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Practice paper, not an official KPM paper
50
Ujian Akhir Sesi AkademikEnd of Academic Session Test

MatematikMathematics

Tingkatan 1, 2 jam / 2 hours, 100 marks
Nama / Name
Kelas / Class
Tarikh / Date
Markah / Marks:      / 100
Instructions
  1. Kertas soalan ini mengandungi tiga bahagian: Bahagian A, Bahagian B dan Bahagian C.This question paper consists of three sections: Section A, Section B and Section C.
  2. Jawab semua soalan.Answer all questions.
  3. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Show your working. It may help you to get marks.
  4. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.The diagrams in this paper are not drawn to scale unless stated.
  5. Anda dibenarkan menggunakan kalkulator saintifik.You may use a scientific calculator.

Answer schemes are in English (DLP).

Practice shows answers as you go. Exam times you and hides answers until you submit.

Bahagian ASection A

20 marks
Jawab semua soalan. Setiap soalan diikuti oleh empat pilihan jawapan, A, B, C dan D. Pilih satu jawapan sahaja.Answer all questions. Each question is followed by four options, A, B, C and D. Choose one answer only.
1

Question 1

Jadual 1 menunjukkan untung (+) dan rugi (−) lima buah gerai di sebuah pasar malam pada satu malam. Susun gerai-gerai itu mengikut tertib menaik berdasarkan untung/rugi.Table 1 shows the profit (+) and loss (−) of five stalls at a pasar malam on one night. Arrange the stalls in ascending order of profit/loss.
Gerai
Stall		PQRST
Untung/Rugi (RM)
Profit/Loss (RM)		+45−12+8−300
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A
On a number line −30 < −12 < 0 < 8 < 45, so the order is S, Q, T, R, P. Option B orders by size without the sign; option D wrongly puts −12 before −30.
For the teacher: Understanding, low difficulty, Chapter 1, standard 1.1
Textbook p. 5
2

Question 2

Aiman mempunyai RM50. Dia membelanjakan 2⁄5 daripada wangnya untuk membeli sehelai baju dan RM12.50 untuk membeli makanan di pasar malam. Berapakah baki wang Aiman?Aiman has RM50. He spends 2⁄5 of his money on a shirt and RM12.50 on food at the pasar malam. How much money does Aiman have left?
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C
Shirt = 2/5 × 50 = RM20. Money left = 50 − 20 − 12.50 = RM17.50.
For the teacher: Applying, medium difficulty, Chapter 1, standard 1.5
Textbook p. 24
3

Question 3

Antara berikut, yang manakah faktor perdana bagi 84?Which of the following is a prime factor of 84?
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B
84 = 2 × 2 × 3 × 7, so the prime factors are 2, 3 and 7. 4, 12 and 21 are factors of 84 but they are not prime numbers.
For the teacher: Remembering, low difficulty, Chapter 2, standard 2.1
Textbook p. 34
4

Question 4

Sebuah gerai menambah stok minuman setiap 4 hari dan menambah stok buah-buahan setiap 6 hari. Kedua-dua stok itu ditambah pada 1 Mac. Bilakah tarikh berikutnya kedua-dua stok itu ditambah pada hari yang sama?A stall restocks its drinks every 4 days and restocks its fruits every 6 days. Both were restocked on 1 March. On what date will both be restocked on the same day again?
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D
LCM of 4 and 6 = 12. 1 March + 12 days = 13 March.
For the teacher: Applying, medium difficulty, Chapter 2, standard 2.2
Textbook p. 41
5

Question 5

Nilai √0.49 ialahThe value of √0.49 is
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B
0.7 × 0.7 = 0.49, so √0.49 = 0.7. 0.245 is 0.49 ÷ 2, which is not a square root.
For the teacher: Remembering, low difficulty, Chapter 3, standard 3.1
Textbook p. 52
6

