shows median incomes in the UK from 9 to. graph should have a title. graph shows an upward trend. This means that in general, as time passes, the median income increases. vertical axis shows the variable which changes over time. Median income ( s) UK median incomes 9 99 horizontal axis always shows units time. Vertical line graphs A vertical line graph is sometimes called a bar-line graph. It works in the same way as a bar chart but the bars are straight, vertical lines. This vertical line graph shows the number pairs trainers owned by the members a class. You can revise bar charts on page 7.! This is like finding the mean from this frequency table: Number pairs trainers 7 Work out the total number pairs trainers owned, then divide by the total number members the class. You can revise how to find the mean from a frequency table on page. You will need to use problem-solving skills throughout your exam be prepared! table on the right gives information about the percentage students who passed a pressional exam each year from 7 to. (a) Draw a time series graph to represent this data. ( marks) (b) Describe the trend. 7 Number pairs trainers What was the mean number pairs trainers owned? ( marks) Total number pairs trainers owned = Total number members class = =. mean is. pairs trainers. 7 9 Percentage (%) 7 You can use a break in your vertical axis.

3 PROBABILITY Problem-solving practice About half the questions in your Foundation GCSE exam will require you to problem-solve, reason, interpret or communicate mathematically. If you come across a tricky or unfamiliar question in your exam you can try some these strategies. Sketch a diagram to see what is going on. Try the problem with smaller or easier numbers. Plan your strategy before you start. Write down any formulae you might be able to use. Use x or n to represent an unknown value. AO AO table shows information about the numbers 7 pupils absent from Keith s school last week. Boys Girls Monday Tuesday 9 Wednesday Thursday Friday Keith wants to compare the data. Draw a suitable diagram or chart. ( marks) Bar charts page 7 Line graphs page In this question you have to choose what type diagram or chart to use. It is best to use a bar chart or a line graph. Label both axes correctly. Draw a key for boys and girls, or make sure it is clear which bars (or lines) are for boys and which are for girls. Abi has five cards. Each card has a number written on it. 7 9? mean the five numbers is. One the numbers is hidden. Work out the hidden number. ( marks) Averages and range page You could try some different values for the hidden number and work out the mean each time. But you can save time by using the rule in the Top tip. re are five numbers and the mean is, so the sum the numbers must be. mean number sum data values data values

4 ALGEBRA Quadratic equations You need to be able to solve a quadratic equation without a calculator by factorising one side. If you need to solve a quadratic equation in your Foundation exam it will look something like this: left-hand side will be a quadratic expression x + x + = right-hand side will be zero Follow the steps below to solve the equation. Factorise the left-hand side the equation: (x + )(x + ) = Set each factor equal to zero: (x + )(x + ) = (x + ) = (x + ) = For a reminder about factorising quadratic expressions look at page. (x 9)(x ) x9 x 9 x x ( marks) Solve x (x + )(x ) = x + = x = Write both solutions in the form x = ( marks) Solve x x 9 Solve the two linear equations to find the two solutions: x + = x+= x = x = x = x = : You can also use inverse operations (+ ) x = ( ) x = x = or x = re are two answers because ( ) = = nd side. Start by factorising the left-ha anding the equation. You can check by exp the brackets: (x + 9)(x ) = x x + 9x 9 = x + x 9. Set each factor equal to zero. two. Solve the linear equations to get solutions. Check it! () () (9) (9) 9 Two to watch When one solution is x = Difference two squares. x x = x(x ) = Solutions are x = and x = x = (x )(x + ) = Solutions are x = and x = For parts (a) and (c) look at the blue box above. (a) Factorise x x ( marks) (b) Write down the two solutions x x Solve (a) x x (b) x x (c) x ( marks) ( marks) ( marks) Both solutions are negative. 7

5 GEOMETRY & MEASURES Symmetry Lines symmetry A line symmetry is a mirror line. One half the shape is a mirror image the other. No lines symmetry line symmetry Using tracing paper You are allowed to ask for tracing paper in your exam. You can use it to check for lines symmetry. If you fold a tracing a shape in half along a line symmetry, the two halves will match up exactly. lines symmetry lines symmetry If a shape fits over itself when it is rotated then it has rotational symmetry. order rotational symmetry tells you how many times it fits over itself in one full turn. No rotational symmetry order Using tracing paper You can use tracing paper to check for rotational symmetry. order order Trace the shape. Rotate the tracing paper and see how many times the shape fits over itself. This shape fits over itself twice: once at and once at. It has rotational symmetry order. (a) Fill in squares the grid below to make a shape with exactly lines symmetry. Worked solution video (b) Fill in squares the grid below to make a shape with rotational symmetry order. 7