Howden School Year 7 Mathematics Homework Booklet Half Term 1 L6-7 Please complete your maths homework regularly – each week is broken into three sections. Section A, which checks your recall of key ideas and skills Section B is a task based on recent work and a ‘challenge’ task (a problem for you to try and solve). Hand your work in regularly and your teacher will let you know how well you are doing and what progress you are making – good luck and have fun! Name Maths Teacher Hand this booklet in Tutor group Dear Parent As outlined on the front cover, mathematics homework in year 7 is organised in a three section format. The Section B tasks are split into different levels and your child should attempt work in line with their working level and target. Your child should attempt Section A and the level ____ task of Section B, each week unless otherwise directed by their teacher – this may mean them completing questions at one or both levels. The challenge tasks are short problem solving activities that any pupil can attempt. These questions are taken from ‘UKMT Mathematics Challenge’ papers – some pupils will take part in the annual national UKMT Challenge during year 7. Your child’s working level at the start of year 7 and their end of year 7 target level is shown at the bottom of this page. Any task that has a bold heading or is marked with an asterisk (*) indicates that the task is linked to a key area of maths, which needs to be understood in order to contribute towards being confident working at that level. These areas will be assessed in more detail in lessons and formal assessments. We hope that your child enjoys attempting their maths homework and achieves success in the process. Howden Mathematics Department. KS2 level End of Year 7 Target 2 HOMEWORK 1 SECTION A 1 What is the area of the shape? Show your working. 2 What is the volume of the solid? Show your working. 4cm 2cm 8cm 3cm 3 Calculate the circumference of a circle with a diameter of 7.4cm. 5 Find the nth term for the following sequence. 3, 5, 7, 9, 11, … 8cm 4 Given the function x→x + 3 What is its inverse? 6 If a = 2, b = 3, and c = 5 What is the value of: b2 – 4ac 7 Multiply 245 by 26. You must show your working. 8 Divide 2871 by 3. You must show your working. 9 Expand the bracket: 10 Find the median for the following data: 5(3a – 4) 3, 8, 5, 3, 0, 1, 11, 4 3 SECTION B Level 6 Work out the area of each of the shapes below: 1) ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… 4 2) ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… 5 3) The letter H below is from a helipad; it is drawn to scale. Each centimetre represents one metre. What is the area of the H on the helipad? (You will need to measure the sides and use a calculator.) ……………………………………………………………… .................................................................. ……………………………………………………………… ……………………………………………………………… ……………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… 6 LEVEL 7 Calculate the area of the following shapes. All measurements are given in centimetres. 1 2 3 7 4 Find the missing length shown on the diagrams. All areas are in square centimetres. 1 2 8 3 4 Challenge Which of these calculations produces a multiple of 5? 1 2 3 4 C 1 2 3 4 E 1 2 3 4 A 1 2 3 4 D 1 2 3 4 B From UKMT 2008 9 HOMEWORK 2 SECTION A 1 What is the area of the shape? Show your working. 2 What is the volume of the solid? Show your working. 9mm 9mm 4.5cm 12mm 3 Calculate the circumference of a circle with a diameter of 12cm. 20mm 4 Given the function x→x - 4 What is its inverse? 5 Find the nth term for the following sequence. 5, 8, 11, 14, 17,… 6 If a = 11, b = 3, and c = 2 What is the value of b2 – 4ac 7 Multiply 84 by 47. You must show your working. 8 Divide 756 by 6. You must show your working. 9 Expand the bracket: 10 Find the mode for the following data. 5, 2, 7, 2, 3, 8, 5, 0 3(5c + 7) 10 SECTION B Level 6 1) Calculate the volume and surface area of the cuboid. Volume= ……………………………………… ……………………………………… 7cm 5cm 9cm ……………………………………… ……………………………………… Surface Area = …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… 11 2) Choose a box. This could be a cereal box Sketch your box in the space below. Label the lengths of the edges. Calculate the volume. …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… Calculate the surface area = …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… LEVEL 7 Calculate the volume and surface area for the following prisms: 12 1. 