Maths Home Learning Task Year 9 Number Name Tutor Group Teacher Given out: Monday 10 October Hand in: Monday 17 October Parent/Carer Comment Staff Comment ATL Level Targets to Improve:
Instructions You should attempt as many of the tasks as you can. These are the minimum amounts expected of you: Set 1: Attempt all of the tasks. Set 2: Set 3: Set 4: Attempt the first 9 tasks. Attempt the first 7 tasks. Attempt the first 5 tasks. This booklet should take 5 hours to complete so spread the work out over all 5 days. Complete the tasks neatly in the spaces provided and show all working. Remember to fill in the evaluation sheet at the end before you hand the booklet in. KEYWORDS: Fraction of amount, equivalent fraction, simplify, percentage, ratio, square root, multiplier, percentage change, standard form, interest, compound interest, surd. Topics to revise: To help with this booklet you may wish to revise the following topics on My Maths or any other resources (including your teacher):- Negative numbers Fractions of amounts Equivalent Fractions Rounding to nearest 100, 1000 Percentages of amounts Sharing into ratio and proportion Multipliers and percentages Interest and percentages Standard form Surds
Task 1: Number Problems (Level 3) a) Triangular Sums:- The numbers in the two circles add together to give the number in the square between them. Fill in the gaps below. 41 52 23 19 23 36 b) Multiplication grids:- Fill in the missing numbers in the grid. X 2 3 7 2 14 4 5 15 6 12 X 3 4 10 1 8 7 21 80 X 1 3 8 16 7 2 12 c) Complete the calculations and use the code to write a word. M T I C E A H S 24 50 18 20 6 8 12 36 6 X 4 = 18 12 = 2 X 9 = 11 3 = 3 X 8 = 4 X 5 = 25 X 2 = 2 X 4 = 9 X 4 = 3 X 4 = 150 100 =
Task 2: Numbers in Europe (Level 4) In the table below is some of Europe s coldest temperatures ever recorded. Country Temp (C) Iceland - 37 United Kingdom - 27 Spain - 32 Malta 2 Portugal -16 Sweden - 53 Italy - 49 a) Put the countries temperatures in order of size, starting with the coldest. b) The temperature in Sweden this year was 39 C warmer than the coldest recorded. Calculate Sweden s temperature for this year. c) Calculate the difference in temperatures between Malta and the UK. d) Charlie says If you add the temperatures in Iceland, Spain and Sweden the total will be bigger than -100 C. Show that he is correct. e) Using the table of European mountain heights, round each height to the nearest 100 and 1000 m. Mountain Height (m) Nearest 100m Nearest 1000m Ben Nevis 1344 Mont Blanc 4807 Matterhorn 4478 Mount Elbrus 5642
Task 3: Shopping style (Level 4) Sandra owns a shop, the layout of the shop is shown in the diagram below. a) Using the diagram calculate the percentage being represented by each section of shop. (HINT: % is out of 100, what is one square worth?) Till Bags Till: % Gifts Clothes Gifts: % Clothes: % Bags: % a) The following items are sold at Sandra s shop. 30 25 55 Sandra has a sale, the items above have 10% off Calculate the new prices. Show your working c) In the gift section, Sandra has the following items. 6.00 10.00 12.00 The items above have 20% off. Amy wants to buy all the items, she has 20. How much do the items cost in the sale? Does Amy have enough? Show your working
Task 4: Problems of Vast Proportion (Level 5) a) Lily wants to make 18 cakes, how much of each ingredient does she need? Eggs: Flour: Sugar: Butter: Vanilla: b) Ben wants to make 30 cakes, how much of each ingredient does he need? Eggs: Flour: Sugar: Butter: Vanilla: Cake Emporium 5 cases for 1.20 Kath s Cakes 10 cases for 2.50 c) Lily wants to buy some spotty cases for her fairy cakes, which shop is the cheapest? How many packs will she need to buy? d) Ben is going to sell his 30 cakes at the school fete. He is going to charge 40p per cake. Ben paid 4.30 for his ingredients. How much profit does he make?