Question 6

Hitung nilai ∛(−64) × √(16⁄25).Calculate the value of ∛(−64) × √(16⁄25).
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A
∛(−64) = −4 because (−4)³ = −64. √(16/25) = 4/5 = 0.8. −4 × 0.8 = −3.2. The cube root of a negative number is negative.
For the teacher: Applying, medium difficulty, Chapter 3, standard 3.2
Textbook p. 62
7

Question 7

Sebuah gerai minuman menjual 45 botol air soya dan 60 botol air cincau. Nyatakan nisbah bilangan botol air soya kepada bilangan botol air cincau dalam bentuk termudah.A drinks stall sells 45 bottles of soya drink and 60 bottles of cincau drink. State the ratio of the number of bottles of soya drink to the number of bottles of cincau drink in its simplest form.
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C
45 : 60 = (45 ÷ 15) : (60 ÷ 15) = 3 : 4. 9 : 12 is equivalent but not in its simplest form.
For the teacher: Understanding, low difficulty, Chapter 4, standard 4.1
Textbook p. 77
8

Question 8

Kak Lina ingin membeli air mineral yang sama jenama untuk jualan di gerainya. Pek manakah yang paling jimat?Kak Lina wants to buy bottled water of the same brand for her stall. Which pack is the best buy?
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B
Price per bottle (rate): A RM1.50, B RM7.00 ÷ 5 = RM1.40, C RM1.50, D RM1.45. The lowest price per bottle is B.
For the teacher: Evaluating, high difficulty, Chapter 4, standard 4.2
Textbook p. 82
9

Question 9

Farid membeli x bungkus nasi lemak dengan harga RM3 sebungkus dan 2 cawan teh tarik dengan harga RMy secawan. Tulis satu ungkapan algebra bagi jumlah harga, dalam RM, yang dibayar oleh Farid.Farid buys x packets of nasi lemak at RM3 each and 2 cups of teh tarik at RMy each. Write an algebraic expression for the total price, in RM, that Farid pays.
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D
Nasi lemak: x × 3 = 3x. Teh tarik: 2 × y = 2y. Total = 3x + 2y. Unlike terms cannot be combined, so 5xy is wrong.
For the teacher: Understanding, low difficulty, Chapter 5, standard 5.1
Textbook p. 107
10

Question 10

Ringkaskan 3(2p − q) − (p − 4q).Simplify 3(2p − q) − (p − 4q).
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A
3(2p − q) − (p − 4q) = 6p − 3q − p + 4q = 5p + q. Option B forgets that −(−4q) = +4q.
For the teacher: Applying, medium difficulty, Chapter 5, standard 5.2
Textbook p. 115
11

Question 11

Diberi x⁄4 + 3 = 8, cari nilai x.Given x⁄4 + 3 = 8, find the value of x.
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C
x/4 = 8 − 3 = 5, so x = 5 × 4 = 20.
For the teacher: Applying, low difficulty, Chapter 6, standard 6.1
Textbook p. 127
12

Question 12

Harga sebiji burger ialah RMx dan harga secawan air ialah RMy. Dua biji burger dan secawan air berharga RM17, iaitu 2x + y = 17. Antara berikut, pasangan (x, y) yang manakah ialah penyelesaian bagi persamaan itu?The price of a burger is RMx and the price of a cup of drink is RMy. Two burgers and a cup of drink cost RM17, that is 2x + y = 17. Which pair (x, y) is a solution of the equation?
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B
Substitute: 2(5) + 7 = 17. The others give 2(6) + 4 = 16, 2(4) + 8 = 16 and 2(7) + 2 = 16.
For the teacher: Understanding, medium difficulty, Chapter 6, standard 6.2
Textbook p. 134
13

Question 13

Garis nombor manakah yang mewakili ketaksamaan x ≥ −2?Which number line represents the inequality x ≥ −2?
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C
≥ uses a solid dot (−2 is included) and the arrow points to the right (values greater than −2). A is x ≤ −2, B is x > −2 and D is x < −2.
For the teacher: Understanding, low difficulty, Chapter 7, standard 7.1
Textbook p. 152
14

