N. E. Lincolnshire Mathematics Team1

2 Sample semi-final question Look at the continuous sequence of squares below Answer sequence What colour will the fifty-third square be? Answer - red 53 rd square

N. E. Lincolnshire Mathematics Team3 Sample semi-final question Answer sequence The sum of two numbers is 15 Their difference is three. What is their product? = 15 is their sum or total = 3 is their difference 9 x 6 = 54 is their product (multiplied together)

N. E. Lincolnshire Mathematics Team4 Sample semi-final question Answer sequence Jack draws the shape below How many rectangles can be found in the drawing?

N. E. Lincolnshire Mathematics Team5 Sample semi-final question Answer sequence In a box of dominoes there are seven ‘double’ tiles What is the total number of spots on the seven doubles tiles altogether? 42

N. E. Lincolnshire Mathematics Team6 Sample semi-final question Answer sequence The perimeter of this rectangle (oblong) is 48 cm. The rectangle is three times as long as it is wide How long and how wide is the rectangle? 18 cm long 6 cm wide The width and length shown in blue are 24 cm long altogether The width is a quarter of 24 cm and the length three-quarters of 24 cm

N. E. Lincolnshire Mathematics Team7 Sample semi-final question Answer sequence Shirt £12.99Sports shoes £16.49Cap £9.50 Tom buys a cap, Amy buys shoes and Jack buys a shirt. Each child pays with a £20 note. How much change does each child receive? Jack £7.01Amy £3.51Tom £10.50 Subtract each price from £20.

N. E. Lincolnshire Mathematics Team8 Sample semi-final question Answer sequence Joe thinks of two 2-digit numbers both less than seventy-five. Both numbers have 6, 3 and 5 as factors. One number is half the size of the other. What are the two numbers? 60 30

N. E. Lincolnshire Mathematics Team9 Sample semi-final question Answer sequence To score a total of 10 on two standard dice you would need to throw a 6 and a 4 or two fives. If you had three dice what are the combinations of scores you could throw to make a total of 10? These may be thrown in any order

N. E. Lincolnshire Mathematics Team10 Sample semi-final question Answer sequence The graph shows the percentage scored by 7 children in a test Jade Paul Lee Amy Jack Tom Chelsey A. Who scored exactly 30% less than Amy? B. What did Paul score in his last test if this score was double his last score? C. Which two children scored exactly 55%between them? A. Chelsey B. 35% (½ of 70%) C. Tom and Jade

N. E. Lincolnshire Mathematics Team11 Sample semi-final question Answer sequence The radius of the yellow circle is 12 cm and x is the centre of the circle What is the area of the red rectangle (oblong)? 288 cm 2 The width of the rectangle equals the radius of the circle 12 cm The length of the rectangle is twice the radius of the circle 24 cm The area of the rectangle is 12 cm x 24 cm = 288 cm 2 x

N. E. Lincolnshire Mathematics Team12 Sample semi-final question Answer sequence The circumference of a bicycle wheel is 140 cm How far in metres does the wheel travel in thirty revolutions? The wheel travels 140 cm x 30 = 4200 cm 42 m 4200 cm is the same distance as 42 metres

N. E. Lincolnshire Mathematics Team13 Sample semi-final question Answer sequence Chloe makes a square with four sticks She then uses some more sticks to make another square on the side She continues the pattern in the same way adding more squares. She uses 19 sticks altogether How many squares are there in her completed sequence?

N. E. Lincolnshire Mathematics Team14 Sample semi-final question Answer sequence Three-fifths of a number is 45 What is one-third of the same number? 25 If three-fifths of the number is 45 then one-fifth is 45 ÷ 3 = 15 One-third of the number is 75 ÷ 3 = 25. NumberThree-fifths45 The whole number is 15 multiplied by 5 = Two-fifths15

N. E. Lincolnshire Mathematics Team15 Sample semi-final question Answer sequence Triangle ABC is equilateral X A BC What is the value of angle X? There are many different ways to find this answer. How many can you find?

