Scrúduithe na Sryan Bruen
Sryan Bruen Examinations
Junior Certificate Examination 2017
Mathematics
Paper 1
Higher Level
Friday 9 June – Afternoon 2:00 to 4:30
For examinerQuestion / Mark / Question / Mark
1 / 11
2 / 12
3 / 13
4 / 14
5
6
7
8
9
10
Grade
300 marks
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 the spaces provided in this booklet. You may lose marks if you do not do so. You may ask the superintendent for more paper. Label any extra work clearly with the question number and part.
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 will lose marks if all necessary work is not clearly shown.
You may lose marks if the appropriate units of measurement are not included, where relevant.
You may lose marks if your answers are not given in simplest form, where relevant.
Write the make and model of your calculator(s) here:
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Question 1 (Suggested maximum time: 15 minutes)
(a) The price of a DVD increases from €12.50 to €13.75.
Express this as a percentage of the original price.
(b) (i) The time taken by Jack to travel from Derry to Waterford, a distance of
378 km, is 6 hours. His return journey from Waterford to Derry, by the
same route, takes an extra 45 mins.
By how many km/h is his average speed slower on the return journey?
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(ii) Jill has a gross income of €50,000.
Her total income tax payable amounts to €10,460.
The standard rate cut off point is €32,000.
The standard rate of tax is 20% and the higher rate is 42%.
What are Jill’s tax credits for the year?
Question 2 (Suggested maximum time: 10 minutes)
(i) By rounding to the nearest whole number, estimate the value of:
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(ii) Now evaluate, , correct to two decimal places.
Question 3 (Suggested maximum time: 10 minutes)
The sets A, B and C are as follows:
A = {2, 6, 8, 10} B = {1, 6, 7, 9} C = {1, 3, 7, 10}
(a) Complete the Venn diagram below:
(b) List the elements in the following sets:
(A ∪ B ∪ C)’ = ______
A ∩ C = ______
B \ A = ______
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Question 4 (Suggested maximum time: 10 minutes)
(a) Derek processed 390 passport applications during the month of July. He
processed 10% fewer applications during the month of August.
How many applications did Derek process in August?
(b) A merchant buys tea for €3.29 per kg and then sells it at a profit of 60% of
the cost price to a customer in England.
The exchange rate is £1 (sterling) = €1.46.
Calculate the selling price of the tea in £ sterling,
correct to two decimal places.
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Question 5 (Suggested maximum time: 10 minutes)
(i) Express this expression in its simplest form.
(ii) Hence, or otherwise, solve this equation.
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Question 6 (Suggested maximum time: 10 minutes)
Factorise the following:
9x² ˗ 16y²
6x² ˗ 19x + 10
17x ˗ 5x²
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Question 7 (Suggested maximum time: 15 minutes)
Let f be the function f : x → 1 – 3x and g be the function g : x → 1− x² .
(i) Find f (-2) and g (5).
(ii) Express f (x + 1) in the form ax + b, a and b ∈ Z.
(iii) Solve for x: f (x + 1) = f (-2) + g (5).
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Question 8 (Suggested maximum time: 5 minutes)
Given that:
Write s in terms of v, u and a.
Question 9 (Suggested maximum time: 10 minutes)
(i) The temperature on Sunday is x°. The temperature rose by 3° each for the
next two days. The temperature then dropped by 4° for the next three days.
Form an expression in x for the temperature on Friday.
(ii) Let f be the function f : x → 35x − 5x² .
Draw the graph of f for 0 ≤ x ≤ 7, x ∈ R on the next page.
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Question 10 (Suggested maximum time: 10 minutes)
(i) Write 316 in the form 2k, k ∈ Q.
(ii) (a) Write down the reciprocal of 72 .
(b) Find the value of this reciprocal, correct to two decimal places.
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Question 11 (Suggested maximum time: 5 minutes)
Put a tick (√) in the correct box in each row of the table below to show whether each number is a natural, integer, real, rational or irrational number. Tick multiple boxes if necessary.
Number / N / Z / R / Q / R\Qπ
2.9
7
128
Question 12 (Suggested maximum time: 10 minutes)
(i) Write 44,100 as a product of its prime factors.
(ii) The price of a playstation game is €59.99. In a sale the price of this playstation game is reduced to €49.99. What is the percentage reduction on the original price of the game in the sale? Give your answer correct to the nearest whole number.
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Question 13 (Suggested maximum time: 5 minutes)
A leisure centre has 110 members. The weights room (W) is used by 82 members and the swimming pool (S) is used by 57 members. 15 members do
not use either facility.
Fill in the Venn diagram below to show the number of members in each part of each set using the information above.
Question 14 (Suggested maximum time: 5 minutes)
Divide x³ + x² - 12x by x + 4
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Junior Certificate 2017 – Higher Level
Mathematics – Paper 1
Friday 9 June
Afternoon 2:00 to 4:30