Junior Certifi cate Ordinary Level Maths Solutions SEC 2013 ...

Junior Certificate Ordinary Level Maths Solutions SEC 2013 Sample Paper 2

1. = 6 ? ( 2 ? 2) = 6 ? 4 = 24 cm2

2. (a)

p r2h = (3.14)(3)(3)(10) = 282.6 cm3

(b) Base of carton B = 5 ? 5 = 25

_2_8_2_.6_ 25

=

11.304

= 11.3 cm

(c) Container: Cylindrical Tin A

Reason: The surface area of Tin A = 2prh = 2(3.14)(3)(10) = 188.4 but that of Carton B = 4(11.3 ? 5) + 2(5 ? 5) = 276

Less material is therefore needed for the cylinder, assuming that the materials used cost the same.

3. (a) 08:50

(b) 10:15 09:75

_?_0_8_:5_0_

=

_0_8_:_5_0_ 1 hour

25

minutes

(c) 75 minutes = 1 hour 15 mins

8:50

_?_1_:1_5_ 07:35

07:35

(d) 133.88 ? 74.99 ? 25.00

= 33.89

(e)

Speed

=

_D_i_s_ta_n_c_e_ Time

=

__4_6_4__k_m___ 1 hour 25 m

=

_4_6_4_ 85

?

60

=327.5 km/hr

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No. of students

4. Multiple possible answers. Examples:

Question Q1. What colour are your eyes?

Q2. What size T-shirt do you wear ? small, medium, large, extra large?

Q3. How many people are in your class? Q4. How old are you? 5. (a) UK 50, Ireland 50 (b)

8

6

4

2

Type of data Categorical data where the categories are not ordered Ordered categorical data Discrete numerical data Continuous numerical data

UK

No. of students

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Number of hours Ireland

8 6 4 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Number of hours

(c) Similarity: UK students and Irish students spent a maximum of 25 hours on social networking sites.

Difference: A lot more UK students spend from 20 to 24 hours on networking sites compared to Irish students.

(d) Answer: Yes

Reason: The majority of UK people spend from 13 to 22 hours networking, whereas Irish people are more varied, ranging from 3 to 20 hours in general.

2

6.

Colour

Frequency

Relative frequency

_F_r_e_q_u_e_n_c_y_ Total

% of total (Relative frequency ? 100)

Red 123

_1_2_3_ 240

51.25%

Blue 78

_7_8__ 240

32.5%

White 39

_3_9__ 240

16.25%

Total 240

(a) There may be more red disks in the bag.

(b)

Colour

Red

Probability

_1_2_3_ 240

Blue

_7__8_ 240

White

_3__9_ 240

(d) Answer: Yes

Reason: There must be a minimum of three disks (red, blue and white) and a students takes out only one at a time and replaces it.

(e) Answer: 5 Red, 3 Blue, 2 White Reason: It might explain why P(Red) = 51%, P(Blue) = 33% and P(White) = 16%

7. (a)

A name is picked at random from a list of 50 girls and 50 boys A = A girl's name is picked

A fair coin is tossed once B = A head is the outcome

One card is drawn at random from a pack of playing cards. C = The card is a diamond

A day is chosen at random from a list of the days of the week. D = The name of the day contains the letter a.

One number is picked at random from the set {1, 2, 3, 4, 5, 7, 11, 13} E = The number chosen is a prime number Prime = {2, 3, 5, 7, 11, 13}

Probability

_5__0_ 100

=

_1_ 2

_1_ 2

_1_3_ 52

=

_1_ 4

1

_6_ 8

=

_3_ 4

3

(b)

B

CX A

E

D

0

0.33 0.5

1

(c) Example: The probability of choosing the letter F from the word FACE.

(d) Example: The probability that tomorrow is Friday if today is Thursday.

(e) See scale above.

8. (a) Multiple answers.

List 1 8 8 8 8 8 List 2 1 8 8 8 9

Any set of five numbers when added together and divided by 5 give 8.