Question 14

Dalam Rajah 1, PQ dan RS ialah garis selari dan TU ialah garis rentas lintang. Cari nilai x.In Diagram 1, PQ and RS are parallel lines and TU is a transversal. Find the value of x.
Parallel lines PQ and RS cut by transversal TU at V and W. Angle TVQ is 58 degrees; angle x is angle RWV.
Rajah 1Diagram 1
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D
∠VWS = ∠TVQ = 58° (corresponding angles). Angles on a straight line RS: x = 180° − 58° = 122°.
For the teacher: Applying, medium difficulty, Chapter 8, standard 8.3
Textbook p. 190
15

Question 15

Rajah 2 menunjukkan sebuah sisi empat ABCD. ADE ialah garis lurus. Cari nilai x.Diagram 2 shows a quadrilateral ABCD. ADE is a straight line. Find the value of x.
Quadrilateral ABCD with angle A 95 degrees, angle B 110 degrees, angle C x, and the exterior angle CDE 80 degrees where AD is extended to E.
Rajah 2Diagram 2
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A
Interior ∠ADC = 180° − 80° = 100°. Sum of interior angles of a quadrilateral = 360°, so x = 360° − 95° − 110° − 100° = 55°. 75° comes from using 80° as the interior angle.
For the teacher: Analysing, high difficulty, Chapter 9, standard 9.3
Textbook p. 216
16

Question 16

Rajah 3 menunjukkan sekeping tanda harga berbentuk trapezium. Hitung luas tanda harga itu.Diagram 3 shows a price tag in the shape of a trapezium. Calculate the area of the price tag.
Trapezium-shaped price tag with parallel sides 6 cm and 10 cm and height 4 cm.
Rajah 3Diagram 3
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D
Area of trapezium = ½ × (sum of parallel sides) × height = ½ × (6 + 10) × 4 = 32 cm². 64 cm² forgets the ½.
For the teacher: Applying, low difficulty, Chapter 10, standard 10.2
Textbook p. 233
17

Question 17

Gambar rajah Venn dalam Rajah 4 menunjukkan set semesta ξ, set A dan set B. Cari n(B′).The Venn diagram in Diagram 4 shows the universal set ξ, set A and set B. Find n(B′).
Venn diagram. A only: 2, 4, 8, 10. A and B: 6, 12. B only: 3, 9. Outside both: 1, 5, 7, 11.
Rajah 4Diagram 4
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C
B′ is every element of ξ not in B: 2, 4, 8, 10, 1, 5, 7, 11, so n(B′) = 8.
For the teacher: Understanding, low difficulty, Chapter 11, standard 11.2
Textbook p. 255
18

Question 18

Carta palang dalam Rajah 5 menunjukkan bilangan bungkus nasi lemak yang dijual oleh Mak Cik Ros di pasar malam dalam lima minggu. Hitung beza antara bilangan bungkus nasi lemak yang paling banyak dengan yang paling sedikit dijual dalam satu minggu.The bar chart in Diagram 5 shows the number of packets of nasi lemak sold by Mak Cik Ros at the pasar malam in five weeks. Calculate the difference between the greatest and the least number of packets sold in one week.
Bar chart: week 1, 24; week 2, 36; week 3, 30; week 4, 42; week 5, 18 packets.
Rajah 5Diagram 5
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A
Greatest = 42 (week 4), least = 18 (week 5). Difference = 42 − 18 = 24.
For the teacher: Understanding, low difficulty, Chapter 12, standard 12.1
Textbook p. 270
19

