MERCHANT TAYLORS’ SCHOOL 11 PLUS MATHS SPECIMAN PAPER – 2 by smoothmaths | Jul 1, 2020 | 0 comments Welcome to your MERCHANT TAYLORS’ SCHOOL 11 PLUS MATHS SPECIMAN PAPER - 2 Time Allowed: 60 minutesInstructions:Answer as many questions as possible. Some of themare easy at the start and become more difficult. Youshould show all your working on this question paper. 1. (a) Draw all of the lines of symmetry on the following shape. (b) How many lines of symmetry has the shape below?52314 (c) Draw a shape with exactly four lines of symmetry in the space below. 2. (a) Write in digits the number seventy three thousand and forty six.7304673406736047364073456 2.(b) Write the answer to the sum of two hundred and six plus two thousand threehundred and twenty in words.Two thousand Five Hundered andTwenty Sixtwo hundred twenty sixTwo thousand one Hundered andTwenty Sixtwo thousand two hundred and fifty sixNone of the Above 3.From the numbers in the box above write down:(a) A multiple of 7:2824153614 3.(b) A square number:3624152818 3.(c) The product of two of the other numbers in the box:45532545 4. (a) Calculate the angles marked x and y in the diagram below:Answer: x = %BLANK% , y = %BLANK%x = 47, y = 123x = 47, y = 143x = 57, y = 153x = 60 , y = 237x = 45, y = 120 (b) Calculate the angles marked p, q, r, s and t in the diagram below:p = \[132^{o}\], q = \[66^{o}\], r = \[66^{o}\], s = \[114^{o}\], t = \[66^{o}\], u = \[114^{o}\]p = \[142^{o}\], q = \[60^{o}\], r = \[60^{o}\], s = \[114^{o}\], t = \[60^{o}\], u = \[100^{o}\]p = \[120^{o}\], q = \[76^{o}\], r = \[56^{o}\], s = \[90^{o}\], t = \[96^{o}\], u = \[114^{o}\]p = \[129^{o}\], q = \[60^{o}\], r = \[60^{o}\], s = \[124^{o}\], t = \[60^{o}\], u = \[124^{o}\]None of the Above 5. (a) Sean scored 27 out of 45 in a test. Write this as a percentage.60%50%40%30%20% 5.(b) In a class of 30 pupils, 21 are girls. What percentage of the class is boys?30%50%60%40%20% 5.(c) Write 0.8 as a fraction in its simplest form.\[\frac{4}{5}\]\[\frac{3}{8}\]\[\frac{8}{5}\]\[\frac{2}{5}\]\[\frac{9}{5}\] 5.(d) Write 85% as a fraction in its lowest terms.\[\frac{17}{20}\]\[\frac{20}{17}\]\[\frac{3}{5}\]\[\frac{3}{14}\]\[\frac{4}{15}\] 5.(e) Rearrange the following in order of size, smallest to largest.\[\frac{9}{25}\] .0.371 , 38% , \[\frac{2}{5}\]\[\frac{2}{5}\] . 38% , 0.371 \[\frac{2}{5}\]0.371 , \[\frac{9}{25}\] . 38% , \[\frac{2}{15}\]38% ,\[\frac{9}{25}\] .0.371 , \[\frac{2}{5}\]None of the above 6. Sarah sat by the river Thames and recorded the number of cyclists that passed byevery minute. She plotted a bar chart of her results.(a) What was the largest number of cyclists to pass in one minute?54361 6.(b) What was the most frequent number of cyclists per minute?13265 6.(c) For how many minutes, in total, was Sarah recording cyclists?2015121025 Sarah now continues to count the number of cyclists for the next 3 minutes. Thenumber of cyclists were: 1, 4, 1.(d) Add this data to the bar chart above. 7. A gardener measures the night time temperatures over two evenings and records theresults in the table shown below:(a) At what time and on which day was the lowest temperature recorded?Tuesday 3:00 a.mTuesday 4:00 a.mTuesday 5:00 a.mTuesday 3:00 a.mTuesday 6:00 a.m 7.(b) What was the difference between the lowest and highest temperature onTuesday?74365 7.