N. E. Lincolnshire Mathematics Team16 Sample semi-final question Answer sequence Which numbers are missing from these number sentences? A. - 7 = 35 B. X 7 = 35 C. + 7 = 35 D. ÷ 7 =

N. E. Lincolnshire Mathematics Team17 Sample semi-final question Answer sequence These shapes each have properties in common. Identify 2 common properties All quadrilaterals All have parallel lines All have at least one line of symmetry Some possibilities

N. E. Lincolnshire Mathematics Team18 Sample semi-final question Answer sequence Jack makes five statements. Some are true, some are false. A. All squares are rectangles, but not all rectangles are squares B. An isosceles triangle has two right angles C. To multiply any number by 10 just put a zero on the end D. For every decimal fraction there is an equivalent ‘ordinary’ fraction E. A regular pentagon has five lines of symmetry Write T or F next to each statement T F F T T

N. E. Lincolnshire Mathematics Team19 Sample semi-final question Answer sequence Jade starts with an even number. She doubles it. She continues to double until she reaches 144. What are the other numbers in her sequence before she reaches her total? Start with 144 and continue halving until she reaches her starting number.

N. E. Lincolnshire Mathematics Team20 Sample semi-final question Answer sequence How many different triangles can you find in this drawing?

N. E. Lincolnshire Mathematics Team21 Sample semi-final question Answer sequence Two of these nets will not make a closed cube. ABCDE Write the letters of the nets that will make a closed cube

N. E. Lincolnshire Mathematics Team22 Sample semi-final question Answer sequence In a football match the score at half time is 1 – 0 to the home side. In the second half three more goals are scored. What are the possible full-time results? Include both home and away possibilities

N. E. Lincolnshire Mathematics Team23 Sample semi-final question Answer sequence A ream of A4 paper is 500 sheets. The height of a ream is 5.5 cm What is the thickness of one sheet of paper in millimetres? 0.11 mm Change 5.5 cm to 55 mm. Divide 55m by 500 = 0.11mm

N. E. Lincolnshire Mathematics Team24 Sample semi-final question Answer sequence Here are some lists. Which is the odd one out in each list? 1a 0.4 b. Two-fifths c. 40% d. 16 e. 4% 40 2a 25 x 15 b. 750 ÷ 0.5 c d. 750 e a rhombus 3b pollygon 3c paralellogram 3d isocseles 3e trapesium

N. E. Lincolnshire Mathematics Team25 Sample semi-final question Answer sequence Each apex of the red equilateral triangle is in the centre of a circle. The circles are the same size. The perimeter of the triangle is 45 cm What is the radius of each of the circles? 7.5 cm Each side of the triangle is 15 cm. The radius of these circles is half the length of one side of the triangle 15 cm ÷ 2 = 7.5 cm

N. E. Lincolnshire Mathematics Team26 Sample semi-final question Answer sequence A shop reduces the price of sports shoes by 20% The new price is £60 What was the original price of the shoes? £75 The new price is four-fifths of the old price. The new price is four parts of the old price, this is £60 ÷ 4 = £15 So the original price was £60 + £15 = £75

N. E. Lincolnshire Mathematics Team27 Sample semi-final question Answer sequence There are three prime numbers between 80 and 100 What is their total? None of the even numbers can be prime in this case. This leaves - Can be divided by 3, 5 or 7 so are not prime numbers. Are prime numbers =

N. E. Lincolnshire Mathematics Team28 Sample semi-final question Answer sequence The two triangles are isosceles and the same size. They each have a perimeter of 20.5 cm. A B 6 cm How long is line AB? 17 cm The two equal sides of each triangle are 6 am long because they are the same length as the short side of the rectangle. The third side is the perimeter of the triangles 20.5cm - 12 cm (the total length of the equal sides) = 8.5 cm Line AB is 2 x 8.5 cm = 17 cm

N. E. Lincolnshire Mathematics Team29 Sample final question Answer sequence A B Two straight lines cross as shown in the drawing What is the size of angle A and angle B? Angle A is = 75 0 Angle B is = 105 0

N. E. Lincolnshire Mathematics Team30 Sample final question Answer sequence A B C The sum of the edges of each of these squares is 1000 Which three numbers are missing?

