Decimals. can be written as a terminating. factor. (1 mark) (1 mark) (2 marks) (b) 25. (1 mark) (1 mark) (1 mark)

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1 Nailed it!nailed it!number HadNearly a go there Nearly there Had a look NUMBER Decimals Factors, multiples and primes Write thesemultiples s in order of size. Start withprimes the smallest. Factors and 0.any whole s The factors of_ a 0. 0 are that divide into it exactly. and the itself are both factors of any.,,, and. The factors of that are, can be written as a terminating Show 0 decimal. Factors come in pairs. Each pair is a with _ multiplication = _the = as its answer. The factor pairs are, and. 0 of00 a that is a factor of A common factor Show thatis 0 cannot be written as a two or more s. terminating decimal. is a common factor of and. The multiples of a are all the s in its times 0 table. = A prime has exactly two factors. It can only be divided by and by itself. The first ten prime s are,,,,,,, 9,, 9.. It has only factor. is notwrite a prime 0 as an equivalent fraction with denominator 00. Factor trees ( marks) You can use a factor tree to find prime Write 0 as a product of its prime factors. factors.. Choose a factor pair of the. If the denominator contains a factor. Circle the prime factors as you go other than or then the fraction cannot along. be written as a terminating decimal. ( marks). Continue until every branch ends with a prime. Bymultiple writing the of its prime factors, state whether the following A common is adenominator thatinisterms a multiple. At the end write down all the circled convert to recurring or terminating decimals. of two orfractions more s. s, putting in multiplication signs. is a common multiple of and. The multiples of are,,,,, 0 (b) Here(c) is a list of s. 9 0 From this list write down a prime (d) 90 Write as the product of prime factors. Give your answer in index form. ( marks) 9 90 Write down as recurring decimal. (b) a multiple of (c) two factors of which have a sum of. ( marks) a factor tree to find all the Usedivision. short or long Convert the following fractions into decimals using s. appears twice and prime factor have (b) (c)tor 0 0 tree, so you in the fac is also a prime. of. (c),, and are all factors Only and have a sum of. to write. Check it! The time taken to travel metres by a toy car is seconds. Sandeep says that the speed of the car is. m/s. Is he correct? Give reasons for your answer. distance speed = time Use long or short division. Here is a list of s. Write 0 as the product of its prime ( marks) factors. From the list, write down Give your answer in index form. Use information of=( mark) 0 to find the value of thethe that is athat multiple ( marks) (b) the0 that is a factor of ( mark) (b) 0.. (c) 0. (c) the that is a multiple of and a can recognise all you e sur ke Ma factor of the prime s below 0. (d) two prime s. ( marks)

2 PROBABILITY & STATISTICS Interquartile range Roseanna recorded the masses, in kg, of people. Here are her results Work out the range. Range = highest value lowest value = = (b) Work out the interquartile range. ( n + ) = ( + ) = So Q = th value = ( n + ) = ( + ) = So Q = th value = Interquartile range = Q Q = = ( marks) The stem-and-leaf diagram shows information about the ages, in years, of some people at a shop. Work out the range. (b) Work out the interquartile range years 0 9 means years Sophie collected some information about the heights, in cm, of some shrubs. years ( marks) 9 How many shrubs did Sophie measure? means cm (b) Work out the range. cm (c) Work out the median. cm (d) Work out the interquartile range cm ( marks)

3 ALGEBRA Linear equations Solve x + 0 = (b) _ x + 0 = ( ) _ (x + 0) = x + 0 = ( 0) x = x = ( ) _ x + = (c) = x _ x = ( marks) x = ( marks) x = ( marks) Solve _ x = x Place brackets (b) around x. x = x ( ) ( x) = ( x ) x = ( x ) x = x x x = Multiply out the brackets. Collect all the x terms on one side. x _ = x + x = ( marks) x = ( marks) Solve x x = (b) _ x _ ( + x) = _ (x ) _ ( x) = x + x = ( ) x = x = x = x = ( marks) x = ( marks) ABC is a triangle. Angle A is (x ) and angle B is (x + ). A The size of angle A is three times the size of angle B. Work out the value of x. (x ) (x ) B C Remember to set up an equation. x = ( marks) 0

4 NUMBER Problem-solving practice One sodium atom has a mass of. 0 grams. Work out an estimate for the of sodium atoms in kg of sodium. (b) Is your answer to part an underestimate or an overestimate? Give a reason for your answer. ( marks) d t = _ f d = 9. correct to significant figures f =. correct to significant figures By considering bounds, work out the value of t to a suitable degree of accuracy. Give a reason for your answer. ( marks) A large rectangular piece of card is ( + ) cm long and ( +) cm wide. A small rectangle cm long and cm wide is cut out of the piece of card. ( ) cm ( ) cm cm cm Work out the shaded area, in cm. Give your answer in the form a + b where a and b are integers. cm ( marks)

5 GEOMETRY & MEASURES Trigonometry Work out the length, in cm, of each of the marked sides. Give each answer correct to significant figures. SOH CAH TOA Start by labelling the sides of the triangle. Then write down the trig ratio that uses the given and unknown side. tan opp hyp x 0 cm adj = opp adj = x (b) y. cm sin = opp hyp = y. (c).9 cm z x = tan 0 y = x = cm ( marks) y = cm ( marks) ( marks) A ladder is m long. The ladder rests against a vertical wall with the foot of the ladder resting on horizontal ground. The ladder makes an angle of with the ground when it is leaning against the wall. How far does the ladder reach up the wall? Draw a diagram. A tower 0 m high stands at a point A. At a point B on the ground which is level with the foot of the tower, the angle of elevation of the top of the tower is. Work out the distance of B from A. m ( marks) m ( marks) The diagram shows a vertical pole standing on horizontal ground. The points A, B and C are in a straight line on the ground. The point D is at the top of the pole so that DC is vertical. The angle of elevation of D from A is. Work out the height of the pole. Give your answer correct to significant figures. D C m B 0 m A (b) Work out the size of the angle of elevation of D from B. Give your answer correct to significant figures. m ( marks) ( marks)