GCSE Problem Solving Questions - Answers

Transcription

1 GCSE Problem Solving Questions - Answers

2 Problem Solving Questions Information This booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes. These are the questions that we have been putting out each day in the run up to GCSE eams. The answers are also provided with each question. GCSE There are problems that are suitable for foundation and higher and ones that are suitable for higher tier only. We hope to release more questions like this over the course of net year that you can use on a regular basis with your classes including some open ended problems. Please keep a look out for our work. In June 2016 we plan to release our new KS3 schemes of work. The schemes build on the work we have been doing within primary. We are keen to work with secondary schools net year who might be interested in implementing this KS3 scheme. As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team Trinity Academy Halifa 2016 For information and comments mathshub@trinityacademyhalifa.org

3 Foundation & Monday 11th April 2016 Version 1 A logo is made up of four congruent triangles. The arc length of this sector is 5cm cm 5cm Find the perimeter of the sector. Give your answer to 3 significant figures. 21cm Find the area of one of the triangles. Height =8cm, base = 5cm Area = 20cm 2 Perimeter = 30 π 5 = 1 π 2r 6 15 π = r + 5 = 14.6 cm

4 Foundation & Monday 11th April 2016 Version 2 A logo is drawn inside a rectangle. It is made up of four congruent triangles. The arc length of this sector is 5cm. 60 5cm 16cm Find the perimeter of the sector. Give your answer in terms of π Height =8cm, base = 5cm Area of one triangle = 20cm 2 21cm Perimeter = 30 π = 1 π 2r 6 15 π = r Fraction of shape shaded = = 5 21

5 Foundation & Monday 11th April 2016 Version 3 A logo is made up of four congruent triangles. The area of this sector is 50cm cm Find the length of the arc. Give your answer to 3 significant figures. 21cm Find the perimeter of the logo. Height =8cm, base = 5cm, hypotenuse = 65 Arc length = = πr 2 r = 300 π 2 π 300 π = 20.5cm Perimeter =

6 Foundation & Diagrams are not to scale. Tuesday 12th April 2016 Version 1 (2 + 3) cm ( 5) cm ( + 6) cm 60 9 cm The perimeter of this rectangle is 44cm. Find the value of 6 4 = 44 6 = 48 = 8 ( 3) cm ( + 6)( 3) = 9( + 1) = = 0 ( 9)( + 3) = 0 ( + 1) cm = 9

7 Foundation & Diagrams are not to scale. Tuesday 12th April 2016 Version 2 (2 + 3) cm ( 5) cm ( + 6) cm 60 9 cm The perimeter of this rectangle is 44cm. Find the length of the rectangle. 6 4 = 44 6 = 48 = 8 Length = = 19cm ( 3) cm Area of rectangles is 90cm 2 ( + 6)( 3) = 9( + 1) = = 0 ( 9)( + 3) = 0 = 9 ( + 1) cm

8 Foundation & Diagrams are not to scale. Tuesday 12th April 2016 Version 3 (2 + 3) cm ( + 1) cm ( 5) cm ( + 6) cm 60 9 cm The perimeter of this rectangle is 44cm. ( 3) cm Find the length of the diagonal. 6 4 = 44 6 = 48 = 8 A shape is made of two rectangles. The two rectangles have the same area. (a) Find the perimeter of the shape. Length = = 19cm Width = 3 cm Length of diagonal = 370 (b) = 62cm Find the length of the diagonal line shown. Length = 481 = 29.1 cm

9 Foundation & Wednesday 13th April 2016 Version 1 Ma is saving to buy a computer game that costs 26 He saves 5p, 10p and 50p coins in a jar. The ratio of 5p to 10p to 50p coins is 2 : 5 : 1 There are 120 coins in the jar. Here is an isosceles triangle. The hypotenuse is 8cm cm How much more does he need to save? = 15 5p coins is 2 15 = 30 which is worth p coins is 5 15 = 75 which is worth p coins is 1 15 = 15 which is worth 7.50 Total saved = To save still = = 9.50 Find the area of the triangle. Call other two sides as they area equal Using Pythagoras = = 64 2 = 32 = 32 = 4 2 Area is = 16 cm 2