N. E. Lincolnshire Mathematics Team31 Sample final question Answer sequence Six people play each other once at golf. How many games are played altogether? 15 Player A Player B Player C Player D Player E Player F 5 Games Player C Player D Player E Player F 4 Games Player D Player E Player F 3 Games Player E Player F 2 Games Player F 1 Game

N. E. Lincolnshire Mathematics Team32 Sample final question Answer sequence Gavin weighs one-third more than Sally. Mum weighs twice as much as Gavin. Mum and dad weigh 140kg altogether. Sally weighs 24kg. How much do mum and dad each weigh? Gavin weighs 24kg + 8kg = 32kg. Mum weighs 32kg x 2 = 64kg. Dad weighs 140kg - 64kg = 76kg. Mum weighs 64kg. Dad weighs 76kg.

N. E. Lincolnshire Mathematics Team33 Sample final question Answer sequence Jade uses five 5s to write a number sentence. She uses two + signs and one x sign. The answer to her sentence is 555. What could her number sentence have been? The 5s in her answer are not part of the five 5s she uses to work out her problem. = 555(5 + 5) x

N. E. Lincolnshire Mathematics Team34 A Sample final question Answer sequence The drawing shows part of number grid six columns wide B Which numbers are missing from squares A and B?

N. E. Lincolnshire Mathematics Team35 Sample final question Answer sequence The area of this square is 64cm 2 Joe uses similar squares to make a new shape. What is the perimeter of the new shape? 80cm The area is 64cm 2 so each side is 8cm. There are ten sides to the new shape. 10 x 8cm = 80 cm

N. E. Lincolnshire Mathematics Team36 Sample final question Answer sequence Amy and Jade live in different villages. Their villages are both 90km away from the town. They agree to meet in the town at noon. Amy travels at a speed of 40km per hour and Jade travels at a speed of 60km per hour. At what time should they each set off from their villages to arrive in the town at noon? Amy sets off at 9:45 a.m. Jade sets off at 10:30 Amy’s journey time is 2¼ hours. Jade’s journey time is 1½ hours.

N. E. Lincolnshire Mathematics Team37 Sample final question Answer sequence There are three mathematical terms jumbled in this sequence of letters. S M S U U Y B L M T T M R I E A P T C L R T Y Y What are the three terms? SUBTRACT MULTIPLY SYMMETRY S M S U U Y B L M T T M R I E A P T C L R T Y Y M U L T I P L Y S U B T R A C T S Y M M E T R Y

N. E. Lincolnshire Mathematics Team38 Sample final question Answer sequence Fred cuts discs this size from a sheet of metal as shown below. Each disc has a diameter of 3cm. What is the area of the sheet of metal? 108cm 2 The sheet is 4 discs (12cm) long The sheet is 3 discs (9cm) wide The area of the sheet is 9cm x 12cm = 108cm 2

N. E. Lincolnshire Mathematics Team39 Sample final question Answer sequence Five children run 50m in a race. Their finishing times are: 7.5 sec., 8.00., 7.75., 8.5 sec. and 6.5 sec. What is their average (mean) time for running 50m? 7.65 sec = 38.25sec ÷ 5 = 7.65 sec.

