O NOW I GET IT EXAMINATION

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O NOW I GET IT EXAMINATION MATHEMATICS Paper 02 General Proficiency 2 hours 40 minutes INSTRUCTIONS TO CANDIDATES 1. Answer ALL questions in Section I, and any TWO in section II. 2. Begin the answer for EACH question on a NEW page.

1 O NOW I GET IT EXAMINATION MATHEMATICS Paper 02 General Proficiency 2 hours 40 minutes INSTRUCTIONS TO CANDIDATES 1. Answer ALL questions in Section I, and any TWO in section II. 2. Begin the answer for EACH question on a NEW page. 3. ALL working must be shown CLEARLY. 4. Mathematical tables and graph paper are provided. A list of formulae is provided on page 2 of this booklet. 5. Mathematical instruments are needed for this paper. 6. Silent electronic calculators may be used for this paper. 7. You are advised to use the first 10 minutes of the examination time to read through this paper. Writing may begin during this 10 minute period. DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

2 Page 2 LIST OF FORMULAE

3 Page 3 ALL working must be shown clearly. SECTION I Answer ALL the questions in this section. 1. (a) Using a calculator or otherwise, determine the EXACT value of: x 6.9 (b) 1.3 x 0.2 (i) correct to 1 decimal place (ii) correct to 2 significant figures (iii) in scientific notation [6 marks] (c) The table below shows a shopping bill prepared for Mrs. Rowe. The prices of some items are missing. Shopping Bill Item Unit Cost Price Total Cost Price 3 kg sugar X $ kg rice Y Z 2 kg flour $50.50 $ (i) Calculate the value of X, the cost of 1kg of sugar. [1 mark] (ii) (iii) If the cost price of 1kg of rice is $12.80 MORE than for 1 kg of flour, calculate the values of Y and Z. A tax of 16.5% of the total cost price of the three items is added to Mrs. Rowe s bill. What is Mrs. Rowe s TOTAL bill including the tax? [3 marks] 2. (a) In the formula below, make a the subject v 2 = u 2 2as (b) Calculate the value of a when u = 10, v = 8 and s = 15 (c) Write as a simple fraction in its LOWEST terms 3x x [3 marks]

4 Page 4 (d) Factorize the following (i) 9e 2 25 (ii) 7mp m 2 p (iii) 6x 2 13x + 6 [6 marks] 3. (a) A school has 90 students in Form students study Physical Education. 42 study Music. 6 students study neither Physical Education nor Music. x students study both Physical Education and Music. Copy the Venn diagram shown below. i. Show on your Venn diagram the information relating to the students in Form 5. [4marks] ii. Calculate the number of students who study BOTH Physical Education and Music. (b) Using a ruler, pencil and a pair of compasses, construct triangle PQR with PQ = 5cm, angle PQR = 60 0 and angle QPR = Measure and state (i) the length of PR (ii) the measure of angle PRQ [6 marks] 4. The coordinates of A and B are (3, 5) and (7, 1) respectively. X is the mid-point of AB. (a) Calculate (i) the gradient of AB (ii) the co-ordinates of the point X (b) Determine the equation of line segment AB Line segment PQ is perpendicular to AB. (c) Determine the equation of the perpendicular bisector of AB. [6 marks]

5 Page 5 5. The diagram below, not drawn to scale, shows two straight lines, LJ and NK, supporting a vertical pole, MJ. LMN is a straight line on the horizontal plane. Angle JML = 90 0 and angle KNM = 30 0, LJ = 13m and LM = 5m and KN = 10m. Calculate, in meters, the length of (i) MK [3 marks] (ii) JM (iii) JK [1 mark] 6. The height, in centimeters, of a sample of seedlings were recorded and grouped as shown below. Height (cm) Number of Seedling Mid-Height (x) (a) In the class interval, 8 12, state the lower class limit [1 mark] (b) Calculate i. the TOTAL number of seedlings in the sample [1 mark] ii. an estimate of the mean height of the seedling in the sample [3 marks] (c) Using a scale of 2cm to represent a height of 5cm on the x axis and 2cm to represent 5 seedlings on the y axis, draw on graph paper the frequency polygon to represent the data given in the table. [5 marks] (d) Calculate the probability that a seedling, selected at random, measures AT MOST 12cm in height.