10 Foundation & Wednesday 13th April 2016 Version 2 Ma is saving some money in a jar. The diagram shows a square inside a circle He saves 5p, 10p and 50p coins. The ratio of 5p : 10p : 50p coins is 2 : 5 : 1 There are 120 coins in the jar. The circle is inside an outer square cm He adds the following coins; 2.50 in 50p coins 2.50 in 10p coins 2.50 in 5p coins What is the new ratio of 5p : 10p : 50p coins? = 15 8 cm 8 cm 4 2 cm 5p coins is 2 15 = 30 10p coins is 5 15 = 75 50p coins is 1 15 = 15 Adds to it 5 50p coins, 25 10p coins and 50 5p coins. So total coins is now 80 : 100 : 20 = 4 : 5 : 1 The length of the outer square is 8cm. Find the distance marked = = (4 2 2) cm

11 Foundation & Diagrams are not to scale. Thursday 14th April 2016 Version 1 A floor is going to be covered in carpet tiles. The tiles measure 40cm by 40cm Three circles with centres A, B and C are shown. 40 cm 40 cm 60 Diameter= 12cm A The floor is 3.2 metres by 2 metres. 8 cm 10 cm 2 m C 6 cm B Diameter= 4cm 3.2 m Tiles are sold in boes of 12 How many boes of tiles will be needed to cover the floor? 8 5 = 40 tiles 4 packs needed Diameter= 8cm Show that triangle ABC is right angled = 10 2 therefore right angled.

12 Foundation & Diagrams are not to scale. Thursday 14th April 2016 Version 2 A room is going to be covered in carpet tiles. The tiles measure 40cm by 40cm A plan of the room is shown below. 0.8 m 0.8 m Three circles with centres A, B and C are shown. 60 Diameter= 12cm A 0.8 m 10 tiles 10 tiles 2 m (r + 6) 10 cm 12 tiles 3.2 m C (r + 4) B A bo of 12 tiles costs 35 Single tiles costs 5 32 tiles needed in total. Cheapest way is 3 packs of 12 tiles. What is the cheapest way of covering the floor in carpet tiles? (r + 6) 2 + (r + 4) 2 = r r + 52 = 100 2r r 48 = 0 r r 24 = 0 (r + 12)(r 2) = 0 r = 2 Diameter= 8cm

13 Foundation & Diagrams are not to scale. Friday 15 th April 2016 Version 1 1 Mr Drake asked his class how many cats and 2 dogs they own. The results are shown in the two way table. Number of cats Number of dogs What fraction of the class own more cats than dogs? Can you write you answer as a percentage? % The circle below has a radius of 5cm. O is the centre of the circle. Angle ABC = A B 50 O 5cm 100 5cm AC 2 = cos 100 AC 2 = AC = 2.62 cm C

14 Foundation & Diagrams are not to scale. Friday 15 th April 2016 Version 2 1 Mr Drake asked his class how many cats and 2 dogs they own. The results are shown in the two way table. Number of cats Number of dogs The circle below has a radius of 5cm. O is the centre of the circle. AB = BC Angle ABC = 50 B 50 5cm O 130 5cm How many dogs do the class own? = 17 dogs A C Area of BOC = 5 5 sin130 Area of shape = Area of BOC 2 Area = 25sin 130 = 19.2

15 Foundation & Diagrams are not to scale. Monday 18 th April 2016 Version 1 The diagram shows two squares. Here are the contents of three boes. Bo Contents The large square has a length 10cm. The small square has a length of 4cm. Find the area of the shaded region. Area = cm 10 cm 2 = 42cm 2 A B C 1.3n = 78 n = 60 All red counters (n red) 30% red counters and the rest blue (0.3n red and 0.7n blue) Empty There are the same number of counters in boes A and B. (n in each one) The counters from boes A and B are put together into bo C. (2n counters in total) There are now 78 red counters in bo C 1.3n red counters in total or 65% of bo is red counters. Blue counters = = 42 counters

