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 is section I, SIX questions in section II and THREE questions in section III 3. Answer ALL questions in sections I, II and III 4. Show ALL working Materials for Exam: Geometry set Graph Paper Non-Programmable electronic calculator DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO GOOD LUCK WELCOME TO SECTION I ANSWER ALL EQUESTIONS IN THIS SECTION Question A (20 marks) Page 1 of 10
Carol, Nickelle, and Camrone are partners in business. They shared the start up cash in a ratio of 5: 4: 3 respectively. If Camrone s share is $100,000, what is the total start up cash for the business? I. The business bought three (3) laptops A, B, and C at a total cost of $175,000. The cost of each laptop is in a ratio of 5: 3: 2 respectively. What cost should the business sell laptop C, and laptop A, to make a profit percentage of 25%, and 35% respectively? II. If laptop B is sold for $75,000, what is the profit made on the three (3) laptops? III. Carol took $50,000 from the business and bought a table set for $25,000 plus(+) TAX. What is the total cost of the table set, if TAX rate is 16%? IV. The business had to borrow a loan of $150,000 at a rate of 16% per annum for Five (5) years. A. What is the simple interest for the first year? B. What is the simple interest for the five (5) years? C. What is the total amount paid to the financial institution? WELCOME TO SECTION II ANSWER ALL THE QUESTIONS IN THIS SECTION Page 2 of 10
1a 3 ( 2 2 3 ) + 7 ( 1 2 2 ) ( 2 6 ) 2 1b 4 2 7 12 8 12 3 12 1c. Using a Calculator, or otherwise find the EXACT value of i. ii. 7.56 3.48 11 6.75 6+7.589 0.987 1d. Write the answer from part 1c i. correct to 3 decimal place ii. correct to 2 significant figures iii. In standard form 2a. Given l = 0.67, m = 0.5 and n = 0.8, evaluate i. 6l + 3.6m 4n ii. l 2 iii. (lmn) 3 2b. Write as a single fraction in its lowest terms 3(m 2n) 3l 2 4(m+n) 3pl 2 2c. The binary operation * is defined by q p = 2(qp) 2 + 2(q p) Page 3 of 10
Find the value of 2 6 2d. Factorize the following completely i. 4a 2 b 2 + 12abc + 9c 2 ii. x 2 + 10x + 25 iii. 9 + 6a + a 2 3a. If the perimeter of the triangle is 12cm, find x if sides a = (4x 1)cm, b = (3x + 1)cm, and c = (x + 4)cm 3b. If the perimeter of the rectangle is 38cm and the length is (3x 1)cm and width is (x + 4)cm, find x. 3c. If the area of a circle is twice the circumference, what is the length of the diameter of the circle in cm. 3d. In circle of part 3c above, an angle of 45 is formed between two radius i. draw the figure ii. what is the name of the section bounded by the 45 and the two radius iii. find the area of that section iv. Find the length of the circumference occupied by that section. 4. U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} A = {Multiples of 2} B = {Multiples of 3} C = {Multiples of 4} a). Draw a venn diagram to represent the above data b). List the members of i. A B C ii. A B C iii. (A B) iv. (B C) v. n(a) vi. n(b) vii. n(a B C) 4b. Using a ruler a pencil and a pair of compasses, construct triangle ABC with BC = 8cm, angle ABC = 90, and angle ACB = 30 Page 4 of 10
i) BC is a straight line that bisect angle ABC ii) Connect and name the diagram ABCD iii) what is the length of BD 5a. The points A, B, C lies on a straight line on horizontal ground. AD is a vertical pole of height 20m. The angle of depression of B and C are 30 and 45 respectively calculate i) BD ii) CD iii) BC 5b. A ship sails from a point P on a course 060 to a point Q which is 10 miles due east of the point R. The point R is at a bearing of 330 from point P i) Draw a carefully labelled diagram to illustrate the given information ii) Calculate to 3 decimal places PQ and QR. 6. Using a scale of 2cm to represent 1unit, use the graph method to solve 3x + 2y = 1 4x y = 16 7a. A load of fuel consisting of 5 tons of coal and 2 tons of coke is bought for $40. If a load containing half this amount of coal and twice this amount of coke can be bought for $35, what is the price of 1 ton of coal and 1 ton of coke? 7b. Fifteen dollars was spent in buying 50 oranges some at $3 for each, others at $4 each How many of each kind were bought? 