Question 19

Carta pai dalam Rajah 6 menunjukkan perbelanjaan Puan Siti di sebuah pasar malam. Dia membelanjakan RM48 untuk sayur-sayuran. Berapakah wang yang dibelanjakannya untuk buah-buahan?The pie chart in Diagram 6 shows Puan Siti's spending at a pasar malam. She spent RM48 on vegetables. How much did she spend on fruits?
Pie chart: food 120 degrees, clothes 90 degrees, vegetables 60 degrees, fruits x degrees.
Rajah 6Diagram 6
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B
Fruits: x = 360° − 120° − 90° − 60° = 90°. 60° stands for RM48, so the total = 48 × 360 ÷ 60 = RM288. Fruits = 90/360 × 288 = RM72.
For the teacher: Analysing, high difficulty, Chapter 12, standard 12.1
Textbook p. 272
20

Question 20

Rajah 7 menunjukkan sehelai bendera hiasan berbentuk segi tiga bersudut tegak PQR di sebuah gerai. Hitung perimeter bendera hiasan itu.Diagram 7 shows a decorative flag in the shape of a right-angled triangle PQR at a stall. Calculate the perimeter of the flag.
Right-angled triangle PQR with the right angle at Q, PQ = 9 cm and hypotenuse PR = 15 cm.
Rajah 7Diagram 7
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D
By Pythagoras' theorem, QR = √(15² − 9²) = √144 = 12 cm. Perimeter = 9 + 12 + 15 = 36 cm. 41.5 cm wrongly treats PR as a shorter side.
For the teacher: Applying, high difficulty, Chapter 13, standard 13.1
Textbook p. 296

Bahagian BSection B

20 marks
Jawab semua soalan. Pilih jawapan yang betul bagi setiap ceraian.Answer all questions. Choose the correct answer for each part.
21

Question 21

Puan Lina mempunyai 48 biji epal dan 36 biji oren. Dia ingin membungkus semua buah itu ke dalam beg yang sama banyak isinya tanpa sebarang baki, dengan bilangan beg yang paling banyak.Puan Lina has 48 apples and 36 oranges. She wants to pack all the fruits into bags with the same contents and nothing left over, using the greatest possible number of bags.
[1 mark] (a)Benar atau palsu: 4 ialah faktor sepunya bagi 48 dan 36.True or false: 4 is a common factor of 48 and 36.
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True
48 ÷ 4 = 12 and 36 ÷ 4 = 9, so 4 divides both numbers exactly.
[1 mark] (b)Faktor sepunya terbesar (FSTB) bagi 48 dan 36 ialahThe highest common factor (HCF) of 48 and 36 is
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12
48 = 2⁴ × 3 and 36 = 2² × 3², so HCF = 2² × 3 = 12. This is the greatest number of bags.
[1 mark] (c)Bilangan biji epal di dalam setiap beg ialahThe number of apples in each bag is
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4
48 apples ÷ 12 bags = 4 apples in each bag (and 36 ÷ 12 = 3 oranges).
[1 mark] (d)Gandaan sepunya terkecil (GSTK) bagi 48 dan 36 ialahThe lowest common multiple (LCM) of 48 and 36 is
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144
LCM = 2⁴ × 3² = 144. 1728 = 48 × 36 is a common multiple but not the lowest; 72 is not a multiple of 48.
For the teacher: Understanding, low difficulty, Chapter 2, standard 2.1
Textbook p. 36
22