6 Page 6 7. (a) The functionf(x)and g(x) are defined as f(x) = 3x 2 1 and g(x) = 5x + 2 Evaluate: i. f( 2) ii. gf( 2) 3x 9 Determine iii. g 1 (x), the inverse of g(x) iv. the value of x for which g(x) is undefined v. the value of x for which g(x) = 0 [5 marks] (b) Solve the following simultaneous equations 2x + 3y = 9 1 3x y = 8 2 [5 marks] (c) The diagram below shows triangle RST and its image R S T after a transformation. i. Describe FULLY the transformation which maps RST onto R S T. ii. Triangle RST is reflected in the line x = 6. On the graph sheet provided, insert the line x = 6 then draw triangler S T, the image of RST, after the reflection. [4 marks] iii. Write down the coordinates of R. TOTAL 20 marks

Page 7 8. The figure below shows the first three diagrams in a sequence. Each diagram is made up of dots connected by line segments. In each diagram, there are d dots and l line segments.

7 Page 7 8. The figure below shows the first three diagrams in a sequence. Each diagram is made up of dots connected by line segments. In each diagram, there are d dots and l line segments. a) Draw the fourth diagram in the sequence. b) Complete the table by inserting the missing values at the rows marked (i) and (ii). c) (i) How many dots are in the SIXTH diagram of the sequence? [1 mark] (ii) How many line segments are in the SEVENTH diagram of the sequences? [1 mark] (iii) Write the rule which shows how l is related to d. TOTAL 10 marks SECTION II Answer TWO questions in this section ALGEBRA AND RELATIONS, FUNCTIONS AND GRAPHS 9. (a) (i) Express the quadratic function f(x) = 3x 2 + 6x 2 in the form a(x + h) 2 + k, where a, h and k are real numbers. (ii) Hence, or otherwise, state the minimum value of f(x) = 3x 2 + 6x 2 (iii) State the equation of the axis of symmetry of the function f(x) = 3x 2 + 6x 2 (iv) Sketch the graph of y = 3x 2 + 6x 2, showing on your sketch, the y intercept and the coordinates of the minimum point [10 marks]

8 Page 8 (b) The table below shows pairs of values for x and y, where y 1. x x 3 4 a 20 y b (i) Express y in terms of x and constant k (ii) Calculate the value of the constant k (iii) Determine the value of a and b. [5 marks] MEASUREMENT, GEOMETRY AND TRIGONOMETRY TOTAL 15 marks 10. The diagram below, not drawn to scale, show tangents CF and CG meeting at a common point C. The size of angle FDH = 39 0 and angle DHE = Calculate, giving reasons for each step of your answer, the measure of angle (a) EAD (d) ECD (b) DEH (e) AEG (c) ADE [5 marks] 11. A post man leaves Town X to make some deliveries to Town Y, a distance of 100 km on a bearing of He then changes course and travels to Town Z, 150 km away on a bearing of The postman then returns to Town X. (a) Draw a suitable diagram to represent the above information. On your diagram, show the North lines, distances and bearings travelled. Calculate: (b) the size of angle XYZ (c) the distance XZ (d) the bearing of X from Z (e) the area of triangle XYZ [10 marks] TOTAL 15 marks

Page 9 VECTORS AND MATRICES 12. The diagram below shows two points relative to the origin, O. (a) Express in the form of ( x y ) i. OP ii. OQ iii. QP (b) Calculate PQ, the length of vector PQ.

9 Page 9 VECTORS AND MATRICES 12. The diagram below shows two points relative to the origin, O. (a) Express in the form of ( x y ) i. OP ii. OQ iii. QP (b) Calculate PQ, the length of vector PQ. (c) X is the midpoint of vector PQ. Determine the coordinates of the X. Express the midpoint as a vector in the form of ( x y ). 13. (a) Given that M = ( 4 6 ), calculate the values of x, if M = x (b) Given the simultaneous equation 3x + 2y = 1 5x + 4y = 6 [6 marks] (i) (ii) (iii) (iv) Express the pair of simultaneous equations in the matrix form, AX = B Determine the determinant of A Determine A 1, the inverse of A Hence, use the matrix method to solve the simultaneous equation for x and y. [9 marks] TOTAL 15 marks

CARIBBEAN CORRESPONDENCE SCHOOL

Final Examination CARIBBEAN CORRESPONDENCE SCHOOL Module Name: Groups: Duration: MATHEMATICS Online 3 Hours INSTRUCTIONS TO CANDIDATES 1. This Paper consists of THREE sections. 2. There is one question