10 cm 7 cm …………………………………………………… 4 cm 3 cm 3 cm 5 cm …………………………………………………… …………………………………………………… ………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… 13 2. 6 cm …………………………………………………………………………………… 14cm cm …………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… 14 Challenge Which of these diagrams could be draw without taking the pen off the page and without drawing along a line already drawn? A B D E C From UKMT 2008 15 HOMEWORK 3 SECTION A 1 What is the area of the shape? Show your working. 2 What is the volume of the solid? Show your working. 3 4 Given the function x→2x What is its inverse? 5 Find the nth term for the following sequence. 4, 9, 14,19, 24, … 6 If a = 7, b = 1, and c =-1 What is the value of b2 – 4ac 7 Multiply 16.5 by 12. You must show your working. 8 Divide 45.6 by 4. You must show your working. 9 Expand the bracket x(x +5) 10 Find the range for the following data: 7, 6, 8 ,2, 9, 0, 12, 4, 7 Calculate the circumference of a circle with a radius of 6cm. 16 SECTION B Level 6 Write the first 6 terms of the following sequences from the descriptions. 1) Starts at -3 and doubles each time. ………………………………………………………………………………………………………………… 2) Starts at -4 and halves each time. ………………………………………………………………………………………………………………… 3) Starts at -3 and decreases by 11. ………………………………………………………………………………………………………………… 4) Start at 7 add 1 then divide by 2. ………………………………………………………………………………………………………………… Fill in the spaces and describe the pattern. 5) ……, 15, 18, ……, 24, ……, ……. ………………………………………………………………………………………………………………… 6) 72, 63, ……, 45, ……, ……, ………………………………………………………………………………………………………………… 7) 1, 1, 2, 3, 5, ……, 13,…… , …… , 55 ………………………………………………………………………………………………………………… 17 LEVEL 7 Find the inverse functions f-1(x) for the following: 1. f(x) = x + 5 2. f(x) = x – 4 3. f(x) = 4x 4. f(x) = 2x + 3 5 3 5. f(x) = 2x 6. f(x) = 2x 5 3 Challenge At Spuds-R-Us, a 2.5kg bag of potatoes costs £1.25. How much would 1 tonne of potatoes cost? A £5 B £20 C £50 D £200 E £500 From UKMT 2008 18 HOMEWORK 4 SECTION A 1 What is the area of the shape? Show your working. 2 What is the volume of the solid? Show your working. 3 4 Given the function x→3x What is its inverse? 5 Find the nth term for the following sequence. 6, 10, 14, 18, 22,… 6 If a = 3, b = -5, and c = 1 What is the value of b2 – 4ac 7 Multiply 5.65 by 17. You must show your working. 8 Divide 13.25 by 5. You must show your working. 9 Expand the bracket 10 Find the mean for the following data. 7, 5, 9, 6, 4, 5, Calculate the circumference of a circle with a radius of 5.7m 4a(3 – 2b) 19 SECTION B Level 6 Find the nth term for the following sequences. a) 3, 5, 7, 9, … …………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………… b) 8, 11, 14, 17, … …………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………… c) 50, 45, 40, 35, … …………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………… d) -5, -11, -17, -23, … …………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………… e) 1, 4, 9, 16, … …………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 20 Write the first 5 terms for the nth terms below. f) 2n + 7 …………………………………………………………………………………… …………………………………………………………………………………… g) 5n – 3 …………………………………………………………………………………… ………………………………………………………………………… h) 3n - 8 …………………………………………………………………………………… ………………………………………………………………………… i) 10 – 3n …………………………………………………………………………………… ………………………………………………………………………… j) n2 + 6 …………………………………………………………………………………… ………………………………………………………………………… 21 LEVEL 7 Generate the first 5 terms for these sequences: a) 2n2 + n ……..………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… b) 5n2 – 2n ……..……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… c) 3n2 + n -12 ……..………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… 22 Find the nth term for the following: a) 2, 8, 18, 32, … ……..