Question 22

Encik Rahim menjual keropok lekor. Harga sebungkus kecil ialah RMp dan harga sebungkus besar ialah RMq. Ungkapan 4p − 3q + 5 digunakan dalam buku akaunnya.Encik Rahim sells keropok lekor. A small packet costs RMp and a large packet costs RMq. The expression 4p − 3q + 5 is used in his account book.
[1 mark] (a)Bilangan sebutan dalam ungkapan 4p − 3q + 5 ialahThe number of terms in the expression 4p − 3q + 5 is
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3
The terms are 4p, −3q and 5.
[1 mark] (b)Pekali bagi q dalam ungkapan itu ialahThe coefficient of q in the expression is
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−3
The term is −3q, so the coefficient of q is −3 (the sign belongs to the coefficient).
[1 mark] (c)Sebutan yang serupa dengan 5pq ialahThe term that is a like term to 5pq is
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−2qp
Like terms have the same variables with the same powers: qp = pq. pq² has q to the power 2.
[1 mark] (d)Nilai 4p − 3q + 5 apabila p = 2 dan q = −1 ialahThe value of 4p − 3q + 5 when p = 2 and q = −1 is
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16
4(2) − 3(−1) + 5 = 8 + 3 + 5 = 16.
For the teacher: Understanding, low difficulty, Chapter 5, standard 5.1
Textbook p. 111
23

Question 23

Rajah 8 menunjukkan dua lorong lurus, AB dan CD, di sebuah pasar malam yang bersilang di O.Diagram 8 shows two straight lanes, AB and CD, at a pasar malam that intersect at O.
Straight lines AB and CD intersect at O. Angle AOC is 38 degrees, x is angle BOD and y is angle COB.
Rajah 8Diagram 8
[1 mark] (a)Sudut x dan ∠AOC ialahAngle x and ∠AOC are
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Vertically opposite angles
x and ∠AOC are opposite each other where two straight lines cross.
[1 mark] (b)Nilai x ialahThe value of x is
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38°
Vertically opposite angles are equal, so x = 38°.
[1 mark] (c)Nilai y ialahThe value of y is
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142°
Angles on the straight line AB add up to 180°: y = 180° − 38° = 142°.
[1 mark] (d)Sudut refleks AOC ialahThe reflex angle AOC is
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322°
Reflex ∠AOC = 360° − 38° = 322° (conjugate angles add up to 360°).
For the teacher: Applying, medium difficulty, Chapter 8, standard 8.2
Textbook p. 186
24

Question 24

Rajah 9 menunjukkan sehelai kain rentang berbentuk trapezium yang digantung di hadapan sebuah gerai.Diagram 9 shows a banner in the shape of a trapezium hung in front of a stall.
Right trapezium with parallel sides 12 cm and 20 cm, height 6 cm and slanted side 10 cm.
Rajah 9Diagram 9
[1 mark] (a)Perimeter kain rentang itu ialahThe perimeter of the banner is
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48 cm
Perimeter = 12 + 10 + 20 + 6 = 48 cm.
[1 mark] (b)Luas kain rentang itu ialahThe area of the banner is
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96 cm²
Area = ½ × (12 + 20) × 6 = 96 cm². 192 forgets the ½ and 120 uses 20 × 6.
[1 mark] (c)Sebuah segi empat tepat berukuran 16 cm × 8 cm mempunyai perimeter yangA rectangle measuring 16 cm × 8 cm has a perimeter that is
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The same as the perimeter of the banner
2 × (16 + 8) = 48 cm, the same as the banner.
[1 mark] (d)Benar atau palsu: Dua bentuk yang mempunyai perimeter yang sama sentiasa mempunyai luas yang sama.True or false: Two shapes with the same perimeter always have the same area.
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False
The rectangle and the banner both have a perimeter of 48 cm, but the rectangle's area is 16 × 8 = 128 cm² and the banner's is 96 cm².
For the teacher: Applying, medium difficulty, Chapter 10, standard 10.3
Textbook p. 239
25

