CSEC Math Worksheet 1

(1)

Question 1: (Paper 2-Question #

Question 1: (Paper 2-Question # 1- May/June1- May/June 2013)

2013)

(a) Using a calculator, or otherwise, calculate the (a) Using a calculator, or otherwise, calculate the EXACT value of EXACT value of [2 marks] [2 marks] [2 marks] [2 marks] (b) Smiley Orange Juice is sold in

(b) Smiley Orange Juice is sold in cartons of twocartons of two different sizes at the prices shown in the table different sizes at the prices shown in the table below.

below.

Which size carton of orange juice is the BETTER Which size carton of orange juice is the BETTER buy? Justify your answer, [3 marks]

buy? Justify your answer, [3 marks]

(c) Faye borrowed $9 600 at 8% per annum (c) Faye borrowed $9 600 at 8% per annum compound interest.

compound interest.

(i) Calculate the interest on the loan for (i) Calculate the interest on the loan for the first year. [1 mark]

the first year. [1 mark]

At the end of the first year, she repaid $ At the end of the first year, she repaid $ 44 368.

368.

(ii) How much did she still owe at the (ii) How much did she still owe at the beginning of the second year? [2 marks] beginning of the second year? [2 marks] (iii) Calculate the interest on the (iii) Calculate the interest on the remaining balance for the second year. [3 remaining balance for the second year. [3 marks]

marks]

Question 2:(Paper 2-Question # 1- May/June 2011) Question 2:(Paper 2-Question # 1- May/June 2011)

(a) Using a calculator, or otherwise, determine (a) Using a calculator, or otherwise, determine the EXACT value of:

the EXACT value of:

Expressing your answer as a fraction. [3 marks] Expressing your answer as a fraction. [3 marks]

(ii) 3.96

×

0.25 0.25

−

− √

√ 0.0256

0.0256

[3 [3 marks]marks] (b) The table below shows Pamela’s shopping (b) The table below shows Pamela’s shopping bill. Some of the information was not included. bill. Some of the information was not included.

CXC/CSEC Mathematics

WORKSHEET #1:

Sets, Consumer Arithmetic, Computations,

Measurements and Statistics

(2)

Calculate the values of W, X, Y and Z. [5 marks]

Question 3:(Paper 2-Question # 3- May/June 2011)

(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}

(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]

(b) (i) Using a ruler, pencil, a pair of

compasses and a protractor, draw

accurately a quadrilateral EFGH using

the following measurements:

EF = 8 cm <EFG = 125° FG = 4 cm

<HEF= 70° EH= 7 cm [5 marks] (ii) Measure and state in centimetres, the

length ofGH . [1 mark]

(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]

(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,

(3)

(i) Using a ruler, a pencil, and a pair of

compasses, construct the rhombusPQRS

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,

xcan ride a bicycle and drive a car,

3xcan do neither.

Bis 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.

(ii) Write an expression in x for the

number of students in the survey.

(iii) Calculate the value of x. [5 marks]

(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]

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 kare 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]

(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.

Calculate

(i) the length of the edge AB, in cm (ii) the total surface area of the prism, in

(4)

Question 8: (Paper 2-Question #3_– May/June2010)

(a) A survey was conducted among 40 tourists. The results were:

28 visited Antigua (A) 30 visited Barbados (B)

3 xvisited both Antigua and Barbados

xvisited neither Antigua nor Barbados

(i) Copy and complete the Venn diagram below to represent the given information

above. [2 marks]

(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]

(b) In the diagram below, not drawn to scale,0is

the centre of the circle of radius 8.5 cm and ABis

a chord of length 14.5 cm.

(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 angleYXZ

(ii) the area of the triangle YXZ, expressing your

answer correct to one decimal place

(5)

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 “10-14” 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]