N. E. Lincolnshire Mathematics Team40 Sample final question Answer sequence Chloe takes the number 2. She then applies a rule (does something to it) and gets the answer 8. She uses the same rule with some other numbers. Start number 4 finish number 18 Start number 3 finish number 13 Start number 6 finish number 28 Start number 1 finish number 3 Can you work out what her rule is? Multiply the start number by 5 then subtract 2

N. E. Lincolnshire Mathematics Team41 Sample final question Answer sequence Calculate the outcome if Tom puts the following sequence into his calculator +794x-0312+= ÷ √ 3

N. E. Lincolnshire Mathematics Team42 Sample final question Answer sequence The number shown by A in the centre of the drawing is the product of the numbers linked by the arrows opposite each other. A 15 3B 8 What are the values of A and B? 12040

N. E. Lincolnshire Mathematics Team43 Sample final question Answer sequence The numbers in this sequence start at 27 and reduce by the same number each time. 27????12 Which numbers are missing from the sequence? The sequence decreases by 3 from left to right. The sequence increases by 3 from right to left.

N. E. Lincolnshire Mathematics Team44 Sample final question Answer sequence One person sits on each side of a square table Jack has five similar tables that he joins together to make one long table. How many people can be seated around the new table? 12

N. E. Lincolnshire Mathematics Team45 Sample final question Answer sequence In a family each boy has one sister and each girl has one brother. How may people are in the family including mum and dad? 4

N. E. Lincolnshire Mathematics Team46 Sample final question Answer sequence What is 25% of one-third of 240? 20 One-third of 240 is % (or ¼) of 80 is 20

N. E. Lincolnshire Mathematics Team47 Sample final question Answer sequence In championship tennis the balls are new at the start of the match. They are changed after the first seven games and then every nine games after that. Roger Federer beats Tim Henman 6 – 3, 7 – 6, 2 – 6, How many sets of new balls are used in the match? 5 40 games are played. Subtract 7 (1st set of balls) leaves games ÷ 9 uses 3 sets of balls (27 games) with 6 extra games left. An extra set is needed for the six games = 5

N. E. Lincolnshire Mathematics Team48 Sample final question Answer sequence Inside the drawing of a square there are 3 shapes. Points A and B are the middle of the sides of the square. The length of each side of the square is 8cm. A B What is the area of each shape? 1. 16cm cm cm2 The area of the square 8cm x 8cm = 64 cm 2 Shape 1 is ¼, shape 2 is ½ and shape 3 is ¼ of the square

N. E. Lincolnshire Mathematics Team49 Sample final question Answer sequence The sum of three single-digit numbers is 10. Their product is 30. What are the three numbers? 235

N. E. Lincolnshire Mathematics Team50 Sample final question Answer sequence A large rectangle is divided into smaller rectangles The perimeter of this rectangle is 18 cm. 3cm 7cm What is the area of the pink rectangle? 42cm 2 The pink rectangle is 7cm by 6cm = 42 cm 2 7cm 6cm

N. E. Lincolnshire Mathematics Team51 Sample final question Answer sequence Which design comes next in this sequence? The pattern is the numbers 1 to 9 made up of straight lines and placed back to back

N. E. Lincolnshire Mathematics Team52 Sample final question Answer sequence A large rectangle is made up of smaller squares. What percentage of the large rectangle is not shaded blue? 75% There are 40 small squares. Ten are blue. This is a quarter, so three- quarters, or 75% are not blue.

N. E. Lincolnshire Mathematics Team53 Sample final question Answer sequence Tom forgets the three-digit combination to his case. He knows that the first number is an odd prime number more than 3. The last number is not odd but is less than six and more than one. No two digits in the combination are the same. The middle number makes the total of the three digits add up to 13. What are the possible combinations for Tom’s lock?

N. E. Lincolnshire Mathematics Team54 Sample final question Answer sequence A regular octagon has an area of 86 cm 2 The square surrounding the octagon has a perimeter of 40 cm. What is the area of one of the small triangles if they are all the same size? 3.5cm 2 The area of the square is 10cm x 10cm = 100 cm 2 The area of the four triangles altogether is 100 cm cm 2 = 14cm 2 14cm 2 ÷ 4 = 3.5cm 2