Coordinates, Ratio and Proportion: Mathematics Darjah 6 questions

Section A: objective questions

8 marks

Choose the correct answer.

Write the ratio 18 : 24 in the simplest form.

9 : 12
6 : 8
3 : 4
2 : 3

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Divide both numbers by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 3 : 4. 9 : 12 and 6 : 8 are equal to 3 : 4 but are not in the simplest form.

For the teacher: Remembering, low difficulty, standard 7.2.1

Textbook p. 193

Diagram 1 shows points P and Q on a Cartesian plane. What is the actual horizontal distance of Q from P?

Cartesian plane with P at (1, 2) and Q at (5, 4). Scale: 1 unit is 1 km. — Diagram 1

4 km
2 km
6 km
5 km

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P is at (1, 2) and Q is at (5, 4). Horizontal distance = 5 − 1 = 4 units = 4 km. (2 km is the vertical distance.)

For the teacher: Understanding, low difficulty, standard 7.1.1

Textbook p. 187

What is the ratio of 600 g to 2 kg in the simplest form?

300 : 1
6 : 2
1 : 3
3 : 10

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2 kg = 2 000 g. 600 : 2 000 = 3 : 10 (divide by 200). The units must be the same before writing the ratio.

For the teacher: Applying, low difficulty, standard 7.2.1

Textbook p. 194

The ratio of the number of boys to the number of girls in a choir is 3 : 2. There are 12 boys. How many girls are there?

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3 parts = 12, so 1 part = 4. Girls = 2 × 4 = 8.

For the teacher: Applying, low difficulty, standard 7.3.1

Textbook p. 198

Diagram 2 shows points R and T. Each unit on the plane represents 2 km. What is the actual vertical distance of T from R?

Cartesian plane with R at (1, 1) and T at (4, 5). Scale: 1 unit is 2 km. — Diagram 2

4 km
16 km
8 km
5 km

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R is at (1, 1) and T is at (4, 5). Vertical distance = 5 − 1 = 4 units. 4 × 2 km = 8 km. (4 km forgets the scale.)

For the teacher: Applying, medium difficulty, standard 7.1.1

Textbook p. 188

Diagram 3 shows some shapes. What is the ratio of the number of squares to the total number of shapes?

6 circles, 4 squares and 2 triangles — Diagram 3

1 : 2
2 : 3
1 : 6
1 : 3

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There are 4 squares and 6 + 4 + 2 = 12 shapes in all. 4 : 12 = 1 : 3. (2 : 3 is squares to circles.)

For the teacher: Understanding, low difficulty, standard 7.2.1

Textbook p. 196

The ratio of Hana's savings to Ima's savings is 5 : 2. Their total savings is RM49. How much does Hana save?

RM35
RM14
RM25
RM28

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5 + 2 = 7 parts = RM49, so 1 part = RM7. Hana: 5 × RM7 = RM35. (RM14 is Ima's.)

For the teacher: Applying, low difficulty, standard 7.3.1

Textbook p. 200

A box has 15 red marbles and 10 blue marbles. 5 red marbles are taken out. What is the ratio of red marbles to blue marbles now?

3 : 2
1 : 1
2 : 3
1 : 2

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Red now = 15 − 5 = 10. Blue = 10. The ratio is 10 : 10 = 1 : 1. (3 : 2 is the ratio before the marbles are taken out.)

For the teacher: Analysing, medium difficulty, standard 7.4.1

Textbook p. 202

Section B: structured questions

35 marks

Answer all questions. Show your working.

Diagram 4 shows the position of three villages. Each unit on the plane is 1 km.

Cartesian plane with Bayu at (1, 5), Cempaka at (4, 3) and Dahlia at (2, 1). Scale bar 0 to 5 km, 1 unit is 1 km. — Diagram 4

[1 mark] (a)State the horizontal distance of Cempaka from Bayu, in km.

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4 − 1 = 3 km [1]1

Tick each point you got.

[1 mark] (b)State the vertical distance of Dahlia from Bayu, in km.

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5 − 1 = 4 km [1]1

Tick each point you got.

[1 mark] (c)A shop is 2 km horizontally and 2 km vertically from Cempaka. Which village is it?

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Dahlia [1]1

Tick each point you got.

For the teacher: Remembering, low difficulty, standard 7.1.1

Textbook p. 189

Write each ratio in the simplest form.

[1 mark] (a)16 : 40

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2 : 5 [1]1

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[2 marks] (b)3 kg : 500 g

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3 000 : 500 [1]1
6 : 1 [1]1

Tick each point you got.

[2 marks] (c)80 sen : RM2

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80 : 200 [1]1
2 : 5 [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 7.2.1

Textbook p. 195

Diagram 5 shows a school, a clinic and a mosque. Each unit on the plane is 1 cm and the scale is 1 : 100 000.