16 Foundation & Diagrams are not to scale. Monday 18 th April 2016 Version 2 The diagram shows two squares. Here are the contents of three boes. The large square has a length 10cm. The small square has a length of 4cm. What percentage of the diagram is shaded? What fraction of the diagram is shaded? Area = cm 10 cm 2 = 42cm 2 Bo A B C Contents All red counters (2n red) 30% red counters and the rest blue (0.3n red and 0.7n blue) 50% red counters and the rest blue (0.5(n + 4) red and 0.5(n + 4) blue) The counters from boes A and B are put together with the counters in bo C. Total red counters = 2n + 0.3n + 0.5n = 2.8n + 2 n = 140 There are now 394 red counters in bo C How many blue counters are there in total? Number of blue counters = = % of diagram is shaded and 21 is shaded. 50

17 Foundation & Diagrams are not to scale. Tuesday 19 th April 2016 Version 1 Here are four number cards Here is a piece of paper. 9 cm A B C D The mean of the four cards is 11 6 cm A, B and C add together to make 40 A is twice the size of D The other two cards are the same number. It is folded over in the following way. 3 5 cm Find the value of each of the cards. Sum of the cards is 4 11 = 44 Card D must equal 4 as the total of the other cards is 40 A is 8 B = C = = = = 2 45 = 2 = 45 = cm 6 cm

18 Foundation & Diagrams are not to scale. Tuesday 19 th April 2016 Version 2 Here are three number cards Here is a piece of paper. 9 cm A B C The mean of the cards is 0 6 cm The sum of A and B is -10 The difference between A and B is 2 It is folded over in the following way. Find the range of the cards cm 3 5 cm Sum of the cards is 3 0 = Card C must be 10 if A and B sum to -10 A is -6 and B is -4 (or accept vice versa) 9 cm 6 cm The range is therefore 16 = tan = = (9 3 5) tan = 2.56 cm

19 Foundation & Wednesday 20th April 2016 Version 1 Here is a number line. Here are three number cards. Three numbers A, B and C are marked. A B C 0 The difference between A and C is 28 Draw an arrow on the number line showing where the mean of the numbers A, B and C lies. If the difference between A and C is 28 then each gap is worth 4 Therefore A = -4, B = 16 and C = 24 The mean of these is = = 36 3 = Find the mean of these numbers. Another card is added. New mean = 6 5 Mean = a Total of cards = = = 3 5 a = = 15 5 = = 1125 a = 1125

20 Foundation & Wednesday 20th April 2016 Version 2 Here is a number line. Here is some data in a frequency table. Three numbers A, B and C are marked. A D B C 0 frequency f The difference between A and B is 1 Find the value of C D is the product of A and B. If the difference between A and B is 1 then each gap is worth 0.2 C = 1.2 Show that the mean of the data is 5 5 Mean = = 25 5 = Draw an arrow on the number line showing where D lies. D = A B D = D = 0.24

21 Foundation & Thursday 21 st April 2016 Version 1 40 children take part in a school show. A goat is grazing in a rectangular field. The ratio of boys to girls in the show is 3 : of the children are dancers. The rest of the children are singers. There are 3 boys who are dancers in the show. How many more girls are dancers than singers? D S Total B G There are 21 4 = 17 more girl dancers than singers. The length of the field is 40 metres and the width is 30 metres. Area of field = πr2 2 40m P 18m = π = 162π m 2 30m The goat is attached to a post, P, which is at the centre of one of the 40 metre sides. It is attached to the post with an 18 metre long rope. Find the area of the grass that the goat could graze.

