25 Junior Certificate Ordinary Level Maths Solutions Sample Paper 2, no. 5 1. 15 × 15 = 225 × 6 = 1,350 cm 2 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 fifty-cent coin is larger than a twenty-cent coin.
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Junior Certifi cate Ordinary Level Maths Solutions Sample ... · 30 Junior Certifi cate Ordinary Level Maths Solutions Sample Paper 2, no. 6 1. Sample answer: He might do a street
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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
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(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.
(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.