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Junior Cycle Final Examination Sample Paper A
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Mathematics Ordinary Level 2 hours
Examination Number
270 marks
Day and Month of Birth
Edco JC Maths OL Sample Exam Paper A
Instructions There are 14 questions on this examination paper. Answer all questions.
Questions do not necessarily carry equal marks. To help you manage your time during this examination, a maximum time for each question is suggested. If you remain within these times you should have about 10 minutes left to review your work.
Write your answers in blue or black pen. You may use pencil in graphs and diagrams only.
This examination booklet will be scanned and your work will be presented to an examiner on screen. Anything that you write outside of the answer areas may not be seen by the examiner.
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Write your answers into this booklet. There is space for extra work at the back of the booklet. Label any extra work clearly with the question number and part.
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The superintendent will give you a copy of the Formulae and Tables booklet. You must return it at the end of the examination. You are not allowed to bring your own copy into the examination. You may lose marks if your solutions do not include supporting work. You may lose marks if you do not include the appropriate units of measurements, where relevant. You may lose marks if you do not give your answers in simplest form, where relevant.
Write the make and model of your calculator(s) here:
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Edco JC Maths OL Sample Exam Paper A
Question 1 (a)
(Suggested maximum time: 5 minutes)
Find the value of each of the following. (i)
409 + 781
(ii)
8 × 6·3
(iii) 12 ÷ (8 − 5)
(c)
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__ of the area of the shape below. Shade in 3 5
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(b)
Write the numbers 4, 5, and 17 into the spaces to make the mathematical statement true. Use each of the numbers once only.
7
+
21
=
21
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Edco JC Maths OL Sample Exam Paper A
Question 2
(Suggested maximum time: 10 minutes)
Tim bought 3 items in a shop.
They cost €2·99, €13·50 and €24·99. (a)
(i) Work out the total cost of the items.
(ii)
Tim paid for the items with a €50 note. How much change did he receive?
What is 35% of €350?
(c)
Subtract 15% of 200 from 42% of 500.
(d)
Which is higher: 20% of €25 or 30% of €20?
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(b)
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Edco JC Maths OL Sample Exam Paper A
(i) List the factors of 18 and 45. Factors of 18 =
Factors of 45 =
(ii)
,
,
,
,
,
,
,
,
,
,
Hence, write down the H.C.F. (highest common factor) of 18 and 45.
(iii) In an Art group, 18 sketching pencils and 45 colouring pencils were distributed among the group. All of the sketching pencils were shared equally among the group.
All of the colouring pencils were also shared equally among the group.
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What is the highest number of people in the Art group?
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(e)
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Edco JC Maths OL Sample Exam Paper A
Question 3
(Suggested maximum time: 5 minutes)
The temperature was recorded one evening. The results are in the table below. Time 6 pm 7 pm 8 pm 9 pm 10 pm
Temperature °C 5 °C 3 °C 1 °C −1 °C
(a)
If the pattern continued, what was the temperature at 10 pm?
(b)
Is the pattern LINEAR or NON-LINEAR? Tick ü one box only. Non-linear
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Give a reason for your answer.
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Linear
Reason:
(c)
What is the rate of change of temperature per hour?
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Edco JC Maths OL Sample Exam Paper A
(d)
The temperatures listed in the table are all Integers. Explain what an Integer is.
(e)
Identify any temperature from the list that is a Natural number.
(f)
Round these numbers to the nearest 10 and to the nearest 100. The first row is completed already. Nearest 10
Nearest 100
137
140
100
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58
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Number
409 684
(g)
765
Convert 296·8 to the form a × 10n where 1 ≤ a < 10, n ∈ N.
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Edco JC Maths OL Sample Exam Paper A
Question 4
(Suggested maximum time: 10 minutes)
The graph shows Simonâ&#x20AC;&#x2122;s journey to school. R
600 m
S
Distance P
0
5
Q
12
Time (mins)
These are 4 statements about the journey.
Match each statement to one of the 4 sections of the graph (OP, PQ, QR, RS).
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(a)
(b)
SECTION
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STATEMENT He stops to chat to his friends. He leaves home and walks at a constant speed for 5 minutes. He walks again at a faster speed. At school, he gets his books from his locker.
How far is his home from his school?
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Edco JC Maths OL Sample Exam Paper A
(c)
During which section does he travel fastest?
How can you decide this from the graph?
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Work out whether his average speed for the journey is higher or lower than 1 m/s.
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(d)
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Edco JC Maths OL Sample Exam Paper A
Question 5
(Suggested maximum time: 5 minutes)
Sets F and G are shown in the Venn diagram below.
(a)
F
G 7
4
1
5 3 6
Answer TRUE or FALSE to these statements. If you answer FALSE, write the true/correct statement. STATEMENT
TRUE/FALSE
TRUE/CORRECT STATEMENT IF NEEDED
F = {1,7,4}
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F ∪ G = {4}
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G\F = {5,6,3} G′ = {5,6,3} {1,7} ⊂ F
Ø⊂G
#(G) = 3 (b)
Set P = {p, i, n, e} List two SUBSETS of set P.