22 Foundation & Thursday 21 st April 2016 Version 2 40 children take part in a school show. A goat is grazing in a rectangular field. The ratio of boys to girls in the show is 3 : of the children are dancers. There are 4 more singers than actors. There are twice as many boys who are singers as boys who are actors. The length of the field is 40 metres and the width is 30 metres. 15m 40m 20m P m 30m There are 21 girls who are dancers in the show. How many girls are singers? D S A Total B G There are two girls who are singers. Find the area of the grass that the goat could graze. Area of sector = πr2 = 106.3(π 252 ) = m Area of triangles = Total area = m = 300 m 2

23 Foundation & Friday 22 nd April 2016 Version 1 Richard is doing a survey. A 7 metre ladder rests against a wall. He asks people to choose their favourite biscuit. The ladder reaches 5.5 metres up the wall. There are four biscuits A, B, C or D. The percentages for B, C and D are shown. A B C D 5.5m 1m 7m 20% 15% 30% 160 people chose B How many people chose A? 20% = 160 people 10% = 80 people New distance from base of wall = = 5.36 = = 1.03 metres Percentage who chose A = = 35% Number of people who choose A = = 280

24 Foundation & Friday 22 nd April 2016 Version 2 Richard is doing a survey. A 7 metre ladder rests against a wall. He asks people to choose their favourite biscuit. The ladder reaches 5.5 metres up the wall. There are four biscuits A, B, C or D. The fraction of people who choose B, C and D is shown in the table. A B C D 1m 7m people chose A. How many people chose B? New distance from base of wall = = 5.36 = = 1.03 metres 1 20 is 12 people 1 = 4 is 4 12 = 48 people 5 20

25 Foundation & Foundation & Monday 25 th April ABCD is a square that has sides of length 2 3cm. E and F are the midpoints of two of the sides. B E 1.5cm A Find the area of the shaded region. Area of triangle = = 2.25 Area of shaded region = (3 3) (2 2.25) = 4.5cm 2 F 3cm C D A jar contains some cookies. The weight of the jar and cookies is 700g. Meghan eats 4 of the cookies. 5 The weight of the jar and cookies is now 400g. How much does the jar weigh? 4 5 = 300g and so 1 5 = 75g Therefore weight of jar = = 325g Each cookie weighs 25g. How many cookies were in the jar at the start? 375g of cookies in jar which is equal to 375 = 15 cookies 25

26 Monday 25 th April 2016 The line P has the equation y = 3 2 y P If y = ( + y) 2 ( y) 2 Calculate 6 4 = ( + y) 2 ( y) 2 (6 + 4) 2 (6 4) 2 = = 96 The line P is reflected in the y-ais. Find the equation of the line. y = 3 2 The line P is reflected in the -ais. Find the equation of the new line = ( + y) 2 ( y) 2 Simplify first ( + y) 2 ( y) 2 = (( + y) + ( y))(( + y) ( y)) = (2)(2y) = 4y Therefore when = y = = = 60 y = or y = 2 3

27 Foundation & Foundation & Tuesday 26 th April 2016 A rectangle is made up of 4 large and 6 small squares. The length of the rectangle is 18cm. 18cm Mary is doing a fitness test. She starts at A and runs to B She then returns to A She then runs to C and then returns to A She then runs to D and then returns to A BC = CD = 22 metres In total Mary runs 318 metres. A B C D Find the perimeter of the rectangle. Each large square is 4.5 by 4.5 Each small square is 3 by 3 So the width of the rectangle is 7.5cm Perimeter = = 51cm Find the distance between A and B. Call AB = Total distance = = = = 186 = 31

28 Tuesday 26 th April 2016 The points A, B, C and D lie in a straight line. A square ABCD has sides of cm. BE = 6cm A B C D AD = 82 cm. The ratio of the distance AB to BC is 2 : 5 The ratio of the distance BC to CD is 3 : 4 Find the distance BC. AB : BC : CD 6 : 15 : 20 AB = 6 2 = 12cm BC = 15 2 = 30 cm CD = 20 2 = 40 cm = 2 Area = So = 0.4 = 0 or = = 12.5 So = 12.5 cm 6cm E B A 4cm 5 = = = (0.4 5) C D