(b) List 1 7 7 7 7 7 7 The number 7 must occur the most often. List 2 7 7 7 1 2 3

230?

9. (a) |ABC| = 50?, |DEF| = 110?

(b)

M

115?

N

P

90?

O 40?

In order of magnitude: O N M P

10. (a) A + B + C = 180?

(b) C + D = 180?

(c) A + B + C = C + D (since equal to 180?) A + B = C ? C + D A + B = D

Hence, | A| + | B| = | D|

(d) 180 ? 112 = 68?

180 ? 47 ? 68 = a

47?

65? = a

?

68? 112?

4

11. (a) 180 ? 36 = 144 ? 2

(b) & (c)

= 72?

A

36?

Bisector D

72? 36? B

72? C

(d) |DBC| = 72? ? 2 = 36? since bisected.

|DCB| = 72?

from part (a)

|BDC| = 180 ? 72 ? 36 = 72?

(e) Yes, BDC is isosceles, since |BCD| = |BDC| = 72?. By theorem |BD| = |BC|.

(f) (g) 12. (a)

|AC| = 9.3 cm, |BC| = 5.7 cm

_|A_C__| |BC|

=

1.632

sin 25? = 0.423 sin 50? = 0.766

cos 25? = 0.906 cos 50? = 0.643

tan 25? = 0.466 tan 50? = 1.192

(b) (i) Answer: Incorrect Reason: tan 50? = 1.192, which is greater than 1.

(ii) Answer: Incorrect Reason: sin 25? = 0.423 But sin 50? = 0.766 and not 0.846.

(iii) Answer: Incorrect Reason: cos 25? = 0.906 But cos 50? = 0.643.

5

13. (a) Multiple possible answers, e.g. 5 metres.

(b)

sin

22

=

_h_ 5

h = 5 sin 22?

5 metres

String

h

h = 1.873032967 h = 1.9 metres

14.

1

2

22? Find the height h of the kite above the ground

3

4

15. (a)

y

5

4 X1 Y1 3 A(0,3)

2

1

?2 ?1 0 ?1

X2 Y2 B(4,0)

x 12345

?2

_______________

(b) _(4__?_0__)2__+_(_0 ? 3)2 _(4_)_2__+_(?3)2

16 + 9

___

25

= 5 units

(c) |OA| = 3, |OB| = 4

(d) |AB|2 = |OA|2 + |OB|2 |AB|2 = 32 + 42 |AB|2 = 9 + 16 |AB|2 = 25

___

|AB| = 25 = 5 units

6

16. (a) (b)

Midpoint of B(1,2) and D(5,6)

( ) _1_+2__5_,

_2_+__6_ 2

= (3,4)

E = (6,7)

(c) Answer: Bee 2

Reason: Journey of Bee 1 = 10__u_n_i_ts__________ _______________

Journey of Bee 2 = _(5__?__1_)2 + (_6__?_7_)_2 + (6 ? 5)2 + (2 ? 6)2

= _1_6_ + 1_+__1 + 16 = 17 + 17

= 8.25 units

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Junior Certificate Ordinary Level Maths Solutions Sample Paper 2, no. 1

1.

250

+ 950

1,200 g

_1_,2_0_0_ 1,000

=

1.2

kg

2. A, D, B, E, C

3. Example of numerical data: How many people are in your family?

Example of categorical data: What is your favourite colour? (Multiple possible answers)

4. (a) 247 km ? 5 = 1,235 km

(b) 175 km ? 3 = 525 km

(c) 1,235 + 525 = 1,760 ? 8 = 220 km

(d) 225 ? 9 = 2,025 ? 1,760 = 265 km 5.

6. (a) A = 110?, B = 90?, C = 300?, D = 55?

(b) 360? - (166? + 32? + 46?) 360? - 244? 116? = X Answer: X = 116? Explanation: A full revolution adds up to 360?.

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