(c) He realises his thermometer is recording incorrectly and that each temperatureshould be 5℃ lower than was recorded. What is the correct temperature at1am on Monday?-4-3243 7.(d) On Wednesday the forecast is for all temperatures to drop by 3º C from whatthey were on Tuesday. Bearing in mind his thermometer is broken, what willthe actual temperature be on Wednesday at 2am?-989-7-6 8. Solve the following equations:(a) 3x = 36Answer: x =128181014 8.(b) c + 7 = −15Answer: c =-222223-2428 8.(c) 4p − 2 = 14Answer: p =412786 9. On the grid below draw the reflection of the shape shown in the mirror line AB: 10. Write the next two terms in each of the following sequences:(a) 5, 11, 17, 2329,3528, 3427, 3330, 3623,25 10.(b) 10, 7, 4, 1-2 , -5-1, -3-1, -40, -30, -5 10.(c) 2, 8, 32, 128512, 2048256, 512384, 1152640, 3200680, 4200 11. The perimeter of a rectangle is 22cm. One of the sides has length 8cm. Calculate thelengths of the other three sides.3, 8, 38, 18, 87, 12, 76, 11, 65 , 9 , 5 12. Estimate the following by first rounding each number to the nearest whole number:(a) 9.47 × 34.5315327318415427 12.(b) 3.752 − 11.63 × 2.87-20720624 13. (a) Explain why 91 is not a prime number.not a prime numberIt is a prime numberOdd NumberNeither prime nor Odd numberEven number 13.(b) What is the 7th prime number?1721132923 14. The contents of part of a wardrobe are shown in the pie chart below:What fraction, in its simplest form, of Footwear are boots?\[\frac{1}{8}\]\[\frac{2}{8}\]\[\frac{3}{8}\]\[\frac{5}{18}\]\[\frac{5}{8}\] 15. (a) Find the highest common factor (HCF) of 66 and 30.65321 15.(b) Find the lowest common multiple (LCM) of 12 and 8.24128634 16. Fazal has £2.60 and Gareth has £5.30. Gareth gives Fazal some 5p coins. Each boynow has the same amount of money. How many 5p coins did Gareth give Fazal?2750302979 17. Circle the most appropriate unit of measure for the following:(i) The length of an airplanemeterskilometrescentimetresmillimetersmilliliters 17.(ii) The weight of a catPoundstonsOuncesstoneskilometers 17.(iii) The capacity of a bathgallonspintsfluid ouncesmillilitresmillimeters 18. A box of celebrations contains one Twix, one Snickers, one Milky Way, and tenBounty chocolates. Jane chooses a chocolate at random. Put a ring around the correctanswer in the list to show the probability that the chocolate will be:(a) A Bountylikelyunlikelyeven chanceimpossiblecertain 18.(b) A Twixunlikelyimpossibleeven chancelikelycertain 18.(c) A Galaxyimpossibleunlikelyeven chancelikelycertain 19. (a) Which is the greater? 3 × 2³ or 2 × 3²3 x \[2^{3}\]2 x \[3^{2}\]3 x \[2^{2}\]both are same2 x \[2^{3}\] 19.(b) By how much?65832 19.(c) Write down two cube numbers which are also square numbers.64, 7298, 49, 2716, 25161, 2564 20.Calculate the value of x.816182436 21. There are x horses, y cows and one three legged dog in a field.(a) Write down an expression in algebra for the total number of legs in the field.4x + 4y = 34x + 4y - 3z4x + 4y +34x - 4y - 34x - 4y = - 3 21) Half of the cows and one quarter of the horses leave the field.(b) Write down an expression in algebra for the number of heads that remain in thefield.\[\frac{3x}{4}\] + \[\frac{y}{2}\] + 1\[\frac{x}{4}\] + \[\frac{3y}{2}\] + 1\[\frac{3x}{2}\] + \[\frac{y}{4}\] + 1\[\frac{x}{4}\] + \[\frac{3y}{2}\] - 1\[\frac{3x}{8}\] + \[\frac{y}{5}\] + 1 22. An alloy contains iron and tungsten in the ratio 5 parts to 1 part.