29 Foundation & Foundation & Wednesday 27 th April 2016 Maryam makes dolls. Taylor has some buttons. She uses the following formula to work out the cost, C, of making n dolls. C = 5n Maryam makes 170 dolls. She sells them for 8.50 each. How much profit does she make? C = = = 1445 Profit = = 163 Wendy has twice as many buttons as Taylor. Yusif has 12 more buttons than Taylor. In total they have 260 buttons. How many buttons does Yusif have? Taylor has buttons Wendy has 2 buttons Yusif has + 12 buttons Yusif has 74 buttons = = 248 = 62

30 Wednesday 27 th April cm Some data is shown in a table. 9cm h frequency, f a The perimeter of the shape is 60cm. The area of the shape is 116cm 2 Find the length of the sides marked w and h 16 + h w h + 16 w = 60 2h + 50 = 60 2h = 10 h = 5 w 16h + 9w = w = 116 9w = 36 w = 4 The mean of the data in this table is 5.3 Find the value of a a = 5.3(26 + a) 5a = a 7.2 = 0.3a a = = 24

31 Foundation & Foundation & Friday 29 th April 2016 Mr Khan buys some potatoes and carrots. 35% of the total weight are carrots. Here is a rectangle. There are 2.7kg more potatoes than carrots. How many kg of potatoes does he have? 4 The length of the rectangle is cm 35% carrots, 65% potatoes 30% = 2.7kg The width of the rectangle is ( 4) cm. 4 10% = 0.9kg 65% = 5.85kg 4 Perimeter = = 58 6 = 66 = 11 The perimeter of the shape is 58cm. Find the value of 4

32 Friday 29 th April 2016 A parcel company delivers two sizes of bo. James has some algebra epressions cards. Size of bo Weight of bo Cost of delivery Large 5.6kg 6 Small 4kg 5.50 Andy also has some too. One day the company delivers 25 boes. The total weight of the boes is 133.6kg. How much does it cost to send the boes? Let be the number of large parcels Let y be the number of small parcels = 21 and y = 4 + y = y = Total cost = = 148 If the mean of James cards is equal to the mean of Andy s cards, find the value of y. 6y y + 1 = 5y + 10 = 4 5y y + 4 = 5y y + 4 = 10 3y = 6 y = 2

33 Foundation & Foundation & Tuesday 3 rd May Adam is writing 720 as a product of its prime 2 factors. He writes his answer in inde form. 720 = a 4 b 2 c Find the values of a, b and c a = 2, b = 3 and c = 5 Here is another number Q. It is written as the product of its prime factors. Q = Find the highest common factor of 720 and Q. HCF = = 60 Eggs are packed into three different sized boes small, medium and large. The number of eggs in each bo is shown in the table. Small Medium Large 6 eggs 10 eggs 15 eggs Vish has 120 full boes. 35% of the boes are small. (42 boes) 2 5 of the boes are medium. (48 boes) The rest are large. (30 boes) How many eggs does Vish have in total? = 1182

34 P Tuesday 3 rd May The bo plot shows the heights in 2 centimetres of 80 people. 12cm = 80 = 4 5 8cm 6cm O 10cm Q The median height is 172cm. The interquartile range is 18cm. Find the height of the tallest person. Each 5 little squares is worth 2cm. Upper quartile = 178cm Tallest person = 190cm PQ is a tangent to the circle with centre O. The radius of the circle is 8cm. ( ) 8 Area = 2 =

35 Foundation & Foundation & Wednesday 4 th May students are asked how they travel to school. 60% say they walk to school. The remaining travel by car or by bus. The ratio of students who travel by car to those that travel by bus is 2 : 3 How many more students walk to school than travel by car? 60% of 300 = 180 students 120 are car or bus 48 : = 132 more students walk to school ABCD is a trapezium. 4cm B C A 6cm BC = 4cm and AD = 6cm The area of the trapezium is 25cm 2 Find the length of CD. Height of trapezium = 5cm Length of CD = = 29 = 5.39 cm D