7c. The tens digit of a two-digit number is half the units digit. When the digits are reversed the number is increased by 27. Find the number. 7d. Two numbers are such that the greater of the two is 4 less than twice the smaller. If the greater is exactly 3 times the difference between the numbers, find the numbers. WELCOME TO SECTION III ANSWER ANY THREE EQUESTIONS IN THIS SECTION Page 5 of 10
8. The table below shows the results of students at University of the Caribbean to the nearest tens for a particular test. Marks Number of students Cumulative frequency 30 39 4 4 40 49 7 11 50 59 10-60 - 69 16-70 - 79 3-80 89 10-90 - 100 15 65 8a. Copy and complete the table above to show the cumulative frequency. 8b. Using a scale of 2 cm to represent 10 marks on the x-axis and 1 cm to represent 5 students on the y-axis, draw the cumulative frequency curve for the data. 8c. Use your graph drawn at 8b above to estimate (i) (ii) the median mark for the data the probability that a student get 65 or below. Draw lines on your graph to show how these estimates were obtained. 8d. y = 3 5x y = x 2 2x + 5 Draw graphs to solve the simultaneous equation, and check your answer by using any of the method listed below i. Elimination method ii. Substitution method iii. Matrix algebra 9A F Page 6 of 10
D A B C G C H In the diagram above, NOT DRAWN TO SCALE, ABCDF are points on the circumference of a circle, centre O. GCH is a tangent to the circle at C, < ACG = 50, < D = 80 and <CAB = 70. Calculate, giving reasons for your answer, the measurement of angle (i) (ii) (iii) (iv) < F < ACB < BCH < ABC 9b. Given that g(x) = 3x+2 2x 5 2x 1 and f(x) = 3x+5 i) Find g 1 (x) and hence find x if g(x) = 0 ii) find f 1 (x) and hence find x if f(x) = 0 10a. Determine the determinant of the Matrix A Page 7 of 10
What type of matrix is A? 10b. 2x + 3y = 12 3x + 2y = 13 A= 3 2 6 4 Use Matrix algebra to solve the simultaneous equation. END OF TEST Formula sheet Page 8 of 10
Areas and Volumes Circumference Area of a circle C = 2πr Where r is the radius of the circle A = πr 2 where r is the radius of the circle Area of a sector A = θ 360 πr2 where θ is the angle of the sector, measured in degrees. Area of trapezium A = 1 (a + b)h where a and b are the lengths of the parallel 2 sides and h is the perpendicular distance between the parallel sides. Length of Arc l = θ 360 2πr where θ is the angle subtended by the arc, measured in degrees. Volume of a right pyramid V = 1 Ah where A is the area of the base and h is the perpendicular height. 3 Volume of cylinder V = πr 2 h where r is the radius of the base and h is the perpendicular height. Volume of a prism V = Ah where A is the area of a cross section and h is the perpendicular length. Area of triangle Area of = 1 bh where b is the length of the base and h is the perpendicular height 2 Area of ABC if it contains an angle C, area = 1 ab sinc 2 Area of ABC with all three lengths, Area = s(s a)(s b)(s c) where s = a+b+c 2 Sine rule Cosine rule a = b = c sina sinb sinc a 2 = b 2 + c 2 2bc cosa Page 9 of 10
Pythagoras s theorem a 2 = b 2 + c 2 Trigonometric ratios sin θ = cos θ = tan θ = opposite side Hypotenuse adjacent side hypotenuse opposite side adjacent side Solution for x in quadratic equations ax 2 + bx + c = 0, Then x = b± b2 4ac 2a Page 10 of 10