(a) If the mass of the alloy is 72kg, how much iron and tungsten does it contain?Answer: Iron: %BLANK% kg, Tungsten: %BLANK% kgIron =60kg, & Tungsten = 12kgIron =50kg, & Tungsten = 10kgIron =55 kg, & Tungsten = 14kgIron =64kg, & Tungsten = 8kgIron =48kg, & Tungsten = 18kg 22.(b) If there is 15kg of iron in a quantity of the alloy, how much tungsten is there?35214 23. A large cube is made by gluing together smaller white and grey cubes of volume 1cm³as shown. If five grey cubes are removed from each face of the larger cube, what isthe total volume remaining?Diagram not drawn to scale95\[cm^{3}\]89\[cm^{3}\]100\[cm^{3}\]79\[cm^{3}\]69\[cm^{3}\] 24. If a basketball weighs 300g plus half its own weight, how much does it weigh?600 g300 g400 g150 g500 g 25. 25 students have taken an exam and the mean number of marks is recorded as 83.The examiner subsequently awards 5 additional marks to 9 of the students and takesaway 2 marks from 10 other students.What will the new mean mark be?8480759470 26. The centre of a square is at the point (1 , 2) and one of the vertices (corners) of thesquare is at the point (4 , 7).(a) Plot the centre of the square and one of the vertices on the grid below.(6, -1), (-2, -3), (-4, 5)(6, 1), (2, -3), (4, -5)(4, 7), (6, 1), (4, 5)(4, -1), (-2, 4), (-6, 5)(4, 2), (-2, 4), (-6, 8) 26.(b) Plot the other three vertices of the square on the grid above, and write downthe co-ordinates of the three points you have just plotted.(6, -1), (-2, -3), (-4, 5)(6, 1), (2, -3), (4, -5)(4, 7), (6, 1), (4, 5)(4, -1), (-2, 4), (-6, 5)(4, -2), (-2, 5), (-6, 8) 27. The number of leaf cutter ants doubles every day for the first week.(a) If there were 10 at the end of the first day how many are there at the end of thesecond day?2018162430 27.(b) How many were there at the end of the week?640720940856664 28. Find in terms of x the perimeter of the following triangle:4x + 34x + 64x + 84x - 34x - 5 29. (a) An egg box holds 6 eggs. How many boxes are needed for 100 eggs?1728181025 29.(b) A toy train travels 6 metres in two seconds. How far will it travel in oneminute?180240360456756 30. One of the angles of an isosceles triangle is 96° . Find the sizes of the other twoangles.\[42^{o}\] , \[42^{o}\]\[42^{o}\] , \[56^{o}\]\[46^{o}\] , \[60^{o}\]\[30^{o}\] , \[48^{o}\]\[50^{o}\] ,\[42^{o}\] 31. Mrs Jones is 24 years older than her daughter. The sum of their ages is 70 years. Howold is Mrs Jones?4752435665 32. A metal rod is metres long. How many short rods ³/10 metres long can be cut from the longer rod?Show full working.3648564632 33. Two different clocks show the time 3 o’clock. The first gains 5 minutes per hour andthe second gains 20 minutes per hour. How long will it be in hours before both clockslook as though they show the same time?4836402844 34. A “double–decker” sandwich has three slices of bread and two layers of filling. (e.g.bread/filling/bread/filling/bread). Each slice of bread has to be buttered on each sidethat is in contact with the filling. I make as many of these sandwiches as possible froma sliced loaf which has 22 usable slices, excluding crusts which are not used. Howmany sides of bread do I have to butter?2818162414 35. The two-digit by two-digit multiplication below has lots of gaps, but most of them canbe filled by logic (not by guesswork). Which digit must go in the position of the * ? Time is Up!