36 Wednesday 4 th May A group of students are asked how they 2 travel to school. B 55% say they walk to school. The remaining travel by car or by bus. The ratio of students who travel by car to those who travel by bus is 2 : more students walk than travel by bus. 13cm A 2 5 5cm C D E How many students travel by car? 55% walk to school 45% travel by car or bus 18% : 27% is car : bus 140 is equal to 28% Therefore 1% is equal 5 students 5 18 = 90 students travelled by bus. AB is parallel to CD = = = 5 = 12.5 Area = 1 (13 + 5) 20 = 180 cm2 2

37 Foundation & Foundation & Thursday 5 th May people attend a theatre show. An adult ticket costs of the people are children. In total the theatre take 1120 in ticket sales. How much does a child ticket cost? ABC is an isosceles triangle. The area of the triangle shown is 30 units 2 y C 5 units B 160 children attend the show. 120 adults attend the show = = = 2.50 per ticket. A (5, 0) Find the co-ordinates of the point B. Height of triangle is 5 units. Base must be 12 units. Therefore B is (0, 6)

38 Thursday 5 th May 2016 Here are two water tanks. A 18cm 80 D 1.2m 50cm Tank A 30cm Volume of water = = cm3 Volume of water in tank B is = 54000cm = π r 2 h = π 30 2 h π = 19.1cm 60cm Tank B 100 O 18cm 50 C B A, B and C lie on the circumference of the circle. Tangents are shown at points A and B. AD = 18cm Angle ACB = 50 Find the length of AB. AB = cos 80 = 23.1cm

39 Foundation & Foundation & Friday 6 th May 2016 Steve and Gina were walking from Redtown to Bluesville at a constant speed. At 3pm they were half way there Four congruent triangles are shown below. y D At 4.20pm they were three quarters of the way there. How long did the journey last? 1 hr 20 mins is one quarter of the journey. Therefore journey lasts 4 1 hr 20 = 5 hours 20 minutes C (5, 7) A (5, 2) E B (18, 2) The coordinates of three points are given. (a) Find the coordinates of D. (10, 15) (b) Find the length of CE. ( 89 = 9.43cm)

40 Friday 6 th May A hospital has some targets for its A&E department. 2 The floor in an art gallery is to be painted blue. 50% of people will be seen within one hour (Yes 54%) 80% of people will be seen within one and a half hours (Yes 83%) All people will be seen within two hours (yes) The histogram shows the waiting times of patients for March. The diagram shows the region of the floor to be painted. 9m 30m Did the A&E department meet all the targets for March? Show workings to support your answer. A tin of paint covers 6.4m 2 Each tin of paint costs How much does it cost to paint the floor? Area of floor = 30 9 = 270 m 2 Area of semi-circle = 81π 2 m2 Area of painted floor = π = 143 (3sf) = 23 tins =

41 Foundation & Foundation & Monday 9 th May 2016 A bo contains some coloured pencils. There are 25 more red pencils than green pencils. 2 5 of the red pencils are blunt. The shape below is made up of a regular heagon and a regular pentagon. 1 3 of the green pencils are blunt. Toby sharpens all of the blunt pencils. If Toby sharpens 15 green pencils, how many red pencils does he sharpen? 45 green pencils in the bo red pencils in the bo. Toby sharpens 28 red pencils. Find the size of the angled marked Give reasons for your answer = = 24

42 Monday 9 th May 2016 Ahmed, Boris and Carl have some marbles. Ahmed and Boris together have 65 marbles. Boris and Carl together have 48 marbles. Ahmed and Carl together have 55 marbles. How many marbles do they have in total? a + b = 65 b + c = 48 a + c = 55 2a + 2b + 2c = 168 a + b + c = 84 ABC is a right-angled triangle. B 7cm D A 24cm BC = 25cm BD = 15 and CD = 10 Angle BCA = tan 1 ( 7 24 ) so cos(bca) = 24 AD = AD = 14.7cm C