Question 25

Rajah 10 menunjukkan jualan aiskrim, dalam RM, di sebuah gerai pasar malam dalam enam minggu.Diagram 10 shows the ice-cream sales, in RM, at a pasar malam stall over six weeks.
Line graph of sales in RM: week 1, 120; week 2, 150; week 3, 120; week 4, 180; week 5, 210; week 6, 150.
Rajah 10Diagram 10
[1 mark] (a)Perwakilan data dalam Rajah 10 ialahThe data representation in Diagram 10 is a
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Line graph
Points joined by straight lines show how the sales change over time: a line graph.
[1 mark] (b)Jualan paling tinggi berlaku padaThe highest sales were in
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Week 5
Week 5 has the highest point, RM210.
[1 mark] (c)Beza jualan antara minggu 4 dengan minggu 2 ialahThe difference between the sales in week 4 and week 2 is
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RM30
Week 4 = RM180, week 2 = RM150. 180 − 150 = RM30.
[1 mark] (d)Benar atau palsu: Jualan aiskrim meningkat setiap minggu.True or false: The ice-cream sales increased every week.
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False
Sales fell from week 2 (RM150) to week 3 (RM120) and from week 5 (RM210) to week 6 (RM150).
For the teacher: Understanding, low difficulty, Chapter 12, standard 12.1
Textbook p. 273

Bahagian CSection C

60 marks
Jawab semua soalan. Tulis jawapan anda di ruang yang disediakan. Tunjukkan langkah-langkah penting dalam kerja mengira anda.Answer all questions. Write your answers in the spaces provided. Show your working.
26

Question 26

Puan Rosnah menyewa sebuah tapak gerai berbentuk segi empat sama di pasar malam. Luas tapak itu ialah 20.25 m².Puan Rosnah rents a square stall lot at the pasar malam. The area of the lot is 20.25 m².
[2 marks] (a)Hitung panjang sisi tapak gerai itu.Calculate the length of a side of the stall lot.
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[1 mark] (b)Dia memasang lampu hiasan di sepanjang semua sisi tapak itu. Berapakah panjang lampu hiasan yang diperlukan?She puts decorative lights along all the sides of the lot. What length of lights does she need?
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[2 marks] (c)Dia menyimpan barang jualannya di dalam sebuah kotak berbentuk kubus yang isi padunya 0.216 m³. Cari panjang sisi kotak itu.She keeps her goods in a cube-shaped box with a volume of 0.216 m³. Find the length of an edge of the box.
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[3 marks] (d)Hitung nilai (−0.4)³ + √(19⁄16).Calculate the value of (−0.4)³ + √(19⁄16).
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For the teacher: Applying, low difficulty, Chapter 3, standard 3.1
Textbook p. 54
27

Question 27

Ketaksamaan linear digunakan semasa membeli-belah di pasar malam.Linear inequalities are used when shopping at the pasar malam.
[1 mark] (a)Semua barang di sebuah gerai berharga paling banyak RM5. Tulis satu ketaksamaan bagi harga, RMh, setiap barang.Every item at a stall costs at most RM5. Write an inequality for the price, RMh, of each item.
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[1 mark] (b)Tulis ketaksamaan yang diwakili oleh garis nombor dalam Rajah 11.Write the inequality represented by the number line in Diagram 11.
Number line from −3 to 3 with an open circle at −1 and an arrow pointing right.
Rajah 11Diagram 11
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[2 marks] (c)Selesaikan ketaksamaan 3x − 4 < 11.Solve the inequality 3x − 4 < 11.
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[4 marks] (d)Hana mempunyai RM30. Dia membeli sehelai kemeja-T berharga RM12 dan beberapa rantai kunci berharga RM2.50 setiap satu. Bentuk satu ketaksamaan linear dan seterusnya cari bilangan maksimum rantai kunci yang boleh dibeli oleh Hana.Hana has RM30. She buys a T-shirt for RM12 and some keychains at RM2.50 each. Form a linear inequality and hence find the maximum number of keychains Hana can buy.
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For the teacher: Applying, low difficulty, Chapter 7, standard 7.2
Textbook p. 160
28