Cartesian plane with School at (2, 4), Clinic at (5, 2) and Mosque at (3, 5). Scale 1 : 100 000, 1 unit is 1 cm. — Diagram 5

[1 mark] (a)How many kilometres does 1 cm on the plane represent?

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100 000 cm = 1 000 m = 1 km [1]1

Tick each point you got.

[2 marks] (b)State the actual horizontal distance and vertical distance of the clinic from the school.

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Horizontal: 5 − 2 = 3 km [1]1
Vertical: 4 − 2 = 2 km [1]1

Tick each point you got.

[1 mark] (c)Which place is 2 km horizontally and 3 km vertically from the clinic?

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Mosque [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 7.1.1

Textbook p. 188

The ratio of Fiza's stickers to Gopal's stickers is 4 : 7. Fiza has 28 stickers.

[2 marks] (a)How many stickers does Gopal have?

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1 part = 28 ÷ 4 = 7 [1]1
7 × 7 = 49 [1]1

Tick each point you got.

[1 mark] (b)How many stickers do they have altogether?

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28 + 49 = 77 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 7.3.1

Textbook p. 198

The ratio of Zack's savings to Yin's savings is 3 : 5. Their total savings is RM96.

[2 marks] (a)Calculate Zack's savings.

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3 + 5 = 8 parts, 1 part = 96 ÷ 8 = RM12 [1]1
3 × 12 = RM36 [1]1

Tick each point you got.

[1 mark] (b)How much more does Yin save than Zack?

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5 × 12 = RM60; 60 − 36 = RM24 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 7.3.1

Textbook p. 200

There are 18 boys and 24 girls in a class. 6 girls move to another school.

[1 mark] (a)How many girls are there now?

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24 − 6 = 18 [1]1

Tick each point you got.

[1 mark] (b)Write the ratio of the number of boys to the number of girls now.

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18 : 18 = 1 : 1 [1]1

Tick each point you got.

[1 mark] (c)Write the ratio of the number of boys to the total number of pupils now, in the simplest form.

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18 : 36 = 1 : 2 [1]1

Tick each point you got.

For the teacher: Analysing, low difficulty, standard 7.4.1

Textbook p. 202

The ratio of the length of ribbon X to the length of ribbon Y is 7 : 4. Ribbon X is 90 cm longer than ribbon Y.

Bar model: ribbon X has 7 equal parts and ribbon Y has 4 equal parts — Diagram 6

[1 mark] (a)How many more parts does ribbon X have than ribbon Y?

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7 − 4 = 3 parts [1]1

Tick each point you got.

[1 mark] (b)Find the length of 1 part, in cm.

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90 ÷ 3 = 30 cm [1]1

Tick each point you got.

[1 mark] (c)Find the length of ribbon Y.

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4 × 30 = 120 cm [1]1

Tick each point you got.

For the teacher: Analysing, high difficulty, standard 7.3.1

Textbook p. 199

Encik Hamid drives from his house to town P and then from town P to town Q. The total distance is 63 km. The ratio of the distance from his house to town P to the distance from town P to town Q is 4 : 5.

[2 marks] (a)Calculate the distance from his house to town P.

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63 ÷ 9 = 7 km for 1 part [1]1
4 × 7 = 28 km [1]1

Tick each point you got.

[1 mark] (b)Calculate the distance from town P to town Q.

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5 × 7 = 35 km [1] (or 63 − 28)1

Tick each point you got.

[1 mark] (c)State the ratio of the distance from his house to town P to the total distance.

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28 : 63 = 4 : 9 [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 7.4.1

Textbook p. 203

The ratio of Rina's money to Sam's money is 5 : 3. They have RM80 altogether. Rina gives RM10 to Sam.

[2 marks] (a)How much money did Rina and Sam have at first?

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1 part = 80 ÷ 8 = RM10 [1]1
Rina RM50, Sam RM30 [1]1

Tick each point you got.

[2 marks] (b)Write the ratio of Rina's money to Sam's money after Rina gives RM10 to Sam. Write it in the simplest form.

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Rina RM40, Sam RM40 [1]1
40 : 40 = 1 : 1 [1]1

Tick each point you got.

For the teacher: Evaluating, high difficulty, standard 7.4.1

Textbook p. 203

Dina says, "12 : 18 in the simplest form is 6 : 9."

[1 mark] (a)Is Dina correct?

YesNo

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[2 marks] (b)Explain your answer and write the correct ratio.

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6 and 9 can still be divided by 3 [1]1
12 : 18 = 2 : 3 [1]1

Tick each point you got.

For the teacher: Evaluating, medium difficulty, standard 7.2.1

Textbook p. 193

Section A: objective questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Section B: structured questions

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18