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Edco JC Maths OL Sample Exam Paper A
Question 6
(i) Solve 3(x − 2) > x + 4 where x ∈ R.
(ii)
(i) 5x − 7 is an expression. Work out the value of the expression when x = 4.
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(b)
Show the solution set on a number line.
(ii)
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(a)
(Suggested maximum time: 5 minutes)
2x + 5 is another expression. Work out its value when x = −4.
(iii) W ork out the value of x that makes the two expressions 5x − 7 and 2x + 5 equal to each other.
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Edco JC Maths OL Sample Exam Paper A
Question 7
(Suggested maximum time: 10 minutes)
Justine has â&#x201A;Ź240 in her savings account. She withdraws a fixed amount of money at the end of each week. The graph shows the amount in her savings account after 10 weeks. y
280
Savings
240 (5, 190)
200 160 120 80 40
x 5 Weeks
10
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How much is in Justineâ&#x20AC;&#x2122;s account after 10 weeks?
(b)
How much did Justine withdraw in total, over the 10 weeks?
(c)
What is the fixed amount that Justine withdraws per week?
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(a)
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Edco JC Maths OL Sample Exam Paper A
(d)
The point (5,190) is shown on the graph. What does this point tell you about Justine’s savings?
(e)
Which of these equations represents the graph? Tick ü one box only. S = 240 + 10w
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How many more weeks can Justine continue to withdraw the same amount at the end of each week?
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(f)
S = 240 − 10w
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Edco JC Maths OL Sample Exam Paper A
Question 8
(Suggested maximum time: 15 minutes) A
B
X
D
52°
52° Y E
B
C C
ABCD is a parallelogram. |∠ADE| = 52° and |∠AED| = 52°.
|∠B| =
|∠C| =
Triangle ADE is an isosceles triangle.
Calculate the measures of the angles marked X and Y in the diagram.
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(b)
Work out the measures of |∠B| and |∠C|.
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(a)
|∠X| =
|∠Y| =
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Edco JC Maths OL Sample Exam Paper A
The line segment [AB] is shown below. Construct its PERPENDICULAR BISECTOR. Show all construction lines clearly.
B
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A
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(c)
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Edco JC Maths OL Sample Exam Paper A
Question 9
(Suggested maximum time: 10 minutes)
A rectangular solid has length 45 cm and a square base of length 15 cm.
45 cm
15 cm
15 cm
Work out the volume of the rectangular solid.
(b)
The solid is cut into 3 equal pieces along the dashed lines, as in the diagram. Explain why each of the 3 pieces forms a cube.
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(a)
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Edco JC Maths OL Sample Exam Paper A
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Show that the volume of the cube is one third of the volume of the original rectangular solid.
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(c)
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Edco JC Maths OL Sample Exam Paper A
Question 10
(Suggested maximum time: 5 minutes)
A function S has a shape as an input. The output is the number of axes of symmetry of that shape. (a)
Complete the table, showing the number of axes of symmetry for each shape. Shape/Input x
Number of axes of symmetry/Output S(x)
Rectangle
2
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Equilateral
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Square
Isosceles
(b)
Write down the range of this function. Range = {2, , , }
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Edco JC Maths OL Sample Exam Paper A
Question 11
(Suggested maximum time: 5 minutes)
The diagram shows a spinner with 3 equal sections. The sections have a red, green and a blue colour.
Green
Red
Blue
The spinner is spun two times. An outcome could be Red, Blue. How many different outcomes are possible when the spinner is spun twice?
(b)
Complete the table, showing the possible outcomes.
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(a)
Red, Blue
(c)
Red, Red
(i) What is the probability of getting Red and Green in any order?
(ii)
What is the probability of getting the same colour on both spins?
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Edco JC Maths OL Sample Exam Paper A
Question 12
(Suggested maximum time: 5 minutes)
10°
13 m
A player stands 13 metres from a goalpost.
He kicks the ball at an angle 10° to the horizontal ground. The height of the goalpost is 2·44 m. (a)
What kind of angle is 10° ? Tick ü one box only.
Reflex angle
Assuming the ball travels in a straight line from the kick, work out whether the ball will go under or over the goalpost.
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(b)
Acute angle
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Right angle
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Edco JC Maths OL Sample Exam Paper A
Question 13
(Suggested maximum time: 5 minutes)
(a)
The mean of two numbers 12 and x is 17. Work out the value of x.
(b)
In this list of 6 numbers, A ∈ ℕ and A ≤ 5:
A, 5, 6, 14, 15, 19
Work out the median of the 6 numbers.
(ii)
If the range of the list of 6 numbers is 17, calculate the value of A.
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(i)
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Edco JC Maths OL Sample Exam Paper A
Question 14
(Suggested maximum time: 10 minutes)
Factorise fully the following expressions: x2 + 6x â&#x2C6;&#x2019; 16
(b)
3x2y + 6xy2
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(a)
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Edco JC Maths OL Sample Exam Paper A
Page for extra work.
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Label any extra work clearly with the question number and part.
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Edco JC Maths OL Sample Exam Paper A
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Edco JC Maths OL Sample Exam Paper A