Question 28

Kak Mira menjual air bandung di pasar malam. Dia mencampurkan sirap ros, susu cair dan air dengan nisbah 2 : 3 : 15 untuk menyediakan 5 liter air bandung.Kak Mira sells air bandung at the pasar malam. She mixes rose syrup, evaporated milk and water in the ratio 2 : 3 : 15 to make 5 litres of air bandung.
[2 marks] (a)Hitung isi padu sirap ros, dalam ml, yang digunakan.Calculate the volume of rose syrup, in ml, that she uses.
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[2 marks] (b)Dia menjual air bandung itu dalam cawan 250 ml dengan harga RM2 secawan. Hitung jumlah wang yang diterima jika semua air bandung itu habis dijual.She sells the air bandung in 250 ml cups at RM2 a cup. Calculate the total money she receives if all of it is sold.
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[2 marks] (c)Dia menjual 20 cawan dalam masa 50 minit. Pada kadar yang sama, berapa minitkah masa yang diambil untuk menjual 32 cawan?She sells 20 cups in 50 minutes. At the same rate, how many minutes does she take to sell 32 cups?
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[2 marks] (d)Sebungkus gula 4 kg berharga RM11.20. Berapakah harga 7 kg gula yang sama?A 4 kg pack of sugar costs RM11.20. What is the price of 7 kg of the same sugar?
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[2 marks] (e)Siti berkata susu cair ialah lebih daripada 1⁄5 daripada campuran itu. Adakah Siti betul? Berikan justifikasi anda.Siti says the evaporated milk is more than 1⁄5 of the mixture. Is Siti correct? Justify your answer.
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For the teacher: Applying, medium difficulty, Chapter 4, standard 4.4
Textbook p. 88
29

Question 29

Gambar rajah Venn dalam Rajah 12 menunjukkan bilangan pengunjung pasar malam yang membeli makanan, F, dan minuman, D. Jumlah pengunjung yang ditemu bual ialah 40 orang.The Venn diagram in Diagram 12 shows the number of pasar malam visitors who bought food, F, and drinks, D. A total of 40 visitors were interviewed.
Venn diagram: F only 15, F and D x, D only 8, outside both 5.
Rajah 12Diagram 12
[2 marks] (a)Cari nilai x.Find the value of x.
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[1 mark] (b)Cari n(F).Find n(F).
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[1 mark] (c)Cari n(D′).Find n(D′).
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[2 marks] (d)Huraikan pengunjung dalam set F ∩ D′ dan nyatakan bilangannya.Describe the visitors in the set F ∩ D′ and state how many there are.
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[2 marks] (e)Diberi ξ = {x : x ialah integer, 1 ≤ x ≤ 12}, A = {faktor bagi 12} dan B = {gandaan bagi 4}. Senaraikan semua unsur set A′.Given ξ = {x : x is an integer, 1 ≤ x ≤ 12}, A = {factors of 12} and B = {multiples of 4}. List all the elements of set A′.
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[2 marks] (f)Adakah B ⊂ A? Berikan sebab.Is B ⊂ A? Give a reason.
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For the teacher: Applying, low difficulty, Chapter 11, standard 11.2
Textbook p. 256
30