Task 5: Fraction Frenzy (Level 5) a) Find sets of equivalent fractions (one has been completed for you). 2 3 10 12 6 8 10 25 3 10 20 24 4 6 30 100 9 12 2 5 3 4 5 6 6 20 8 12 4 10 b) Sam is following a recipe and is using some ingredients, the recipe is given in fractions of amounts. Calculate how much of each ingredient she needs. i) 3 of 450g (flour) = 5 ii) 5 of 220g (sugar) = 11 iii) 4 of 45ml (golden syrup) = 9 iv) 5 of 480ml (milk) = 6 1 c) Johnny inherits 450 from his nan. He spends 25 on sweets, 4 on a games 9 console, and 1 on clothes. How much does he have left? SHOW YOUR WORKING 10
Task 6: Primes, Factors and Multiples (Level 6) a) Find the HCF (highest common factor) of the following pairs of numbers: i) 30 and 42 = ii) 18 and 66 = b) Find the LCM (lowest common multiple) of the following pairs of numbers: i) 15 and 25 = ii) 33 and 21 = c) Tom, Sam and Matt are counting drum beats. Tom hits a snare drum every 2 beats Sam hits a kettle drum every 5 beats Matts hits a bass drum every 8 beats. Tom, Sam and Matt start by hitting their drum at the same time. How many beats is it before they next hit their drums at the same time? d) Find the prime factor decomposition of 72 (HINT find factor pairs).
Task 7: Roaring Ratios (Level 6) a) On Friday, the ratio of Ralph the Lion s sleeping to the time awake was 3 : 5. Ralph slept for less time than he was awake. How many hours was Ralph sleeping? (Show your working) b) On Saturday Ralph slept for one hour more than he did on Friday. Show the ratio of the time he is sleeping to being awake. (Simplify the ratio) c) Ralph eats 63 kg worth of food per week. He eats vegetables, fruit and meat in the ratio of 1: 2: 4. How much of each food type does Ralph eat? Vegetables = Fruit = Meat =
Task 8: Getting to the Root of the Problem (Level 6) a) Tom is wanting to fence his garden. However, the length of his garden has been given as roots of numbers. Calculate the perimeter of his garden in metres. 81 36 Not drawn accurately Perimeter = b) Sarah bought a ring in a cube-shaped box with a volume 8 cm³. She put the ring box in her jewellery box, also a cube. The jewellery box is 6 times as long as the ring box. i) What is the volume of the jewellery box? ii) How many ring boxes can Sarah fit in her jewellery box?
Task 9: Polly s Percentages (Level 7) a) Match each percentage change to the correct multiplier ticket. 10% Rise 15% Fall 25% Rise 5% Loss 15% Rise 50% Decrease 0.85 1.1 0.95 0.5 1.25 1.15 b) Polly has done a stock take of clothing in her shop and has decided to change the prices of the following items. Calculate the new prices using multipliers. (YOU MUST SHOW YOUR WORKING) Shirt = Jeans = Shoes =
Task 10: Population Percentages (Level 7) The table below shows the country s population (in millions) in 2000 and 2012. Country Population (2000) Population (2012) Percentage Change China 1269 1343 5.8% increase India 1004 1205 United States 282 313 Indonesia 214 248 Brazil 176 193 Pakistan 146 190 Nigeria 123 170 Bangladesh 130 161 Russia 147 143 Japan 127 127 Calculate the percentage change of each country and fill in the table above. Which country had the biggest percentage change? Example:- China = 1343 1269 = 74 74 1269 x 100 = 5.8% increase Working
Task 11: Spacey Standard Form (Level 8) The table shows the diameters of the planets in the solar system in standard form. a) Which planet has the biggest diameter? (Give your answer as an ordinary number) b) Which planet has the smallest diameter? (Give your answer as an ordinary number) c) The planet Zog has a diameter of 5 340 000 metres. Write this number in standard form. a) Put the planets in order of size, starting with the smallest. 1. 5. 9. 2. 6. 3. 7. 4. 8.
Task 12 : Sort After Savings. (Level 8) Bertie s Bank Receive 100 bonus when you invest 2000 or more. 5.1% interest Sally s Savings 5.1% interest on the first 3000 then 6.4% on any further investment. Percy s Pennies 50 set-up fee. Invest a maximum if 3600 a year. 6.4% interest Josie has 3500 she wants to invest into a savings account, she wants to save for 3 years. Which savings account shown above will give her the most interest after the 3 years? (HINT: After the 1 st year, Josie will gain interest on the interest earned already in year 2 and so on.) SHOW ALL YOUR WORKING Bank:
Task 13: Soapy Surds (Level 8) Chris and Mary are decorating their kitchen and bathroom and have purchased new sinks. 11 + 2 11-2 a) The lengths of the kitchen sink is shown above. Calculate the perimeter of the sink. Simplify your answer, leave in surd form b) The area of the square bathroom sink is 80 cm² (to the nearest cm). Calculate the length of one side. Give your answer in surd form. (HINT: Simplify surd)
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