Algebraic expressions: Mathematics Tingkatan 1 questions

Section A: objective questions

12 marks

Choose the correct answer.

Which of the following variables has a fixed value?

t, the temperature in a classroom during a school day
w, the number of days in a week
v, the number of visitors to Zoo Negara each day
h, the height of a student from Form 1 to Form 5

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A week always has 7 days, so w never changes. Temperature, visitors and height all change over time, so they have varied values.

For the teacher: Remembering, low difficulty, standard 5.1.1

Textbook p. 106

Which algebraic expression means "subtract 7 from a number x"?

x − 7
7 − x
7x
x7

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Start with x and take away 7: x − 7. 7 − x takes x away from 7, which is the wrong way round.

For the teacher: Understanding, low difficulty, standard 5.1.2

Textbook p. 108

Given that p = 3 and q = −2, find the value of 5p − 3q + 1.

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5(3) − 3(−2) + 1 = 15 + 6 + 1 = 22. 10 comes from 15 − 6 + 1, forgetting that −3 × (−2) = +6.

For the teacher: Applying, low difficulty, standard 5.1.3

Textbook p. 109

How many terms are there in the expression 4x² − 3xy + y − 9?

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The terms are 4x², 3xy, y and 9. A number on its own, such as 9, is also a term, so there are 4 terms.

For the teacher: Remembering, low difficulty, standard 5.1.4

Textbook p. 110

What is the coefficient of q in the term −6p²q?

−6
−6p²
6p²
p²

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−6p²q = −6p² × q, so the coefficient of q is −6p². −6 is the coefficient of p²q, and the minus sign must be kept.

For the teacher: Understanding, medium difficulty, standard 5.1.4

Textbook p. 111

Which pair of terms are like terms?

3ab and −5ba
2x and 2x²
4pq and 4pr
7m and 7mn

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ba is the same as ab, so 3ab and −5ba have the same variables with the same powers. The other pairs have different variables or different powers, even though the numbers are the same.

For the teacher: Understanding, medium difficulty, standard 5.1.5

Textbook p. 111

Simplify (5x − 2y) − (3x − 4y).

2x − 6y
8x − 6y
2x − 2y
2x + 2y

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5x − 2y − 3x + 4y = 2x + 2y. The − before the bracket changes −4y to +4y. 2x − 6y comes from forgetting to change that sign.

For the teacher: Applying, low difficulty, standard 5.2.1

Textbook p. 113

(2k − 3) × (2k − 3) × (2k − 3) = ______

3(2k − 3)
2k − 3³
(2k − 3)³
2k³ − 3

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The whole expression (2k − 3) is multiplied 3 times, so it is (2k − 3)³ with brackets. 3(2k − 3) is adding it 3 times.

For the teacher: Applying, low difficulty, standard 5.2.2

Textbook p. 115

Simplify 4m²n × 3mn³.

12m³n⁴
7m³n⁴
12m²n³
12m³n³

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4 × 3 = 12; m × m × m = m³; n × n × n × n = n⁴. So the answer is 12m³n⁴. 7m³n⁴ adds the numbers instead of multiplying them.

For the teacher: Applying, medium difficulty, standard 5.2.3

Textbook p. 116

Simplify 18x³y² ÷ 6xy³.

3x²y
12x²y
3x³y
3x²y

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18 × x × x × x × y × y6 × x × y × y × y: 18 ÷ 6 = 3, two x's are left on top and one y is left at the bottom, so 3x²y.

For the teacher: Applying, medium difficulty, standard 5.2.3

Textbook p. 116

Diagram 1 shows a watermelon of mass 5 kg and two durians of the same mass on an electronic balance. The reading is m kg. Find the mass, in kg, of one durian.

A 5 kg watermelon and two durians on an electronic balance that reads m kg — Diagram 1

m − 5
m − 52
m2 − 5
2(m − 5)

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The two durians together have a mass of m − 5 kg. One durian is half of this: m − 52 kg. m − 5 is the mass of both durians.

For the teacher: Analysing, medium difficulty, standard 5.1.2

Textbook p. 112

Diagram 2 shows a rectangle with an area of 12a³b² cm² and a width of 3ab cm. Find its length.

