Neston High School Mathematics Faculty Homework Booklet

Transcription

1 Neston High School Mathematics Faculty Homework Booklet Year: 11 Scheme: Higher

2 Homework Sheet 1 Week Commencing: 11 th December : The number of bacteria doubles in size every 3 hours. If C11: Find the volume of this sphere. there are 40 bacteria at the start of the day, how many are there 6 hours later? C2: An area of 16 m 2 can be covered by 1.5 litres of paint. How many litres are needed to cover 20 m 2? 12: Alan asks his friends to fill in a questionnaire for him. Suggest why this is not a suitable sampling method. C3: 35% of a number is 17. Work out the number. 13: Give the equation of the straight line graph that passes through the coordinates (0, 5) and (2, 9). 4: people attend a concert. Tickets for the concert cost Use approximations to estimate the total amount of money the concert makes. 14: Find the value of x. C5: Concrete is made by mixing cement, sand and gravel in the ratio 1:2:3. James is mixing 90 kg of concrete when he accidently adds an extra 6 kg bucket of sand. How much cement and gravel will he need to add to ensure the correct ratio for the concrete? 15: The formula P = 2(l + w) calculates the perimeter of a rectangle. Find w if P = 21 and l = 8. C6: The equation 0 = x 3 2x 2 5x + 7 has 3 solutions. The iterative formula u n+1 = u n 3 2u 2 n +7 can find one of the 5 solutions. Use u1 = 1 and solve the equation to 2 dp. 16: I think of a number. I multiply it by 4 and add 5. The answer I get is 33. What number was I thinking of? C7: Find the circumference of this circle. C17: A right-angled triangle has short sides of 5 cm and 9 cm. Find the longest side of the triangle. C8: Find the area of this shape. C18: A right-angled triangle has short sides of 5 cm and 9 cm. Which trigonometry ratio applies to these two sides? C9: Find the volume of this cylinder. C19: Find the length AC. C10: Find the volume of this cone. 20: Write down the exact value of sin 30 o without using a calculator Mark: Effort:

3 Exam Question Homework: Growth and Decay problems

4 Homework Sheet 2 Week Commencing 18 th December 2017 C1: The number of bacteria doubles in size every 3 hours. If C11: Find the surface area of this sphere. there are 40 bacteria at the start of the day, how many are there 12 hours later? C2: A group of 50 people have rations that would last for 3 months. For how many months would the same amount of food last 30 people? 12: Joan wants to survey pupils in her school about the school lunches. Describe a way that Joan could collect a sample of students. C3: 17% of a number is 35. Work out the number. 13: Give the equation of the straight line graph that passes through the coordinates (4, 5) and (2, 9). C4: people attend a concert. Tickets for the concert cost Calculate the amount of money the concert earns. Give your answer to an appropriate accuracy. 14: Find the value of x C5: Russell, Sarah, and Terry share money in the ratio 2:5:8. Russell gets 120 less than Terry. Work out how much each gets. C6: The equation 0 = x 3 2x 2 5x + 7 has 3 solutions. The iterative formula 3 u n+1 = 2u 2 n + 5u n 7 can find two of the solutions. Use u1 = 3 and solve the equation to 2 dp. C15: The formula A = ½bh calculates the area of a triangle. Find b if A = 7, and h = 5. 16: Jen is 5 years older than Ross. Jen and Ross have a total age of 33 years. Work out Jen s age. C7: Find the area of this circle. C17: A right-angled triangle has short sides of 7 cm and 12 cm. Find the longest side of the triangle. C8: Find the perimeter of this shape. C18: The hypotenuse of a right-angled triangle is 11 cm and another side is 6 cm. Which trigonometric ratio would be used to find the angle between the two sides? C9: Find the surface area of this cylinder. C19: Find the length AF. C10: Find the surface area of this cone. 20: Write down the exact value of sin 60 o without using a calculator. Mark: Effort:

5 Exam Question Homework: Proportion and Percentage problems

6 Homework Sheet 3 Week Commencing 8 th January 2018 C1: The number of bacteria doubles in size every 3 hours. If C11: Find the volume of this sphere. there are 40 bacteria at the start of the day, how many are there a day later? C2: An area of 16 m 2 can be covered by 1.5 litres of paint. What area can be covered with 2.5 litres of paint. 12: A graph has the equation y= 5x + 2. What is a) Its gradient? b) the coordinate of the y-intercept C3: A bottle of lemonade has 12.5% extra free. The bottle is normally 1.25 litres. Work out the size of the new bottle. Give the equation of the straight line graph that passes through the coordinates (2, 5) and (4, 9). 4: people attend a football match. Tickets cost Estimate the amount of money that the club make from tickets. 14: Find the value of x. C5: Use trial and improvement to solve the equation x 3 + 2x = 10. Start with x = 2. Give your answer to 1 dp. C15: The formula y = 3x + 2 plots the graph of a straight line. Find x when y = 7. C6: The equation 0 = x 3 2x 2 5x + 7 has 3 solutions. The iterative formula 3 u n+1 = 2u 2 n + 5u n 7 can find two of the solutions. Use u1 = -2 and solve the equation to 2 dp. 16: The cost to hire a bicycle is 2.50 per hour plus a 5 hire charge. If James pays 22.50, how long can he have the bicycle? C7: Find the circumference of this circle. C17: A right-angled triangle has short side of 6 cm and longest side of 18 cm. Find the middle side of the triangle. C8: Find the area of this shape. C18: Use your calculator to find the value of sin 82 o to 3 significant figures. C9: Find the volume of this cylinder. C19: Find the angle CA ˆ F C10: Find the volume of this cone. 20: Write down the exact value of sin 45 o. Mark: Effort:

7 Exam Question Homework: Accuracy Problems (a) A plant costs 4.99 How many of these plants can be bought for 50? Answer... (2) (b) Jill writes = 998 Is she correct? Explain your answer (2) (Total 4 marks) A car travels 200 kilometres in 3 hours 30 minutes. Calculate its average speed in kilometres per hour. Give your answer to an appropriate degree of accuracy Answer... kilometres per hour (4) Francis has 45 to spend at the garden centre. He wants to buy a bird table costing and six bags of birdseed costing 2.95 each. Show how he can work out in his head that 45 will be enough. Do not work out the exact amount. [2]

8 Homework Sheet 4 Week Commencing 15 th January 2018 C1: A ball bounces to ¾ of its previous height. If the ball is C11: Find the surface area of this sphere. dropped from 2 metres, what is its height after one bounce? C2: A group of 50 people have rations that would last for 3 months. How many people could survive on the same food for 8 months? 12: A graph has the equation y= 8-3x. What is a) Its gradient? b) the coordinate of the y-intercept? C3: A jacket has its price reduced by 30% in a sale. If the sale price is Work out the original price of the jacket. Give the equation of the straight line graph that passes through the coordinates (5, 4) and (9, 2). C4: people attend a football match. Tickets cost Calculate the amount of money that the club make from tickets. Give your answer to a suitable accuracy. 14: Find the value of x. C5: Use trial and improvement to solve the equation x 3 + 2x = 10. Start with x = 2. Give your answer to 2 dp. C15: The formula A = πr 2 finds the area of a circle. Find r if A = 628. C6: The equation 0 = x 3 + x 2 5x 1 has 3 solutions. The iterative formula 3 u n+1 = u 2 n + 5u n + 1 can find two of the solutions. Use u1 = 1 and solve the equation to 2 dp. 16: I think of a number. I divide it by 3 and subtract 5. The answer I get is 7. What number did I think of? C7: Find the area of this circle. C17: A right-angled triangle has a longest side of 25 cm and a middle side of 9 cm. Find the shortest side of the triangle. C8: Find the perimeter of this shape. C18: Use your calculator to find the value of cos 11 o to 3 significant figures. C9: Find the surface area of this cylinder. C19: Find the angle AF ˆ C C10: Find the surface area of this cone. 20: Write down the exact value of cos 30 o. Mark: Effort:

9 Exam Question Homework: Iterative methods

10 Homework Sheet 5 Week Commencing 22 nd JJanuary 2018 C1: A ball bounces to ¾ of its previous height. If the ball is C11: Find the volume of this shape. dropped from 2 metres, what is its height after two bounces? C2: An area of 16 m 2 can be covered by 1.5 litres of paint. How many litres are needed to cover 40 m 2? 12: A graph has the equation 3x + y= 5. What is a) Its gradient? b) the coordinate of the y-intercept C3: An investment earns 4.6% per annum. If Umar invests for 3 years, how much will he have at the end of the 3 years. 4: A new car costs Erin is pays 8000 deposit and then pays the remainder of the balance over 5 years. Use approximations to estimate Erin s monthly payment for the car. 13. Give the equation of the straight line graph that passes through the coordinates (9, 4) and (5, 2). 14: Find the value of x C5: Use trial and improvement to solve the equation x 3 + 2x = 50. Start with x = 3. Give your answer to 1 dp. C15: The formula E = Ri 2 calculates electrical energy. Find R if E = 12 and i = 3. C6: The equation 0 = x 3 + x 2 5x 1 has 3 solutions. The iterative formula 3 u n+1 = u 2 n + 5u n + 1 can find two of the solutions. Use u1 = -2 and solve the equation to 2 dp. 16: A cup of tea costs x pence. Coffee costs 20 pence more. Hermes buys 2 cups of tea and one cup of coffee. In total Hermes pays Work out the cost of a cup of tea. C7: Find the circumference of this circle. C17: A right-angled triangle has short sides of 2 cm and 13 cm. Find the longest side of the triangle. C8: Find the area of this shape. C18: Use your calculator to find the value of tan 50 o to 3 significant figures. C9: Find the volume of this cylinder. C19: Find the length BD. C10: Find the volume of this cone. 20: Write down the exact value of cos 60 o. Mark: Effort:

11 Exam Question Homework: Circles and Part Circles

12 Homework Sheet 6 Week Commencing 29 th January 2018 C1: A ball bounces to ¾ of its previous height. If the ball is C11: Find the surface area of this shape. dropped from 2 metres, what is its height after five bounces? C2: A group of 50 people have rations that would last for 3 months. For how many months would the same amount of food last 15 people? 12: A graph has the equation 2y = 8x + 3. What is a) Its gradient? b) the coordinate of the y-intercept C3: 107% of a number is Work out the number. 13: Work out the length of the line between the corrdinates (2, 5) and (5, 9). C4: A new car costs Erin is pays 8000 deposit and then pays the remainder of the balance over 5 years. Calculate Erin s monthly car payment. Give your answer to a suitable accuracy. 14: Find the value of x C5: Use trial and improvement to solve the equation x 3 + 2x = 50. Start with x = 3. Give your answer to 2 dp. C15: The formula I = PRT calculates simple interest. Find P if 100 I = 3, R = 5, and T = 12. C6: The equation 0 = x 3 + x 2 5x 1 has 3 solutions. The iterative formula u n+1 = u n 3 +u 2 n 1 can find one of the 5 solutions. Use u1 = 0 and solve the equation to 2 dp. 16: Thomas is going hiking. He buys a bottle of water for 80p and 4 chocolate bars. Thomas pays Work out the cost of one chocolate bar. C7: Find the area of this circle. C17: A right-angled triangle has short sides of 8 cm and 9 cm. Find the longest side of the triangle. C8: Find the perimeter of this shape. C18: A right-angled triangle has short sides of 5 cm and 9 cm. Find the size of the angle between the 9 cm side and the hypotenuse. C9: Find the surface area of this cylinder. C19: Find the length BH. C10: Find the surface area of this cylinder. 20: Write down the exact value of cos 45 o. Mark: Effort:

13 Exam Question Homework: Volume of Curved shapes

14 Homework Sheet 7 Week Commencing 5 th February 2018 C1: A ball bounces to ¾ of its previous height. If the ball is C11: Find the volume of this sphere. dropped from 2 metres, what is its height after two bounces? C2: An area of 16 m 2 can be covered by 1.5 litres of paint. How much space can be covered with 7 litres? 12. Write the equation of the line that is parallel to y=3x + 9 and goes through the coordinate (0, 4) 3: Find 52% of : Work out the length of the line between the corrdinates (5, 5) and (3, 9). 4: A car s milometer shows miles. The car is 12 years old. Use approximations to estimate the number of miles travelled every month. 14: Find the value of x. C5: Use trial and improvement to solve the equation x 3 10x = 50. Start with x = 5. Give your answer to 1 dp. C15: The formula E = ½mv 2 calculates the energy of a moving body. Find m if E = 45, and v = 5. C6: The equation 0 = x 3 5x 1 has 3 solutions. The iterative formula u n+1 = u n 3 1 can find one of the solutions. 5 Use u1 = 0 and solve the equation to 2 dp. C16: Harim buys t-shirts online. Shipping costs 6.99 for the order. Each t-shirt costs Harim has 75 to spend. How many t-shirts can he buy? C7: Find the circumference of this circle. C17: A triangle has sides of 8 cm, 15 cm and 17 cm. Is the triangle right-angled? Show how you decide. C8: Find the area of this shape. C18: The hypotenuse of a right-angled triangle is 11 cm and another side is 6 cm. Find the angle between the two sides. C9: Find the volume of this cylinder. C19: Find the angle AB ˆ D. C10: Find the volume of this cone. 20: Write down the exact value of tan 30 o. Mark: Effort:

