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Junior Certifi cate Ordinary Level Maths Solutions
Sample Paper 2, no. 5
1. 15 × 15 = 225 × 6 = 1,350 cm2
2. (a)
70°
(b)
(c) To bisect means to divide an angle into two equal parts.
3. (a)
k
Object
Image
(b) No, the length remains 8 units and the width remains 4 units.
4. (a) 16
___
40 =
2 __
5
(b) 12
___
40 =
3 ___
10
(c) 4 ___
40 =
1 ___
10
(d) 8 ___
40 =
1 __
5
(e) Agree. All the coins are not the same size; for example, a fi fty-cent coin is larger than a twenty-cent coin.
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5. (a) [YZ] Reason: Opposite sides of a parallelogram are equal in measure.
(b) [XY] Reason: Opposite sides are equal in measure.
(c) |∠XYZ| Reason: Opposite angles are equal in measure.
(d) 104 cm2 = 52 × 2. Two triangles make up the parallelogram.
6. (a) 5 + 5 + 8 + 8 = 26 cm
(b) 30 × 18 × 16 = 8,640 cm3
(c) 15 × 7 × 8 = 840
8640 − 840 = 7,800 cm3
7. Answer: 35°
Explanation: |∠xyw| = 180° − 115° = 65°
|∠xwy| = 180° − 100° = 80°
The 3 angles add up to 180° in a triangle so
|∠yxw| = 180° − 65° − 80°
B = 35°
8. (a) Marks scored 10 20 30 40 50
Number of students 4 3 6 2 5
(b)
10 20 30Marks
40 50
9. (a) Primary data is data that you collect yourself.
(b) Secondary data is data obtained from a book or the internet or gathered by alternative surveyors.
(c) Primary, Secondary, Secondary, Secondary, Secondary
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10. (a)
x
y
1
–4 –3 –2 –1 100
2 3 4
2
3
4
–4
–3
–2
–1
C(4,–4)F(0,–4)D(–4,–4)
B(4,4)E(0,4)A(–4,4)
(b) (−4,−4)
(c) |AB| = 8, |BC| = 8, |CD| = 8, |DA| = 8
(d) E = (0,4)
(e) F = (0,−4)
(f) See diagram in part (a)
(g) Multiple possible answers: (0,0), (0,1), (0,2), … (0,−1), (0,−2)...
11. (a) 80 × 2 = 160 km
(b) 150
____
100 = 1.5 hours
(c) 2 + 1.5 = 3.5 hours
12. (a) King Queen Jack AceKing (K,K) (Q,K) (J,K) (A,K)
Queen (K,Q) (Q,Q) (J,Q) (A,Q)
Jack (K,J) (Q,J) (J,J) (A,J)
Ace (K,A) (Q,A) (J,A) (A,A)
(b) 1 ___
16
(c) 7 ___
16
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(d) 4 ___
16 =
1 __
4
(e) 9 ___
16
(f) 9 ___
16
13. (a) People would be more likely to answer Yes in order to seem ‘normal’. Alternative question: ‘Do you like movies?’
(b) Unclear. Alternative question: ‘How many times do you go to the cinema in a year?’
Never, 0–5 times, 6–10 times, More often
(c) The question is too personal. Alternative question: ‘What is your monthly income?’
0–500 euro, 501–1,000 euro, more than 1,001 euro
(d) It is a leading question.
Alternative question: ‘What is your opinion about actors’ pay?’
14. (a) A = 7°
(b) A = 70°
(c) A = 37°
15. (a)
14 m
40°
x
(b) sin 40° = 14
___ x
x sin 40° = 14
x = 14 ______
sin 40°
x = 21.78
x = 22 m
16. Line a contains points (0,2) and (−3,0).
Its slope is 0 − 2
______
−8 − 0 =
2 __
3 .
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Its equation is y − 0 = 2 __
3 (x + 3)
3y = 2x + 6 or 3x − 2y = −6
Line b contains (−1,0) and (0,−2).
Its slope is −2
___
1 = −2.
Its equation is y − 0 = −2(x + 1)
y = −2x − 2
2x + y = −2
Line c is the line y = −2 or y + 2 = 0.
