Year 11 General Mathematics Linear relations and equations: Assessment Part 2 Name:_________________________________ 1 Marks : _____/34 % Grade: Find the values of the following: a E = IR when I = 5 and R = 3 b A= c S = 90(2n – 4), when n = 6 rl when = 3.14, r = 5, l = 20 (3 marks) 2 Solve 𝑧 = 4𝑥 − 3𝑦 for 𝑦. (2 marks) Page 1 of 5 Year 11 General Mathematics Linear relations and equations: Assessment Part 2 3 Density plays an important role in our understanding of the physical properties of Earth materials. The equation for density is similar to that for velocity and, as such, it can be manipulated so that you can solve for any of the variables involved. The next few problems utilize the equation for density: a) Rearrange the density to create an equation for mass. b) Rearrange the density equation to create an equation for volume. Use the equations that you manipulated above to solve the following problems: c) The continental crust of the earth has a density of about 2.75 g/cm3. What volume would 1000 g (1 kg) of continental crust occupy? d) The outer core of the earth has a density of about 10.5 g/cm3. What volume would 1000 g (1 kg) of the outer core occupy? (4 marks) Page 2 of 5 Year 11 General Mathematics Linear relations and equations: Assessment Part 2 4 Terry’s Car Rentals charges $20 per day plus 55c/km for the hire of a small car. a Complete the table showing the costs for hiring a car and travelling various distances in 1 or 2 days. Distance (km) 50 100 200 300 500 1 day ($) 2 day ($) b Write a formula relating charges (C) to distances (d) and to the number of days (n) of the hire. (2 marks) c Use your formula to find out how far you can travel (to the nearest kilometre) for $500 in I 2 days ii 3 days (2 marks) Use simultaneous equations to solve Questions 4, 5 and 6. 5 Three kilograms of jam and two kilograms of butter cost $29 and six kilograms of jam and three kilograms of butter cost $54. i Find the cost of one kilogram of jam and one kilogram of butter. (2 marks) ii Show your solution graphically. (2 marks) Page 3 of 5 Year 11 General Mathematics Linear relations and equations: Assessment Part 2 6 Find a pair of numbers whose sum is 45 and whose difference is 11. (2 marks) 7 A party was organised for thirty people at which they could either have a hamburger or a pizza. If there were five times as many hamburgers as pizzas, calculate the number of each. (2 marks) 8 The sum of two consecutive numbers is 37. What are the numbers? (Must be solved algebraically) (Note: consecutive numbers follow one after the other) (2 marks) Page 4 of 5 Year 11 General Mathematics Linear relations and equations: Assessment Part 2 9 The sum of two numbers is 84. One of the numbers is 12 more than the other number. What are the two numbers? (2 marks) 10 Martin bought 2 kilograms of bananas and 3 kilograms of oranges for $16.50. If oranges were 0.50 cents a kilogram more than the bananas, how much did the oranges and bananas cost per kilogram? (3 marks) 11 The linear recurrence relation is given by tn = tn − 1 + 3, t0 = 7. a Write the first 4 terms of the relation. b Write the corresponding difference equation. c Write the rule connecting the nth term with n. Hence, find the 20th term. (2 + 2 + 2 = 6 marks) Page 5 of 5