CXC/CSEC Mathematics WORKSHEET #1: Sets, Consumer Arithmetic, Computations, Measurements and Statistics Question 1: (Paper 2-Question # 1- May/June 2013)
At the end of the first year, she repaid $ 4 368. (ii) How much did she still owe at the beginning of the second year? [2 marks] (iii) Calculate the interest on the remaining balance for the second year. [3 marks]
(a) Using a calculator, or otherwise, calculate the EXACT value of
[2 marks] [2 marks] (b) Smiley Orange Juice is sold in cartons of two different sizes at the prices shown in the table below.
Question 2:(Paper 2-Question # 1- May/June 2011)
(a) Using a calculator, or otherwise, determine the EXACT value of:
Expressing your answer as a fraction. [3 marks] (ii) 3.96 × 0.25 − √ 0.0256 0.0256 [3 marks] Which size carton of orange juice is the BETTER buy? Justify your answer, [3 marks] (c) Faye borrowed $9 600 at 8% per annum compound interest. (i) Calculate the interest on the loan for the first year. [1 mark]
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(b) The table below shows Pamela’s shopping bill. Some of the information was not included.
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EF = 8 cm
(ii) Measure and state in centimetres, the length of GH . [1 mark] Question 4:(Paper 2-Question # 3- May/June 2009)
Calculate the values of W, X, Y and Z. [5 marks] Question 3:(Paper 2-Question # 3- May/June 2011)
(a) In a survey of 50 students, 23 owned cellular phones 18 owned digital cameras x owned cellular phones and digital cameras 2x owned neither. Let C represent the set of students in the survey who owned cellular phones, and D the set of students who owned digital cameras. (i) Copy and complete the Venn diagram below to represent the information obtained from the survey. [2 marks]
(a) The Venn diagram below shows the number of students who study Music and Art in a class of 35 students. U = {students in the class} M = {students who study Music} A = {students who study Art}
(ii) Write an expression in x for the TOTAL number of students in the survey. [1 mark] (iii) Calculate the value of x. [2 marks] (b) The diagram below, not drawn to scale, shows a rhombus, PQRS, with the diagonal PR = 6 cm, and the angle RPQ = 60°.
(b)
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(i) How many students study neither Art nor Music? [1 mark] (ii) Calculate the value of x. [3 marks] (iii) Hence, state the number of students who study Music only. [1 mark] (i) Using a ruler, pencil, a pair of compasses and a protractor , draw accurately a quadrilateral EFGH using the following measurements:
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(i) Using a ruler, a pencil, and a pair of compasses, construct the rhombus PQRS accurately. [4 marks] (ii) Join QS. Measure and state, in centimetres, the length of QS. [2 marks] Question 5: (Paper 2-Question # 3b- May 2006)
(b) In a survey of 39 students, it was found that 18 can ride a bicycle, 15 can drive a car, x can ride a bicycle and drive a car, 3x can do neither. B is the set of students in the survey who can ride a bicycle, and C the set of students who can drive a car. (i) Copy and complete the Venn diagram to represent the information.
More information about the number of oranges and mangoes associated with the good bargain is represented by y < 2 x. (iii) Write the information represented by this inequality as a sentence in your own words. [2 marks] (iv) On the answer sheet provided , draw the lines associated with the two inequalities obtained in (i) and (ii) above. [3 marks] (v) Shade on your graph the region which represents the solution set for the three inequalities. [1 mark] (b) (i) Write 3 ‒ 12 x + 8 in the form a ( x + ℎ) + k where a, h and k are constants. [3 marks] (ii) Sketch the graph of y = 3 ‒ 12 x + 8, showing on your sketch a) the intercept on the y-axis b) the coordinates of the minimum point. [4 marks] Question 7: (Paper 2-Question # 4b- May 2007)
(ii) Write an expression in x for the number of students in the survey. (iii) Calculate the value of x. [5 marks]
(b) The diagram below, not drawn to scale, shows a prism of volume 960 cm3. The cross-section ABCD is a square. The length of the prism is 15 cm.
Question 6:(Paper 2-Question # 9- May/June 2013)
(a) An answer sheet is provided for this question. Trish wishes to buy x oranges and y mangoes which she intends to carry in her bag. Her bag has space for only 6 fruits. (i) Write an inequality to represent this information. [1 mark] To get a good bargain, she must buy AT LEAST 2 mangoes. (ii) Write an inequality to represent this information. [1 mark]
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Calculate
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(i) the length of the edge AB, in cm (ii) the total surface area of the prism, in c [5 marks]
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Question 8: (Paper 2-Question #3 – May/June2010)
Question 9: (Paper 2-Question # 11b- May 2008)
(a) A survey was conducted among 40 tourists. The results were: 28 visited Antigua (A) 30 visited Barbados (B) 3 x visited both Antigua and Barbados x visited neither Antigua nor Barbados (i) Copy and complete the Venn diagram below to represent the given information above. [2 marks]
(b) In the diagram below, not drawn to scale, 0 is the centre of the circle of radius 8.5 cm and AB is a chord of length 14.5 cm.
(ii) Write an expression, in x, to represent the TOTAL number of tourists in the survey. [2 marks] (iii) Calculate the value of x. [2 marks] (b) The diagram below, not drawn to scale , shows a wooden toy in the shape of a prism, with cross section ABCDE . F is the midpoint of EC , and ∠ BAE = ∠CBA = 90°.
Calculate (i) the length of EF [1 mark] (ii) the length of DF [2 marks] (iii) the area of the face ABCDE . [3 marks]
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(i) Calculate the value of to the nearest degree. [3 marks] (ii) Calculate the area of triangle AOB. [2 marks] (iii) Hence, calculate the area of the shaded region. [Use = 3.14]. [3 marks] (iv) Calculate the length of the major arc AB. [3 marks] Question 10: (Paper 2-Question # 12a- May 2007)
(a) The figure below, not drawn to scale, is a regular octagon with centre X, and XY = 6 cm.
Calculate (i) the size of angle YXZ (ii) the area of the triangle YXZ, expressing your answer correct to one decimal place (iii) the area of the octagon. [6 marks]
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Question 11: (Paper 2-Question # 7- May 2006)
An answer sheet is provided for this question. In an agricultural experiment, the gains in mass, of 100 cows during a certain period were recorded in kilograms as shown in the table below.
(a) Copy and complete the mid-interval values column. [1 mark] (b)
(i) Calculate an estimate of the mean gain in mass of the 100 cows. Hint: EACH of the 29 cows in the “1014” interval is assumed to have a mass of 12 kg. [ 3 marks] (ii) On your answer sheet, complete the drawing of the frequency polygon for the gain in mass of the cows. ( 5 marks)
(c) Calculate the probability that a cow chosen at random from the experimental group gained 20 kg or more. [ 2 marks]
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