Equations Sketched line
x = −2y + 2 = 02x − 3y = −62x + y = −2x −3y = 4
cab
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Junior Certifi cate Ordinary Level Maths Solutions
Sample Paper 2, no. 6
1. Sample answer: He might do a street survey on the main street; he could randomly stop people of all ages and ask them what foods they like.
2. (a) All three angles are 60° and the lengths of the three sides of the triangle are equal.
(b)
6 cm
6 cm
60°
60°
60°
6 cm
3. (a) 80 cm ÷ 2 = 40 cm
(b) pr2h = (3.142)(40)(40)(440)
= 2,211,968 cm3
(c) 2,211,968 × 8 = 17,695,744 cm3
4. Equation of the line Line
x = 2y = –3x = −4y = 2
wzxy
5. (a) 5.2 × 10 = 52 mm
(b) 1250 ÷ 1000 = 1.25 kg
(c) 3.75 × 1000 = 3,750 m
6. (a)
F B
U = 50
30 – x 25 – x
8
x
31
(b) 50 = 30 – x + x + 25 − x + 8
50 = 63 − x
x = 63 − 50
x = 13
(c) 8 ___
50 =
4 ___
25
(d) 17 + 12
_______
50 =
29 ___
50
7. (a)
D A
C B
(b) Spinner
A B C D
Die
1 (A,1) (B,1) (C,1) (D,1)
2 (A,2) (B,2) (C,2) (D,2)
3 (A,3) (B,3) (C,3) (D,3)
4 (A,4) (B,4) (C,4) (D,4)
5 (A,5) (B,5) (C,5) (D,5)
6 (A,6) (B,6) (C,6) (D,6)
(c) 3 ___
24 =
1 __
8
(d) 3 ___
24 =
1 __
8
8. (a) Stem Leaf
2 8
3 6 6 7 7 7 7 7 8 9 9
4 1 2 2 2 2 3 4 7 9
Key: 4|1 = 41
(b) 37 cm
(c) 39 cm
(d) In this case both are ideal, as they are relatively close in value.
(e) 49 − 28 = 21 cm
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9. (a) From looking at the graph, it seems that double the amount of money was spent in 2014 compared with 2012.
(b) Based on the y-axis, it seems that each year double the amount of money is spent on new buildings, but without a scale we cannot be sure. Also, the bars are increasing in width, suggesting it maybe more than double.
10. (a) Use the midpoint formula:
( 2 + 8 _____
2 ,
3 + 11 ______
2 ) = ( 10
___
2 ,
14 ___
2 ) = (5,7)
(b) Use (0,0) and (2,3)
√_______________
(2 − 0)2 + (3 − 0)2
= √_____
4 + 9 = √___
13 = 3.6 units
11. (a) 1st line: Positive; 2nd line: Negative
(b) Slope
Stage A 0
Stage B 5 __
2
Stage C 1 __
4
12. (a) tan 30° = 0.5773502692 = 0.577
(b), (c), (d)
30°
Adjacent100 m
Opp
osite
Hypotenuse
(e) tan 30° = height
______
100
height = 100 tan 30°
height = 57.73502692
height = 57.7 m
13. The diagonal bar:
(diagonal)2 = (1.8)2 + (2.5)2
(diagonal)2 = 3.24 + 6.25
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(diagonal)2 = 9.49
diagonal = √____
9.49
= 3.1 m
Total number needed 4(2.5) + 2(1.8) + 3.1 = 16.7 metres
14. Transformation Co-ordinates of vertices
Axial symmetry in the y-axis (3,2) (7,2) (7,6) (3,6)
Central symmetry in the point (0,0) (3,−2) (7,−2) (7,−6) (3,−6)
Axial symmetry in the x-axis (−7,−2) (−3,−2) (−3,−6) (−7,−6)
15. The mode, as it is the county that appears most often, in this case Kerry.
16. (a)
4 axes of symmetry
No axis of symmetry
5 axes of symmetry
(b) A = 60°
In a straight line, the angles add up to 180°.
A + 120 = 180
A = 180 − 120
A = 60°
(c) B = 50°
The three angles in a triangle add up to 180°.