43 Foundation & Foundation & Tuesday 10 th May 2016 Four points lie on a straight line. A B C D The diagram shows a five pointed star. All of the ten sides are the same length. The distance AD is 129 metres. The distance BC is 15 more metres than the distance CD. The distance AB is twice the distance BC Calculate the distance from B to C. AB = BC = + 15 CD = AD = = 129 = 21 therefore the distance BC is 36 metres Find the size of the angle marked = 36

44 Cumulative Frequency Tuesday 10 th May 2016 The area of the trapezium is 30 cm Gemma sells hand-made gifts. The cumulative frequency diagram shows the weights of 120 gifts that she sold this month. 1 d + 4 Find the length of d ( 1)(2 + 5) = = = 0 (2 + 13)( 5) = 0 = 5 Therefore d = = 52 = less than 500g costs = more than 500g cost 45 4 = 180 Total cost = Students may use 76 and 44 or 74 and 56

45 Foundation & Foundation & Wednesday 11 th May 2016 Amy has some identical rectangular blocks. 9cm 4cm She uses five of these blocks to make a tower. 18cm Two cars are travelling from A to B. The first car travels at an average speed of 40mph. The first car leaves A at 13:30 and arrives at B at 16:00 The second car travels at an average speed of 50mph. If the second car sets off at the same time, how much earlier does the car arrive at B? 13cm = = 2hrs Arrives 30 mins earlier 2 = = 6 = 3

46 Wednesday 11 th May The diagram shows three rows of rectangles. 2 Each row in the diagram is the same height. The 1 st row is made up of 2 equal sized rectangles. The 2 nd row is made up of 3 equal sized rectangles. The 3 rd row is made up of 4 equal sized rectangles. The diagram shows a square inside another square. The area of the blue square is 32cm 2 The area of the orange region is 40cm 2 Find the distance marked in the diagram. Length of each side of the blue square is 4 2 Length of each side of the large square is = = = = 2 2

47 Foundation & Foundation & Thursday 12 th May 2016 (a) Here are two number cards. The diagram shows a trapezium ABCD. A B The co-ordinates of the four vertices are shown. 20% of A equals 36 (A = 180) 15% of B equals 30 (B = 200) Find B A (20) A (3, 5) B (10, 5) (b) Here is another number card. C 40% of C equals 18 (C = 45) Find 1 of C (15) 3 D(1, 1) C (12, 1) Find the area of the trapezium. Area = 1 4 (7 + 11) = 36cm2 2

48 Weight of Mouse (g) Thursday 12 th May 2016 Here are two number cards. The scatter diagram shows the length and weight of 12 pet mice. A B A is 12 more than B 20% of A is equal to 15% of B Find 1 (A + B) 3 B = A A = 0.15(A+12) 0.2A = 0.15A A = 1.8 A = 36 and B = 48 therefore 1 ( ) = 28 3 P(Both over 19g) = = = 1 11

49 Foundation & Foundation & Monday 16 th May Mr and Mrs Spencer and their two children are 2 going to a theme park. The entry price to a theme park is; Two points are marked on the number line. M is eactly halfway between the two points. Today there is a special offer on. 1 5 Adult 20 Child 14 off the price of an adult ticket. 35% off a child ticket. How much does it cost the family to go into the theme park? Find the value of M. Give your answer as a fraction in its simplest form. 1 2 = and Midpoint = M 4 5 = Adult ticket = 20 4 = 16 Child ticket = = adult + 2 child = 50.20

50 Monday 16 th May Here are two triangles. 2 Three lines are shown below. B y y = y (7,13) A C y = 5 = 7 Q (3,5) (7,5) P 150 y R O The area of triangle ABC is 40cm 2 Find the area of triangle PQR. Find the area of the shaded region. Area = 4 8 = 16units2 40 = 1 y sin = y Area PQR = 1 y sin = = 40 3 = 23.1cm2