15 Exam Question Homework: Surface area of curved shapes A test tube is formed from a cylinder and a hemisphere as shown. Work out the total surface area of the test tube. (4) The diagram shows an object made from two cones, one on top of the other. The top cone has a slant height of 8 cm and the bottom cone has a slant height of 10 cm. Both cones have a radius of 5 cm. Find the total surface area of the object.

16 Homework Sheet 8 Week Commencing 12 th February 2018 C1: The height of a tree increases by 1 every 4 months. If the C11: Find the surface area of this sphere. tree is originally planted when it is a metre tall, work out how tall it would be four months later. 20 C2: A tank of oil can be emptied in 16 minutes if 3 outlet valves are opened. How quickly could the oil be emptied with 4 valves open? C3: Susan is on a diet. She starts off weighing 80 kg. In 3 months she loses 4.2%. Find her weight after 3 months. 12. Write the equation of the line that is parallel to y= 9-3x and goes through the coordinate (0, 4) C13: Work out the length of the line between the corrdinates (1, 5) and (5, -1). Give your answer to 1 decimal place. C4: A car s milometer shows miles. The car is 12 years old. Calculate the average number of miles the car travels every month. Give your answer to a suitable accuracy. 14: Find the value of x C5: Use trial and improvement to solve the equation x 3 10x = 50. Start with x = 5. Give your answer to 2 dp. C15: The formula P = E calculates power. Find E if P = 1.6 t and t = 25. C6: The equation 0 = x 3 5x 1 has 3 solutions. The 3 iterative formula u n+1 = 5u n + 1 can find two of the solutions. Use u1 = 3 and solve the equation to 2 dp. C16: Padraig earns 2000 a month plus 5% commission on his sales. In one month he earns How much were Padraig s sales? C7: Find the area of this circle. C17: C8: Find the perimeter of this shape. C18: A right-angled triangle has a side of 8 cm separated from the hypotenuse by an angle of 28 o. Find the length of the hypotenuse. C9: Find the surface area of this cylinder. C19: Find the angle BD ˆ A. C10: Find the surface area of this cone. 20: Write down the exact value of tan 60 o. Mark: Effort:

17 Exam Question Homework: Sampling and Questionnaires The number of rabbit in a field increases by a quarter every year. At the start of the first year there are 20 rabbits. How many rabbits will there be after 5 years? [2 Marks]

18 Homework Sheet 9 C1: The height of a tree increases by 1 every 4 months. If the tree is originally planted when it is a metre tall, work out how tall it would be eight months later. 20 Week Commencing Spring Half Term C11: Find the volume of this sphere. C2: The dosage of medicine is based upon the weight of the person taking the medicine. A person weighing 40kg is allowed a dosage of 1.8 mg. Work out the safe dosage of a person weighing 50 kg. 12. Write the equation of the line that is parallel to y = 3x + 9 and goes through the coordinate (5, 9) C3: A fridge freezer has its price reduced by 15%. If its new price is 76.49, what was the original price. 13: Work out the length of the line between the corrdinates (-2, 5) and (-8, 1). Give answer to 1 decimal place. 4: A 25-year mortgage is worth Use approximations to estimate the monthly cost of the mortgage. 14: If the perimeter of this rectangle is 30, find the value of x. C5: Use trial and improvement to solve the equation x x = 50. Start with x = 2. Give your answer to 1 dp. C15: The formula E = mgh calculates the potential energy of an object due to gravity. Find h if E = 245, m = 10 and g = 9.8. C6: The equation 0 = x 3 5x 1 has 3 solutions. The 3 iterative formula u n+1 = 5u n + 1 can find two of the solutions. Use u1 = -3 and solve the equation to 2 dp. C16: I think of a number. I multiply the number by 5. I then subtract the result from 40. The answer I get is 27. Work out the number I was thinking of. C7: Find the perimeter of this shape. C17: C8: Find the area of this shape. C18: A right-angled triangle has a hypotenuse of 12 cm separated from another side by an angle of 68 o. Find the length of the third side. C9: Find the volume of this shape. C19: Find the angle DB ˆ H. C10: Find the volume of this cone. 20: Write down the exact value of tan 45 o. Mark: Effort:

19 Exam Question Homework: Equations and Shapes

20 Homework Sheet 10 C1: The height of a tree increases by 1 every 4 months. If the tree is originally planted when it is a metre tall, work out how tall it would be two years later. 20 C11: Find the surface area of this sphere. C2: A tank of oil can be emptied in 16 minutes if 3 outlet valves are opened. How many valves need to be open for the tank to be emptied in under 10 minutes? 12. Write the equation of the line that is perpendicular to y = 3x + 9 and goes through the coordinate (6, 9) C3: The price of a car depreciates by 6% every year. After 6 years the car is worth Work out its price when new. 13: Work out the length of the line between the corrdinates (-2, 5) and (-8, 1). Give answer to 1 decimal place. C4: A 25-year mortgage is worth Calculate the monthly cost of the mortgage. Give your answer to a suitable accuracy. 14: Find the value of x C5: Use trial and improvement to solve the equation x x = 50. Start with x = 2. Give your answer to 2 dp. C15: The formula a = v u calculates the average acceleration t of a moving body. Calculate v if a = 0.3, u = 7 and t = 4. C6: The equation 0 = x 3 3x has 3 solutions. The 3 iterative formula u n+1 = 3u 2 n 1 can find one of the solutions. Use u1 = 2 and solve the equation to 2 dp. C16: The difference between two numbers is 7. The larger number is 5 less than 3 times more the smaller number. Work out the smaller number. C7: Find the area of this shape. C17: Two sides of a right-angled triangle are 11 cm and 6 cm. Find the two possible third lengths. C8: Find the perimeter of this shape. C18: A ramp has a length of 6 m and is at an angle of 50 o above the horizontal. Work out the vertical distance the ramp covers. C9: Find the surface area of this shape. C19: Find the angle DH ˆ B. C10: Find the surface area of this shape. 20: Find the exact size of the hypotenuse in this triangle. Mark: Effort:

21 Exam Question Homework: Equation problems

22 Homework Sheet 11 C1: Atmospheric pressure decreases by 1 for every 1000 metres climbed. The pressure at sea level is about 1050 hpa. Work out the pressure at 1000 metres. 10 C11: Find the volume of this shape. C2: The dosage of medicine is based upon the weight of the person taking the medicine. A person weighing 40kg is allowed a dosage of 1.8 mg. Work out the weight of a person with a safe dosage of 2.5 mg. 12. Write the equation of the line that is perpendicular to y = 9-3x and goes through the coordinate (6, 9) C3: A house increases in price by 2.4% every year. If the house costs in 2012, work out its price in : Work out the length of the line between the corrdinates (-2, 5) and (-8, 1). Give answer to 1 decimal place. 4: There are people living in a city. The city has an area of km 2. Use approximations to estimate the population density of the city. 14: If the perimeter is 40, find the value of x. C5: Use trial and improvement to solve the equation x 3 5x = 15. Start with x = 3. Give your answer to 1 dp. C6: The equation 0 = x 3 3x has 3 solutions. The iterative formula u n+1 = u n 3 +1 can find one of the 3 solutions. Use u1 = 0 and solve the equation to 2 dp. C15: The formula v = u + at calculates the velocity of an accelerating body. Calculate the value of a if v = 12, u = 2 and t = 5. C16: Sarah hires a car for her holiday. The cost is 60 hire charge plus 28 per day. Sarah pays 312. How many days does Sarah hire the car for? C7: Find the perimeter of this shape. C17: An equilateral triangle has sides of 6 cm. Find its perpendicular height. C8: Find the area of this sector. C18: Calculate the perimeter of this triangle. C9: Find the volume of this shape. C19: Find the length AC in this square based pyramid. C10: Find the volume of this cone. 20: Find the exact size of the hypotenuse in this triangle. Mark: Effort:

23 Exam Question Homework: Pythagoras

24 Homework Sheet 12 C1: Atmospheric pressure decreases by 1 for every 1000 metres climbed. The pressure at sea level is about 1050 hpa. Work out the pressure at 3000 metres. 10 C11: Find the surface area of this shape. C2: A tank of oil can be emptied in 16 minutes if 3 outlet valves are opened. How quickly could the oil be emptied with 10 valves open? Give your answer in minutes and seconds. 12. Write the equation of the line that is perpendicular to y = 1 x + 3 and goes through the coordinate (1, 9) 2 C3: 65% of a number is Work out the number. 13: Work out the length of the line between the corrdinates (-2, 5) and (-8, 1). Give answer to 1 decimal place. C4: There are people living in a city. The city has an area of km 2. Calculate the population density of the city. Give your answer to a suitable accuracy. 14: Find the value of x C5: Use trial and improvement to solve the equation x 3 5x = 15. Start with x = 3. Give your answer to 2 dp. C15: The formula v 2 = u 2 + 2as calculates velocity of an accelerating body. Calculate a if v = 5, u = 7 and s = 8. C6: The equation 0 = x 3 3x has 3 solutions. The iterative formula u n+1 = 2u n 3 1 3(u n 2 u n ) can find one of the solutions. Use u1 = -1 and solve the equation to 2 dp. C16: I think of a number. I multiply it by 6 and subtract 9. The answer I get is the same as 4 times my original number. Work out the number I thought of. C7: Find the area of this shape. C17: An isosceles triangle has two sides of 5 cm and a base of 8 cm. Work out the perpendicular height. C8: Find the perimeter of this sector. C11: Calculate the area of this triangle. C9: Find the surface area of this shape. C19: Find the length AO in this square based pyramid. C10: Find the surface area of this cone. 20: Find the exact size of x in this triangle.

25 Mark: Exam Question Homework: Trigonometry Effort: Triangle ABC has a right angle at B. Angle BAC = 38 AB = 7.21 cm Not drawn accurately Calculate the length of BC. Give your answer to an appropriate degree of accuracy. (Total 4 marks)

26 Homework Sheet 13 C1: Atmospheric pressure decreases by 1 10 for every 1000 metres climbed. The pressure at sea level is about 1050 hpa. Work out the pressure at metres. C11: Find the volume of this shape. C2: The dosage of medicine is based upon the weight of the person taking the medicine. A person weighing 40kg is allowed a dosage of 1.8 mg. Work out the safe dosage of a person weighing 85 kg. 12. Write the equation of the line that is perpendicular to y = 1 x + 3 and goes through the coordinate (1, 9) 2 C3: The amount of radioactive material in a given mass reduces by 5% every 10 years. Work out the percentage reduction after a century. 13: Work out the length of the line between the corrdinates (-2, 5) and (-8, 1). Give answer to 1 decimal place. 4: A holiday costs 489 per person. A family of 4 is going on the holiday. They pay a 200 deposit and then the balance in 8 instalments. Use approximations to estimate the amount of each instalment. 14: Find the value of x. C5: Use trial and improvement to solve the equation x 3 + 5x = 15. Start with x = 1. Give your answer to 1 dp. 15: The formula s = ut + ½at 2 gives the displacement of an accelerating body. Find a if s = 30, u = 3, and t = 2. C6: The equation 0 = x 3 3x 2 x + 1 has 3 solutions. The iterative formula u n+1 = 3u n 2 +u n 1 can find one of the u n solutions. Use u1 = 2 and solve the equation to 2 dp. C16: A year group is going on a trip. They book coaches with 48 seats. The last coach is only half full. Altogether 360 people are going on the trip. Work out how many coaches the school books. C7: Find the perimeter of this shape. C17: Calculate the perimeter of this trapezium. C8: Find the area of this sector. C18: The value of sin θ = 0.7. Find the size of the angle θ to the nearest degree. C9: Find the volume of this shape. C19: Find the length AV in this square based pyramid. C10: Find the volume of this cone. 20: Find the exact size of the side x. Mark: Effort:

27 Exam Question Homework: Exact trig angles Ali uses this method to estimate the height of a flag pole. He stands, as shown, so that his angle of sight is 45 when he looks up to the top of the flag pole. He then measures his distance from the flagpole. Finally he measures the distance that his eyes are above the ground. This sketch shows Ali s measurements. Not drawn accurately Use Ali s measurements to calculate the height of the flag pole, explaining why he uses an angle of 45. (2) The diagram shows two right-angled triangles. AD = 40 cm CD = 7 cm cos x = Not drawn accurately Find the exact value of sin y. (Total 6 marks)

28 Homework Sheet 14 C1: Atmospheric pressure decreases by 1 for every 1000 metres climbed. The pressure at sea level is about 1050 hpa. Work out the height at which the pressure falls below 105 hpa. C2: A tank of oil can be emptied in 16 minutes if 3 outlet valves are opened. How many valves would be needed to empty the tank in 7 minutes? 10 C11: Find the surface area of this shape. 12. Write the equation of the line that is perpendicular to y = 2 x + 3 and goes through the coordinate (8, 9) 3 C3: The amount of radioactive material in a given mass reduces by 5% every 10 years. Work out the time taken for the radioactivity to reduce to less than 50% of its initial value. 13: Work out the length of the line between the corrdinates (-2, 5) and (-8, 1). Give answer to 1 decimal place. C4: A holiday costs 489 per person. A family of 4 is going on the holiday. They pay a 200 deposit and then the balance in 8 instalments. Calculate the cost of each instalment. Give your answer to a suitable accuracy. 14: The perimeter of the rectangle is 15. Find the value of y. C5: Use trial and improvement to solve the equation x 3 + 5x = 15. Start with x = 1. Give your answer to 2 dp. 15: The formula F = 9 C + 32 converts temperature in 5 Celsius to temperature in Fahrenheit. Find the temperature that is the same when measured in Fahrenheit or Celsius. C6: The equation 0 = x 3 3x 2 x + 1 has 3 solutions. The iterative formula u n+1 = u n 3 u n +1 can find one of the 3 solutions. Use u1 = 0 and solve the equation to 2 dp. C16: Nick is x years old. His brother is 12 years older. In 8 years Nick will be ½ his brothers age. Work out Nick s age. C7: Find the area of this shape. C17: Calculate the area of this trapezium. C8: Find the perimeter of this sector. C18: A ladder of length 6m leans against a wall. The foot of the ladder is at a distance of 3m from the base of the wall. Calculate the angle between the ladder and the ground. C9: Find the surface area of this shape. C19: Find the angle AV this square based pyramid. O ˆ in C10: Find the surface area of this cone. 20: Find the exact size of the side x. Mark: Effort:

29 Exam Question Homework: 3D Pythagoras and Trigonometry

30 Sheet Mark Question Topic 1 Growth and Decay problems 2 Direct and Inverse Proportion 3 Percentage problems 4 Accuracy problems 5 Ratio 6 Iterative methods 7 Circles 8 Arc Length and Sector Area 9 Cylinders 10 Cones 11 Spheres 12 Linear Lines parallel and perpendicular 13 Linear Lines equation and length 14 Equations and Shapes 15 Equations and Formulae 16 Equations and problems 17 Pythagoras Theorem 18 Trigonometry 19 3D Pythag and Trig 20 Exact angles and trigonometry Homework 1 Homework 2 Homework 3 Homework 4 Homework 5 Homework 6 Homework 7 Homework 8 Homework 9 Homework 10 Homework 11 Homework 12 Homework 13 Homework 14 Homework 2 Target Homework 3 Target Homework 4 Target Homework 5 Target Homework 5 Target Homework 6 Target Homework 7 Target Homework 8 Target Homework 9 Target Homework 10 Target Homework 11 Target Homework 12 Target Homework 13 Target Homework 14 Target

31 Exam Question Holiday Homework: For a ladder to be safe it must be inclined at between 70 and 80 to the ground. (a) The diagram shows a ladder resting against a wall. Not to scale Is it safe? You must show your working. (3)

32 (b) Another ladder rests against a wall. Not to scale Work out the closest distance that the bottom of the ladder can be from the wall so that it is safe Answer... m (3) (Total 6 marks)

33