B + 70 + 60 = 180
B + 130 = 180
B = 180 − 130
B = 50°
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Junior Certifi cate Ordinary Level Maths Solutions
Sample Paper 2, no. 7
1. A
P Q
2. (a) [BC] = 6 cm
(b) h = 3.5 cm
(c) Area = Answer from (a) × Answer from (b) = 21 cm2
3. (a) Radius = 40 ÷ 2 = 20 cm
(b) 2(3.14)(20) = 125.6 = 126 cm
(c) Radius = 50 cm
2(3.14)(50) = 314 cm
(d) 314 – 126 = 188 cm
(e) 314 × 150 = 47,100 cm or 471 m
4. Data Type of data
1. The number of horses in a race Numerical
2. Blood types of students in your class Categorical
3. The area of a garden Numerical
4. The score on a die Numerical
5. The colour of a t-shirt Categorical
6. The temperature in a fridge Numerical
5. (a) 3 __
6 =
1 __
2
(b) 1 __
6
(c) 3 __
6 =
1 __
2
6. (a) Letting (x = 0) 2(0) − y = −1
1 = y (0,1)
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Letting (y = 0) 2x − 0 = −1
2x = −1
x = − 1 __ 2
( − 1 __ 2 ,0 )
(b) Letting x = 0 0 + y = 4 (0,4)
Letting y = 0 x + 0 = 4 (4,0)
(c)
–2
–3
–4
–5
–6
–1
1
2
3
4
5
6
y
–1
x + y = 4
2x – y = –1
–2–3–4–5–6 1 2 3 5 640x
(d) (1,3)
7. (a) 360 − 135 − 45 − 30 − 90 = 60°
(b) Computer games
(c) 90° = 24 students so 360° = 96 students
8. (a) Mode of travel Walk Car Cycle Bus
Number of students 7 11 4 5
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(b)
Walk Car Cycle Bus
(c) Cycle
(d) It would be typical for a day with good weather, but if it was raining, some students who normally walk or cycle might choose to travel by car instead.
9. (a) Acute: 45° Right-angled: 90° Obtuse: 130° Straight: 180° Refl ex: 270° Null: 0°
(b) x = 130°, as it is vertically opposite 130°
(c) y = 50°; straight line ⇒180 − 130
(d) z = 50°, as it is vertically opposite angle y
(e) Angles Y and Z are equal in measure or vertically opposite or acute angles, but angles X and Y together make a 180° angle.
10. (a) A B C
1 (A,1) (B,1) (C,1)
2 (A,2) (B,2) (C,2)
3 (A,3) (B,3) (C,3)
4 (A,4) (B,4) (C,4)
5 (A,5) (B,5) (C,5)
6 (A,6) (B,6) (C,6)
(b) 18 outcomes
(c) 6 ___
18 =
1 __
3
(d) 3 ___
18 × 100 = 17%
(e) 3 ___
18 =
1 __
6
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11. (a) 01:25 ≈ 25:25
− 22:40
2:45
2 hours and 45 minutes
(b) 2 3 __
4 × 5 × €1.83 = € 25.16
12. (a)
–2
–3
–4
–5
–6
–1
1
2
3
4
5
6
y
–1
C
BA
–2–3–4–5–6 1 2 3 5 640x
(b) (−3,−3)
(c) ( −3 + 3 ______
2 ,
3 − 3 _____
2 ) = (0,0)
(d) ( 3 − 3 _____
2 ,
3 − 3 _____
2 ) = (0,0)
(e)
CD
BA
(f) Both diagonal intersect at the point (0,0), the midpoint of both diagonals.
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13. (a)
20°25 m
(b) tan 20° = h ___
25
h = 25 tan 20°
h = 9 metres
14. sin A = 3 __ 5 or cos A = 4 __
5 or tan A = 3 __
4
sin A = 0.6 cos A = 0.8 tan A = 0.75
A = 37°
15. (a) 120 × 80 × 50 = 480,000 cm3
(b) 240,000 ÷ 1,000 = 240 litres
16. Central symmetry in the point O: Δ BGO; axial symmetry in [HF]: Δ CGO; axial symmetry in [KG]: Δ AKO