SYDENHAM HIGH SCHOOL Sample Mathematics Entrance Examination Paper – 1 by smoothmaths | Jul 7, 2020 | 0 comments Welcome to your SYDENHAM HIGH SCHOOL Sample Mathematics Entrance Examination Paper - 1 Time allowed: 1 hour Only use a pencil and a rubber Do all your rough working in the space near the question Do not rub it out If you cannot do a question go on to the next one NO CALCULATORS OR RULERS ARE ALLOWED Maximum marks available = 75 1. Work out 4825 + 175465795579655055506680 2. Work out 1741 – 9687731227783873883 3. Work out 418 x 729262826287629762930 4. Work out 2136 ÷ 8267276256250260 5. Work out 5/7 of 1128050706040 6. Write down the next number in the sequence 15, 21, 27, 33, 39 , ———–4544464843 7. Complete these calculations by writing a number in the box.(a) 4.92 × 1000 = –———492049249200492000both a&b 7.(b) ———— ÷ 100 = 0.27927.92792790279002.79 8. Using numerals write the number that is six hundred and thirty less than one thousand.3704701630450380 9. Think of two integers that have a product of 18 and a difference that is the same as one of the two integers that you are thinking of.3&62&43&44&65&8 10. Given that 37 × 56 = 2072, write down the answers to the following calculations:(a) 370 × 5602072002072020720002072200720 10.(b) 38 × 5621282028122822182250 10.(c) 207.2 ÷ 563.7370.370.0373.07 11. A recipe for making 12 cupcakes includes the following ingredients: Sugar 120g Eggs 3 Butter 150g Flour 180g(a) Calculate the quantities needed to make 16 cupcakesAnswer: Sugar ———— g Butter ———— g Eggs ———— g Flour ———— gSugar=160g,Butter=200g,Egg=4,Flour=240gSugar=180g,Butter=200g,Egg=4,Flour=240gSugar=160g,Butter=100g,Egg=4,Flour=240gSugar=160g,Butter=200g,Egg=4,Flour=140gSugar=160g,Butter=200g,Egg=8,Flour=240g 11.(b) If you have plenty of all of the other ingredients but only 7 eggs, how many cupcakes can you make?2825302024 12. Write in the missing digits to make this correct.Answer: ———— And ————1&82&73&64&55&8 13. Sam thinks of a number. If you double the number and add 6 you get the same answer as multiplying it by 3 and subtracting 3.Find the number that Sam was thinking of.9361.45 14. A square and an equilateral triangle are shown in the diagram.Work out the size of the angle marked x.110130160120180 15. Write the missing sign ( = , < or > ) in the box.><=both a&bnone of the above 16. Here are three squares that overlap.The non-overlapping parts of the squares have a total area of 90cm2The areas of overlapping parts are 2cm2 , 3cm2 and 4cm2Work out the area of one of the squares.36\[cm^{2}\]33\[cm^{2}\]30\[cm^{2}\]39\[cm^{2}\]42\[cm^{2}\] 17.This diagram is made up of 7 identical regular hexagons and 12 identicalequilateral triangles.Note: the sides of the triangles are the same length as the sidesof the hexagons.Find the fraction of the diagram that is shaded.\[\frac{2}{9}\]\[\frac{1}{3}\]\[\frac{9}{2}\]\[\frac{1}{4}\]\[\frac{2}{5}\] 18. In Glasgow, the temperature is -7°C and in Exeter the temperature is 12 degrees warmer.What is the temperature in Exeter?51962010 19. What is the difference between 20% of 90 and 90% of 20?05264 20. Jamie left school at 3:55pm and arrived home 55 minutes later.At what time did Jamie get home?4:50pm4:55pm4:45pm4:30pm5:00pm 21. Joey has the six number cards shown belowThe number cards are to be placed next to each other to form different numbers.For example using three of the cards you could make two hundred and fifty one like this:a) What is the largest 4-digit even number that can be made?85428452825484252458 21.b) What is the smallest two-digit prime number that can be made?1312151814 21.c) Using 5 cards, make a multiple of 3.12345453123124521345all of the above 21.d) Make a three-digit number that is a multiple of both 3 and 5.135315345435all of the above 22. Sujatha’s marks in 4 tests were 16, 15, 16 and 10.What was her mean score?14.2512.51.425142.514 23. (a) On the grid, shade in one more square so that the completed shape has one line of symmetry. (b) On the grid below, shade in three more squares so that the completed shape has a rotational symmetry of order 2 24. Tom goes to a theme park. There are 4 activities at the theme park. The table gives information about these activities.Tom wants to do all 4 activities.He arrives at the theme park at 10 20 He needs to leave the theme park by 14 30Plan a schedule for Tom's visit to the theme park so he can do all 4 activities. 25. Here is a parallelogram.(a) Write down the order of rotational symmetry of this parallelogram.23416 Here is a shape. (b) Draw all the lines of symmetry on this shape. 26. Here is a coordinate grid.(a) Write down the coordinates of the point M.(8,1)(1,8)(8,4)(7,1)(8,2) 26.LM is the shortest side of an isosceles triangle.(b) Mark with a cross (×) a point N, so that LNM is an isosceles triangle.(5,7)(5,8)(5,9)(5,10)all of the above 27. Here is a rectangle.All measurements on the diagram are in centimetres.(a) Find the value of x.53768 27.Here is a triangle.(b) Find the size of the angle marked y.3036282540 28. A cuboid hasa volume of 40 cm³a length of 5 cma width of 2 cm(a) Work out the height of the cuboid.4cm3cm6cm5cm2cm 28.(b)A carton measures 200 cm by 100 cm by 100 cm.The carton is to be completely filled with boxes.Each box measures 50 cm by 20cm by 20 cm.Work out the number of boxes which can completely fill the carton.10020802560 29. Here are some patterns made up of dots.(a) In the space below, draw Pattern number 4. (b) Complete the table. 29.(c) How many dots are used in Pattern number 10?461405010080 30. Four strips of paper are stuck on a table as shown. Each one is a rectangle that is 12cm long and 2cm wide.What area of the table is covered?80 \[cm^{2}\]70 \[cm^{2}\]40 \[cm^{2}\]60 \[cm^{2}\]50 \[cm^{2}\] 31. A cuboid has faces with areas of 24cm2, 32cm2 and 48cm2What are the lengths of its edges?4cm,6cm,8cm2cm,6cm,8cm4cm,3cm,8cm4cm,6cm,4cm6cm,6cm,8cm 32. This is the graph of a firework rocket showing its height at different times.(a) Estimate from the graph how many seconds the rocket is more than 25m above the ground.5s4s3s2s7s 32.(b) Estimate from the graph how far the rocket climbs between the times of 1s and 2s.9m8m6m7m5m 33. What is the angle between the hands of a clock at 2:30pm. (Remember that the hour hand moves as well)105120180110108 34. Three friends went to a burger restaurant.Tom had a burger and chips and he paid £8.00Fred had two burgers and a drink. Fred paid £15.00Jo had a burger and a drink. Jo paid £8.50Work out the cost of the burger, the chips and the drink. Time is Up!