Working: Answers: (a)... (b)... (c) In the Venn diagram below, A, B and C are subsets of a universal set U = {1,2,3,4,6,7,8,9}.

Transcription

1 1. The total weight of 256 identical pencils is 4.24 kg. Calculate the weight of one pencil, in kg. (a) Give your answer exactly. Give your answer correct to three significant figures. (c) Write your answer to part in the form a 10 k where 1 a < 10 and k. 2. In the Venn diagram below, A, B and C are subsets of a universal set U = {1,2,3,4,6,7,8,9}. List the elements in each of the following sets. (a) A B A B C (c) (A C) B

2 3. A Swiss bank shows currency conversion rates in a table. Part of the table is shown below, which gives the exchange rate between British pounds (GBP), US dollars (USD) and Swiss francs (CHF). This means that the bank will sell its British pounds to a client at an exchange rate of 1 GBP = CHF. Buy Sell GBP USD (a) What will be the selling price for 1 USD? Andrew is going to travel from Europe to the USA. He plans to exchange 1000 CHF into dollars. The bank sells him the dollars and charges 2% commission. How many dollars will he receive? Give your answer to the nearest dollar. 4. A swimming pool is to be built in the shape of a letter L. The shape is formed from two squares with side dimensions x and as shown. (a) Write down an expression for the area A of the swimming pool surface. The area A is to be 30 m 2. Write a quadratic equation that expresses this information. (c) Find both the solutions of your equation in part. (d) Which of the solutions in part (c) is the correct value of x for the pool? State briefly why you made this choice. (d)...

3 5. Given the set of integers, the set of rational numbers, the set of real numbers. (a) Write down an element that belongs to. Write down an element that belongs to ʹ. (c) Write down an element that belongs to ʹ. (d) Use a Venn diagram to represent the sets, and. (d)... (Total 6 marks) 6. The table below gives the monthly repayments for a loan of 1000 Australian dollars (AUD). The interest rates are 18% per annum and 18.5% per annum, respectively. Monthly repayments on AUD 1000 Number of years of the loan 18% p.a. 18.5% p.a From the table, (a) find the monthly repayment on a loan of AUD 1000 at 18.5% per annum taken over 1 year; calculate the total amount to be repaid on a loan of AUD 8000 taken over 5 years, if the interest rate is 18% per annum. (a).. (Total 4 marks)

4 7. The figure below shows part of the graph of a quadratic function y = ax 2 + 4x + c. (a) Write down the value of c. Find the value of a. (c) Write the quadratic function in its factorized form. 8. Consider the statement If a figure is a square, then it is a rhombus. (a) For this statement, write in words (i) its converse; (ii) its inverse; (iii) its contrapositive. Only one of the statements in part(a) is true. Which one is it? (a) (i) (ii) (iii)

5 9. The cost c, in Australian dollars (AUD), of renting a bungalow for n weeks is given by the linear relationship c = nr + s, where s is the security deposit and r is the amount of rent per week. Ana rented the bungalow for 12 weeks and paid a total of 2925 AUD. Raquel rented the same bungalow for 20 weeks and paid a total of 4525 AUD. Find the value of (a) r, the rent per week; s, the security deposit. (a) The following table gives the postage rates for sending letters from the Netherlands. All prices are given in Euros ( ). Destination Weight not more than 20 g Each additional 20 g or part of 20 g Within the Netherlands (Zone 1) Other destinations within Europe (Zone 2) Outside Europe (Zone 3) (a) Write down the cost of sending a letter weighing 15 g from the Netherlands to a destination within the Netherlands (zone 1). Find the cost of sending a letter weighing 35 g from the Netherlands to a destination in France (zone 2). (c) Find the cost of sending a letter weighing 50 g from the Netherlands to a destination in the USA (zone 3).

6 11. The diagram shows a function f, mapping members of set A to members of set B. (a) (i) Using set notation, write down all members of the domain of f. (ii) Using set notation, write down all members of the range of f. (iii) Write down the equation of the function f. The equation of a function g is g(x) = x The domain of g is. Write down the range of g. (Total 6 marks) (a) (i)... (ii)... (iii) The conversion formula for temperature from the Fahrenheit (F) to the Celsius (C) scale is given by C = (F 32) * 5/9. (a) What is the temperature in degrees Celsius when it is 50 Fahrenheit? There is another temperature scale called the Kelvin (K) scale. The temperature in degrees Kelvin is given by K = C What is the temperature in Fahrenheit when it is zero degrees on the Kelvin scale?