2009. S.
32
FOR THE EXAMINER EXAM. NUMBER:
Total Marks:
Coimisin na Scrduithe Stit State Examinations Commission
JUNIOR CERTIFICATE EXAMINATION, 2009 MATHEMATICS - ORDINARY LEVEL - PAPER 1 (300 marks)
THURSDAY, 4 JUNE - MORNING, 9:30 to 11:30
Time: 2 hours Attempt ALL questions. Each question carries 50 marks. Answers and supporting work should be written into the boxes provided. Extra paper and graph paper can be obtained from the Superintendent, if needed. The symbol indicates that supporting work must be shown to obtain full marks.
Make and model of calculator used: Question 1 For Superintendent/Examiner use only: Centre Stamp 2 3 4 5 6 Total Grade
Page 1 of 16
Mark
1.
(a)
P = {w, x, y, z}
Q = {v, w, x}
Fill the elements of P and Q into the following diagram.
1(b)
U is the universal set. A = {1, 5, 6, 9, 10} B = {1, 3, 5, 8}
U A 6 10 9 5 8 4 C 7
1 3 2
C = {4, 5, 8, 10}
(i) List the elements of B C .
(ii) List the elements of A' , the complement of the set A.
(iii) List the elements of ( B C ) \ A .
(iv) Write down #B.
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1(c)
In a survey, a group of students were asked if they were studying French or German at school. 80 of these students said they were studying French (F). 24 of these students said they were studying German (G). 15 of these students said they were studying both French and German. 11 of these students said they were studying neither of the two languages.
(i)
Represent this information in the Venn diagram below.
(ii)
How many students were in the group?
(iii) How many students did not study German?
Page 3 of 16
2.
(a)
9 metres of cloth cost 1395. Find the cost of 20 metres of the same cloth.
2(b)
(i)
a9 a3 Simplify 6 , giving your answer in the form a n , where n N. 2 a a
a9 a3 = a6 a2
(ii)
By rounding each of these numbers to the nearest whole number, 18 207 estimate the value of . 3 7 + 2 08
18 207 3 7 + 2 08
is approximately equal to:
= +
(iii)
Using a calculator, or otherwise, find the exact value of
18 207 . 3 7 + 2 08
Page 4 of 16
2(c)
(i)
1 13 and as decimals. 8 80 Hence or otherwise, put the following numbers in order, starting with the smallest and finishing with the largest: 1 13 , , 01525. 8 80
Using a calculator, or otherwise, write
1 = 8
13 = 80
(ii)
Using a calculator, or otherwise, find the exact value of (3 61) 2 .
1
(3 61) 2 =
(iii)
Using a calculator, or otherwise, evaluate 1 94 09 (2 75) 2 . 0 3125 Give your answer correct to two decimal places.
Page 5 of 16
3.
(a)
Aideen owns 6000 shares in a certain company. She sells two-thirds of her shares. How many shares does she now own in the company?
3(b)
(i)
Brians gross annual pay is 26 000. His annual tax credit is 2800. He pays income tax at the rate of 20%. What is his annual take-home pay?
Gross Pay Tax @ 20% Tax Credit Tax Due Take-home Pay
26 000
2800
Page 6 of 16
(ii)
A dealer buys a car for 17 500. He sells the car for 23 800. Calculate his profit as a percentage of the cost price.
3(c)
(i)
20 000 is invested at 5 2% per annum. What is the amount of the investment at the end of one year?
(ii)
5000 is withdrawn from this amount at the beginning of the second year. The interest rate for the second year is 6 25% per annum. What is the amount of the investment at the end of that year?
Page 7 of 16
4.
(a)
If a = 5, find the value of :
(i) 4a + 1
(ii)
a2 3a + 6
4(b)
(i)
Solve the equation
5 x 10 = 3( x + 2) .
(ii)
Multiply ( x 3) by (2 x + 1) . Write your answer in its simplest form.
Page 8 of 16
4(c)
(i)
The cost of a cinema ticket is t for an adult and 5 for a child. The cost of tickets for 2 adults and 3 children is 33. Write down an equation in t to represent this information.
(ii)
Solve the equation you formed in part (i) above, for t.
(iii)
Solve for x and for y:
5x 4y = 16 2x + 3y = 11
x=
y=
Page 9 of 16
5.
(a)
Write in its simplest form 3(x + 2) + 4(3x + 1).
5(b)
Factorise
(i)
5cd + 7 d
(ii)
ax + 3ay + 4 x + 12 y
(iii)
x 2 49
Page 10 of 16
5(c)
(i)
5x + 1 x+6 as a single fraction. 3 5 Give your answer in its simplest form. Express
(ii)
Verify your answer to part (i) by substituting x = 4 into
and into your answer to part (i).
5x + 1 x + 6 3 5
(iii)
Solve the equation x 2 4 x 21 = 0.
Page 11 of 16
6.
(a)
f (x) = 4x 5.
Find:
(i) (ii)
f (3) f (-2)
6(b)
Draw the graph of the function f : x x 2 2x 1 in the domain 1 x 3, where x R.
Page 12 of 16
6(c)
Use the graph drawn in 6(b) to estimate:
(i)
the values of x for which x 2 2 x 1 = 0 Work to be shown on the graph and answer to be written here.
(ii)
the value of f(x) when x =1 5 .
Work to be shown on the graph and answer to be written here.
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Space for extra work
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