……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………….. b) 2, 11, 27, 47. … ……..……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… c) -2, 5, 16, 31, … ……..……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… 23 Challenge The diagram shows a single floor tile in which the outer square has side 8cm and the inner square has side 6cm. If Adam Ant walks once around the perimeter of the inner square and Annabel Ant walks once around the perimeter of the outer square, how much further does Annabel walk than Adam? A 2 cm E 16 cm B 4 cm C 6 cm D 8 cm From UKMT 2008 24 HOMEWORK 5 SECTION A 1 What is the area of the shape? Show your working. 5cm 2 What is the volume of the solid? Show your working. 4 Given the function x→2x + 6 What is its inverse? 5 Find the nth term for the following sequence. 15, 12, 9, 6, … 6 If a = -1 , b = 4, and c = 2 What is the value of √𝑎 2 + 𝑏 2 7 Multiply 32.5 by 4.3. You must show your working. 8 Divide 39.48 by 12. You must show your working. 9 Expand the brackets and simplify. 3(x – 4) + 2(2x + 5) 10 Find the median for the following data 5, 9, 5, 6, 3, 4, 7,12 6cm 8cm 3 Calculate the area of a circle with a radius of 4cm 25 Section B of homework 5 will be issued as a separate booklet by your teacher. 26 HOMEWORK 6 SECTION A 1 What is the area of the shape? Show your working out. 2 What is the volume of the solid? Show your working. 3 4 Given the function Calculate the circumference of a circle with a What is its inverse? 5 Find the nth term for the following sequence. 6 If a = , b = , and c = What is the value of 7 Multiply by . You must show your working out. 8 Divide by . You must show your working out. 9 Expand the bracket 10 Find the for the following data 27 SECTION B Level 6 Complete the table: X10 X100 X1000 ÷10 ÷100 ÷1000 5.5 13.45 248.9 603.07 28 LEVEL 7 Work out the following without using a calculator 1. 4.8 x 0.2 = 2. 324 x 0.1 = 3. 72.5 x 0.01 = 4. 14.6 x 0.04= 5. 15.4 ÷ 0.1 = 6. 12.8 ÷ 0.02 = 7. 245 ÷ 0.05 = 8. 0.4 x 0.4 = 9. 1.22 = 10. 2.25 ÷ 0.15 = 29 Work out the following showing a clear written method: 23.54 x 1.25 0.35672 ÷ 0.14 = Challenge All of the Forty Thieves were light-fingered, but only two of them were caught red-handed. What Percentage was that? A2 B5 C 10 D 20 E 50 From UKMT 2008 30 HOMEWORK 7 SECTION A 1 What is the area of the shape? Show your working. 2 What is the volume of the solid? Show your working. 4cm 2cm 8cm 3cm 3 Calculate the circumference of a circle with a diameter of 7.4cm. 5 Find the nth term for the following sequence. 3, 5, 7, 9, 11, … 8cm 4 Given the function x→x + 3 What is its inverse? 6 If a = 2, b = 3, and c = 5 What is the value of: b2 – 4ac 7 Multiply 245 by 26. You must show your working. 8 Divide 2871 by 3. You must show your working. 9 Expand the bracket: 10 Find the median for the following data: 5(3a – 4) 3, 8, 5, 3, 0, 1, 11, 4 31 SECTION B Level 6 Round the following to 2 and 3 decimal places 2 dp 3 dp 37. 4275 …………… …………… 12.05062 …………… …………… 84.3969 …………… …………… 21.25843 …………… …………… 248.0118 …………… …………… 34.89959 …………… …………… 32 Worded problems 1. Holly buys three items costing £1.35, £5.47 and £6. 99. She calculates the price then rounds to the nearest pound. How much change, to the nearest pound, will she get from a £20 note? ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… 2. If Holly rounds the original prices to the nearest pound and calculates the change. Why are the answers different? ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… 33 Level 7 Round the following to 1 and 2 significant figures 1 sig fig 2 sig fig 37. 4275 …………… …………… 12.05062 …………… …………… 84.3969 …………… …………… 21.25843 …………… …………… 248.0118 …………… …………… 34.89959 …………… …………… Estimate the solutions to the following, show your method. 214 x 29 19 x 34 945 ÷ 8.91 28.19 ÷ 6.33 5.4122 15.21 – 3.842 34 Challenge King Harry’s arm is twice as long as his forearm, which is twice as long as his hand, which is twice as long as his middle finger, which is twice as long as his thumb. His new bed is as long as four arms. How many thumb lengths is that? A 16 E 256 B 32 C 64 D 128 From UKMT 2008 35