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MATHEMATICS Tertiary Preparation Certificate 29603 Mathematics/Science 29601 STRUCTURE Both courses comprise six mathematical subjects; three at A-level and three at B-level. Each subject takes one semester to complete with four hours of class-time per week. You will need to study one mathematical subject per semester with the exception that Calculus and Advanced Maths can be studied together in semester 2. The diagram shows the structure and pathways you may take to reach your goal. For most students their goal is expressed as an HSC equivalence to gain entry into a university or TAFE course that demands pre-requisite knowledge and skills. A-LEVEL SUBJECTS MATHS A3 B-LEVEL SUBJECTS (HSC EQUIVALENCE) ADVANCED MATHS Extension Maths CALCULUS Mathematics FURTHER MATHS B General Maths if combined with STATISTICS A MATHS A2 MATHS A1 The diagram shows three steps through the A-level subjects. It is important for you to start on the right step. This depends upon your current skills, the length of time since you studied mathematics and your goals. Selecting the a unit of mathematics in TPC. 17/6/14 1 SELECTING THE BEST SUBJECT Select Maths A1 if you need to revise the basic skills of arithmetic, algebra and geometry. A good pass in this subject provides the foundation for Further Maths B. Select Maths A2 if you aim to study higher B-level maths subjects but need to consolidate your skills in algebra, trigonometry and the Cartesian plane before studying Maths A3. Select Maths A3 if you aim to study Calculus and/or Advanced Maths, have studied maths recently and already have the skills taught in Maths A2. ASSESSING YOUR CURRENT SKILL LEVEL The following self-assessment paper is designed to help you make an appropriate choice of A-level mathematics elective subject for your first semester. Work the paper in about 30 minutes. You may use a calculator and formulae are provided. Mark your answers. (See the back page.) SELF-ASSESS YOUR CURRENT SKILL-LEVEL If you found the paper easy and achieved a mark greater than 17, Maths A3 may be suitable. If you did well but found a few topics difficult and scored at least 10, Maths A2 is appropriate. You could pass Maths A2 in your first semester then progress to Maths A3 in your second semester. If you found much of the paper a challenge or you did not manage to complete in the time, studying Maths A1 is your best option. Selecting the a unit of mathematics in TPC. 17/6/14 2 MATHEMATICS A-LEVEL SELF ASSESSMENT PAPER Attempt all questions. Write down the letter that corresponds to the correct answer for each question. Each question has one (1) correct answer. Question 1 After removing brackets, 5x -(3x -1) = A: 2x -1 B: 2x +1 C: 15x -1 D: 15x - 5 Question 2 3 The value of the expression, 4 2 - 30 is equal to: A: 7 B: 4 C: 5 D: 8 Question 3 The expression 2a ´ 4a is equal to: 3 A: 6a 2 6 B: 8a 6 C: 6a 5 D: 8a 5 Question 4 After expanding the brackets and simplifying (3x - 5) 2 = A: 9x - 30x - 25 2 B: 9x + 25 2 C: 9x - 30x + 25 2 D: 9x -15x + 25 2 Question 5 After simplifying, A: x 2x + = 3 5 11x 15 B: 3x 8 C: 3x 15 2 D: 2x 15 Question 6 Consider the following student’s solution to the equation 4x - 3 = 12 4x - 3 = 12 4x - 3+ 3 = 12 + 3 4x = 15 4x 15 = 4 4 x = 3.75 A: There is an error in line 3 B: There is an error in line 4 C: There is an error in line 5 D: The method and solution are correct. Selecting the a unit of mathematics in TPC. 17/6/14 3 Question 7 The solution to the equation 5x - 2 = 7 is: A: 1.6 B: 1.8 C: 3.4 D: 5 Question 8 When factorised, the quadratic expression 6x 2 +11x -10 = A: (2x - 2)(3x + 5) B: (3x - 5)(2x + 3) C: (3x + 2)(2x - 5) D: (3x - 2)(2x + 5) Question 9 The volume of a cylinder is given by the formula V = p r h , then: 2 A: r = V - p h pr C: h = V B: h = V pr V D: h = pr 2 2 Question 10 7m Applying Pythagoras’ Theorem to this triangle suggests: x 6m A: x = 14 -12 B: x = 49 + 36 C: x = 7 - 6 2 Question 11 D: x = 7 + 6 2 2 x To find the value of x in this right-angled triangle, the 2 51 m 23 m appropriate formula is: A: c = a + b 2 2 2 B: tanq = opp adj C: cosq = adj hyp D: sinq = opp hyp Question 12 -1 Correct to the nearest minute, tan 2.5 is: A: 68 12¢ B: 68 11¢ C: 68 20¢ D: 68 19¢ Question 13 A straight line joins the points (- 2, 7) and (4, - 3) . The midpoint of the line is: A: (1, 2) B: (1, - 2) Selecting the a unit of mathematics in TPC. 17/6/14 C: ( 2, 4 ) D: (- 2, - 4) 4 Question 14 A straight line joins the points P(1, - 3) and Q(- 3, -1 ) . The length of the line PQ is exactly: A: 4.5 C: 32 B: 20 D: 20 Question 15 The gradient of the straight line through the points A( - 2 , - 5) and B( 3, - 2 ) is: A: - 3 5 B: 5 7 C: -7 D: 3 5 Question 16 Which of the following points does not lie on the line y = 3x -1: B: (0, -1) A: (2, 5) C: (-1, - 2) D: (- 2, - 7) Question 17 The graph of the function y = 5x -1 has: A: Gradient 5 and y-axis intercept of -1 B: Gradient 5 and y-axis intercept of -3 C: Gradient -1 and y-axis intercept of 5 D: Gradient -1 and y-axis intercept of 2 Question 18 The best linear model for the data shown in the diagram is: X X X A: y = -3x + 5 X X B: y = - 0.6x + 3 Selecting the a unit of mathematics in TPC. 17/6/14 C: y = -1.5x + 3 D: y = 3x + 5 5 Question 19 The diagram below shows the graph of the equation: 1 A: y = - x -1 2 B: y = -2x +1 C: y = 2x +1 D: y = 1 x +1 2 Question 20 The diagram shows the graph of the equation y = 3x -1 On the same diagram draw the graph of the equation y = 0.5x +1.5. The solution to the pair of simultaneous equations: A: x = 1 and y = 2 B: x = 2 and y = 1 Selecting the a unit of mathematics in TPC. 17/6/14 y = 0.5x + 1.5 ïü ý is: y = 3x - 1 þï C: x = 0 and y = -1 D: x = 1.2 and y = 3 6 FORMULAE Trigonometry Cartesian Plane y mx b c a b 2 2 tan opp adj m sin opp hyp x x y y2 M 1 2 , 1 2 2 cos adj hyp d ( x2 x1 ) ( y2 y1 ) 2 y2 y1 x2 x1 2 2 SOLUTIONS Q1 B Q2 A Q3 D Q4 C Q5 A Q6 D Q7 B Q8 D Q9 B Q 10 C Q 11 C Q 12 A Q 13 A Q 14 B Q 15 D Q 16 C Q 17 A Q 18 B Q 19 D Q 20 A Selecting the a unit of mathematics in TPC. 17/6/14 7