1. The first five terms of an arithmetic sequence are shown below. 2, 6, 10, 14, 18 Write down the sith number in the sequence. Calculate the 200 th term. Calculate the sum of the first 90 terms of the sequence......... 2. The numbers of games played in each set of a tennis tournament were 9, 7, 8, 11, 9, 6, 10, 8, 12, 6, 8, 13, 7, 9, 10, 9, 10, 11, 12, 8, 7, 13, 10, 7, 7. The raw data has been organised in the frequency table below. games frequency 6 2 7 5 8 n 9 4 10 4 11 2 12 2 13 2 Write down the value of n. Calculate the mean number of games played per set. 1
(d) What percentage of the sets had more than 10 games? What is the modal number of games?....... (d)... 3. The equation M = 90 2 t/20 gives the amount, in grams, of radioactive material held in a laboratory over t years. What was the original mass of the radioactive material? The table below lists some values for M. t 60 80 100 M 11.25 v 2.8125 Find the value of v. 2
Calculate the number of years it would take for the radioactive material to have a mass of 45 grams......... 4. The diagram below shows the graph of y = c + k 2, where k and c are constants. y Q O Find the values of k and c. P(5, 0) 3
Find the coordinates of Q, the highest point on the graph...... 5. The local council has been monitoring the number of cars parked near a supermarket on an hourly basis. The results are displayed below. Parked Cars/Hour Frequency Cumulative Frequency 0 19 3 3 20 39 15 18 40 59 25 w 60 79 35 78 80 99 17 95 Write down the value of w. 4
Draw and label the Cumulative Frequency graph for this data. Determine the median number of cars per hour parked near the supermarket...... 5
6. The graphs of three trigonometric functions are drawn below. The variable is measured in degrees, with 360 360. The amplitude 'a' is a positive constant with 0 < a 1. Graph A a Graph B 2 y 0 90 180 270 360 90 180 270 360 a Graph C a 0 90 180 270 360 a Write the letter of the graph net to the function representing that graph in the bo below. FUNCTION y = acos() y = asin(2) y = 2 + asin() GRAPH State the period of the function shown in graph B. 6
State the range of the function 2 + asin() in terms of the constant a....... 7. Sandra is attempting an eam question. She has to choose two correct statements from a list of five. Below is a tree diagram showing Sandra's possible choices. One of the probability values is missing. correct correct 2 5 incorrect 3 4 incorrect 3 5 correct 2 4 incorrect 2 4 Fill in the missing probability value on the diagram. 7
(i) If Sandra makes two guesses, what is the probability that she will get only one of them correct? (ii) Sandra definitely knows the first correct statement but has to guess the second. What is the probability that she will answer both correctly? (i)... (ii)... 8. A swimming pool is to be built in the shape of a letter L. The shape is formed from two squares with side dimensions and as shown. Diagram not to scale Write down an epression for the area of the swimming pool surface. The area A is to be 30 m 2. Write a quadratic equation that epresses this information. Find both the solutions of your equation in part. 8
(d) Which of the solutions in part is the correct value of for the pool? State briefly why you made this choice........ (d).......... 9. Given = 2.6 10 4 and y = 5.0 10 8, calculate the value of w = y. Give your answer in the form a 10 k where 1 a < 10 and k. 9
Which two of the following statements about the nature of, y and w above are incorrect? (i) (ii) (iii) (iv) (v) y y w < y + y (vi) 1 < w..... 10. A farmer wants to construct a new fence across a field. The plan is shown below. The new fence is indicated by a dotted line. 75 Diagram not to scale 410 m 40 Calculate the length of the fence. (5) 10
The fence creates two sections of land. Find the area of the smaller section of land ABC, given the additional information shown below. A B Diagram not to scale 245 m 24 C (3) 11. Find the volume of the following prism. 8 cm Diagram not to scale 5.7 cm 42 (Total 4 marks) 12. Let p stand for the proposition I will walk to school. Let q stand for the proposition the sun is shining. Write the following statements in symbolic logic form (i) (ii) If the sun is shining then I will walk to school. If I do not walk to school then the sun is not shining. (4) Write down, in words, the converse of the statement If the sun is shining then I will walk to school. (2) (Total 6 marks) 11
13. Copy and complete the table below by filling in the three empty columns. p q p q p q p (p q) p (p q) p q T T T T T F F T F T F T F F F F What word is used to describe the argument (p q) p q? (3) (1) (Total 4 marks) 14. The following results were obtained from a survey concerning the reading habits of students. 60 % read magazine P 50 % read magazine Q 50 % read magazine R 30 % read magazines P and Q 20 % read magazines Q and R 30 % read magazines P and R 10 % read all three magazines (d) Represent all of this information on a Venn diagram. What percentage of students read eactly two magazines? What percentage of students read at least two magazines? What percentage of students do not read any of the magazines? (4) (1) (1) (1) (Total 7 marks) 12
15. A number of employees at a factory were given additional training sessions each. They were then timed on how long (y seconds) it took them to complete a task. The results are shown in the scatter diagram below. A list of descriptive statistics is also given. n = 9, time taken (seconds) sum of values: Σ = 54, sum of y values: Σ y = 81, mean of values: = 6, mean of y values: y = 9, 14 12 10 standard deviation of : s = 1.94, standard deviation of y: s y = 2.35, covariance: s y = 3.77. 8 6 4 2 2 4 6 8 10 number of additional training sessions Determine the product-moment correlation coefficient (r) for this data. What is the nature of the relationship between the amount of additional training and the time taken to complete the task? n Calculate ( i )( yi y) given that the covariance s y = 3.77. i= 1 (2) (2) (1) (d) (i) Determine the equation of the linear regression line for y on. (ii) Find the epected time to complete the task for an employee who only attended three additional training sessions. (4) (Total 9 marks) 13