51 Foundation & Foundation & Tuesday 17 th May A florist is making some bunches of flowers for a 2 wedding. Each bunch contains some carnations, roses and lilies. Each bunch is the same. A bunch contains 40 flowers 60% of the flowers are lilies The ratio of carnations to roses is 3 : 5 The florist only has 130 carnations. How many bunches of flowers can the florist make? 60% of 40 =24 lilies = 16 (6 carnations and 10 roses) = (21 bunches of flowers) The perimeter of the rectangle is 46 cm. Find the area of the rectangle. Length = 20 cm Width = 3 cm Area = 60cm = 46 8 = 48 = 6 3

52 Tuesday 17 th May Martin and Brian are driving from Leeds to 2 London. The distance is 270km. They both set off at 9am. When Martin reaches London Brian still has 48km to drive. Brian arrives in London 40 minutes after Martin. Brian and Martin each drive at a constant speed. What times does Martin arrive in London? It takes Brian 40 mins to drive 48km. Brian s speed is 72km/h. It takes Brian 3 hours 45 minutes = 3.75 In the quadrilateral below AB = BC 4y + 1 A B The perimeter of the shape is 178cm. Find the angle marked AC 2 = = y y 2 = y = 180 y = 12 C 2y 5 D It takes Martin 3 hours 05 minutes. Martin arrives at 12:05pm. = cos 1 ( ) =

53 Foundation & Foundation & Wednesday 18 th May A bag contains some red, blue and white counters. 2 The diagram shows a quadrilateral ABCD. The probability of getting a red counter is 1 3 The perimeter of the quadrilateral is 80cm. The ratio of blue to white counters is 2 : 3 B There are 18 white counters in the bag. What is the probability of getting a blue counter from the bag? 23 cm 4y + 1 6y cm C 18 white counters 12 blue counters A 5y + 1 D 30 non red counters in total 28.5 cm 45 counters in the bag in total P(Blue) = y 10 = 4y + 1 2y = 11 y = 5.5 CD = 80 - ( ) = 5.5cm

54 Wednesday 18 th May A shape is made of up two circles. 2 A spinner can land on either a 10, 20 or 30 The table shows the probability that it lands on each value. Outcome Probability The spinner is spun twice π 12cm Area of small circle = π = = π r 2 = r = 4.48 Find the probability that the total scored from the two spins is eactly = = 1 = 0.2 P(eactly 40) = = 0.29 Diameter = 8.96 cm

55 Foundation & Foundation & Thursday 19 th May Mike earns 1250 per month. 2 30% of his earnings are spent on rent. He also buys a new TV for 249 He saves 1 of what he has left. 4 How much money does he have left now? 30% of 1250 = = 624 y = = = Find the size of the angle marked y = = 42 = 14 y = 180 ( ) y = 58

56 Thursday 19 th May Empty cans are packed into boes. 2 The diameter of each can is 6cm and the height is 10cm. 10cm h 10cm 6cm The measurements of the bo are shown below. 40 7cm 1.5m 80cm 60cm Find the height, h, of the triangle shown. = 7 sin 40 = 9.39 Cans are packed into the bo until it is full. h = = 8.83 cm How many cans can be packed into the bo? Total cans = = 2000

57 Foundation & Foundation & Friday 20 th May A machine mies red and white paint in the ratio 4 : Red paint costs 1.80 per litre White paint costs 85p per litre The machine fills 3 litre tins with this paint miture. Each 3 litre tin sells for 5.99 How much profit is made on each tin of paint? 2.4 litres of red paint ( 4.32) 0.6 litres of white paint ( 0.51) Solve the following equation p = 2.5 Give your answer as a fraction in its simplest form = = 5 7 Profit = = 1.16

58 Friday 20 th May people take part in a race. 2 The ratio of children to adults in the race is 2 : 3 ABCD is a rectangle. The mean time for the adults is 2 mins 15 seconds. 20 The mean time for all 80 people is 3 mins. 20 y Find the mean time for the children. 32 children, 48 adults = 108 minutes = 240 minutes Children take 132 minutes Mean time = = or 4 mins 7.5 seconds. = 15 sin 65 = sin 50 = y sin 85 y = 21.5 BC = 21.5 sin 70 BC = 20.2 cm