Question 30

Poligon dapat dilihat pada papan tanda dan barang hiasan di pasar malam. Rajah 13 dan Rajah 14 digunakan dalam ceraian (b) dan (c).Polygons can be seen on the signboards and decorations at the pasar malam. Diagram 13 and Diagram 14 are used in parts (b) and (c).
Isosceles triangle PQR, PQ = PR, angle QPR 40 degrees; QR is extended to S and y is the exterior angle PRS.
Rajah 13Diagram 13
Kite JKLM with JK = JM and LK = LM; angle KJM is 70 degrees and angle KLM is 50 degrees.
Rajah 14Diagram 14
[2 marks] (a)Sebuah papan tanda berbentuk poligon dengan 6 sisi. Namakan poligon itu dan nyatakan bilangan pepenjurunya.A signboard is a polygon with 6 sides. Name the polygon and state its number of diagonals.
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[3 marks] (b)Rajah 13 menunjukkan sebuah segi tiga sama kaki PQR dengan PQ = PR. QRS ialah garis lurus. Cari nilai y.Diagram 13 shows an isosceles triangle PQR with PQ = PR. QRS is a straight line. Find the value of y.
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[4 marks] (c)Rajah 14 menunjukkan sebuah lelayang JKLM yang dijual di sebuah gerai. Hitung (i) ∠JKL, (ii) sudut peluaran pada bucu K.Diagram 14 shows a kite JKLM sold at a stall. Calculate (i) ∠JKL, (ii) the exterior angle at vertex K.
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[3 marks] (d)Aida mendakwa bahawa sebuah segi tiga dengan sudut-sudut 2x, 3x dan 5x ialah segi tiga bersudut tegak. Adakah dakwaan Aida benar? Tunjukkan pengiraan anda.Aida claims that a triangle with angles 2x, 3x and 5x is a right-angled triangle. Is Aida's claim true? Show your calculation.
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For the teacher: Analysing, medium difficulty, Chapter 9, standard 9.2
Textbook p. 208
31

Question 31

Di sebuah gerai pasar malam, harga secawan cendol ialah RMx dan harga sepinggan rojak ialah RMy.At a pasar malam stall, a cup of cendol costs RMx and a plate of rojak costs RMy.
[3 marks] (a)Sebelum menyelesaikan masalah harga, selesaikan persamaan linear 5(m − 2) = 3m + 8.Before solving the price problem, solve the linear equation 5(m − 2) = 3m + 8.
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[5 marks] (b)Dua cawan cendol dan sepinggan rojak berharga RM13. Tiga cawan cendol dan dua pinggan rojak berharga RM22. Tulis dua persamaan linear dan seterusnya cari harga secawan cendol dan harga sepinggan rojak.Two cups of cendol and a plate of rojak cost RM13. Three cups of cendol and two plates of rojak cost RM22. Write two linear equations and hence find the price of a cup of cendol and of a plate of rojak.
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[2 marks] (c)Farid mempunyai RM30. Dia ingin membeli 4 cawan cendol dan 3 pinggan rojak. Adakah wangnya mencukupi? Berikan justifikasi anda.Farid has RM30. He wants to buy 4 cups of cendol and 3 plates of rojak. Is his money enough? Justify your answer.
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[2 marks] (d)Farid ingin membeli sekurang-kurangnya 6 item, dengan sekurang-kurangnya secawan cendol dan sepinggan rojak, tanpa melebihi RM30. Cadangkan satu gabungan yang boleh dibelinya dan tunjukkan bahawa gabungan itu memenuhi syarat.Farid wants to buy at least 6 items, with at least one cup of cendol and one plate of rojak, without spending more than RM30. Suggest a combination he can buy and show that it meets the conditions.
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For the teacher: Creating, high difficulty, Chapter 6, standard 6.3
Textbook p. 140
Test specification (JSU)
ChapterRememberingUnderstandingApplyingAnalysingEvaluatingCreatingItemsmarks
1. Rational numbers–1 (1)1 (1)–––22
2. Factors and multiples1 (1)1 (4)1 (1)–––36
3. Squares, Square Roots, Cubes and Cube Roots1 (1)–2 (9)–––310
4. Ratios, Rates and Proportions–1 (1)1 (10)–1 (1)–312
5. Algebraic expressions–2 (5)1 (1)–––36
6. Linear equations–1 (1)1 (1)––1 (12)314
7. Linear inequalities–1 (1)1 (8)–––29
8. Lines and angles––2 (5)–––25
9. Basic polygons–––2 (13)––213
10. Perimeter and area––2 (5)–––25
11. Introduction of set–1 (1)1 (10)–––211
12. Data handling–2 (5)–1 (1)––36
13. The Pythagoras' Theorem––1 (1)–––11
Total2 (2)10 (19)14 (52)3 (14)1 (1)1 (12)31100
Each cell shows items (marks).