Rectangle with area 12a cubed b squared cm², width 3ab cm, length unknown — Diagram 2

9a²b cm
36a⁴b³ cm
4a²b cm
4a³b² cm

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Length = area ÷ width = 12a³b² ÷ 3ab = 4a²b cm. Check: 3ab × 4a²b = 12a³b². 36a⁴b³ multiplies instead of dividing, and 9a²b subtracts 12 − 3.

For the teacher: Analysing, high difficulty, standard 5.2.3

Textbook p. 117

Section B: structured questions

28 marks

Answer all questions. Show your working.

Siti records two quantities: (i) the number of students absent from her class each day, and (ii) the number of months in a year.

[2 marks] (a)Represent quantity (i) with a suitable letter. Does it have a fixed value or a varied value? Give a reason.

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Letter, e.g. s, with varied value [1]1
Because the number of absent students changes from day to day [1]1

Tick each point you got.

[1 mark] (b)Quantity (ii), the number of months in a year, has

a fixed valuea varied value

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a fixed value

Every year has 12 months, so the value never changes.

For the teacher: Understanding, low difficulty, standard 5.1.1

Textbook p. 106

Diagram 3 shows eight term cards.

Term cards: 5x, −3y squared, 2xy, 3x squared, −x, 4y squared, 6yx, 7 — Diagram 3

[2 marks] (a)Write two pairs of like terms from the cards.

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Any 2 points

5x and −x [1]1
−3y² and 4y² [1]1
2xy and 6yx [1]1

5x and 3x² are unlike: the powers of x are different.

Tick each point you got.

[1 mark] (b)State the coefficient of x in the term 2xy.

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2y [1]1

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For the teacher: Understanding, low difficulty, standard 5.1.5

Textbook p. 111

Diagram 4 shows the prices of a pen and a notebook at a school bookshop. Aiman buys 3 pens and 2 notebooks. He pays with a RM20 note.

Price tags: pen RMx, notebook RMy — Diagram 4

[1 mark] (a)Write an expression for the total cost of Aiman's items.

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RM(3x + 2y) [1]1

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[1 mark] (b)Write an expression for the balance Aiman receives.

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RM[20 − (3x + 2y)] or RM(20 − 3x − 2y) [1]1

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[2 marks] (c)Given x = 1.50 and y = 4.20, find the balance.

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3(1.50) + 2(4.20) = 4.50 + 8.40 = 12.90 [1]1
20 − 12.90 = RM7.10 [1]1

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For the teacher: Applying, medium difficulty, standard 5.1.3

Textbook p. 109

Simplify each of the following.

[2 marks] (a)(4a + 3b) + (2a − 5b)

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4a + 2a + 3b − 5b [1]1
= 6a − 2b [1]1

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[2 marks] (b)(7mn − 2p + 5) − (3mn − 6p + 8)

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7mn − 2p + 5 − 3mn + 6p − 8 [1]1
= 4mn + 4p − 3 [1]1

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For the teacher: Applying, low difficulty, standard 5.2.1

Textbook p. 113

Diagram 5 shows a triangle.

Triangle with sides (2x + 3) cm, (x + 4) cm and (3x − 2) cm — Diagram 5

[2 marks] (a)Write an expression, in its simplest form, for the perimeter of the triangle.

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(2x + 3) + (x + 4) + (3x − 2) [1]1
= (6x + 5) cm [1]1

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[1 mark] (b)Given x = 5, show that two sides of the triangle are equal.

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2(5) + 3 = 13 and 3(5) − 2 = 13, so both are 13 cm [1]1

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[1 mark] (c)Hence, find the perimeter of the triangle when x = 5.

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6(5) + 5 = 35 cm [1]1

Check: 13 + 9 + 13 = 35.

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For the teacher: Analysing, medium difficulty, standard 5.2.1

Textbook p. 117

Diagram 6 shows a cube. Each edge is 3mn cm long.

[1 mark] (a)Find the volume of the cube in its simplest form.

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3mn × 3mn × 3mn = 27m³n³ cm³ [1]1

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[2 marks] (b)Find the total surface area of the cube.

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Area of one face = 3mn × 3mn = 9m²n² [1]1
6 × 9m²n² = 54m²n² cm² [1]1

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For the teacher: Applying, high difficulty, standard 5.2.3

Textbook p. 117

Diagram 7 shows Mei Ling's working to simplify (6x − 4y + 3) − (2x − y + 5).

Mei Ling's working. Line 1: 6x − 4y + 3 − 2x − y + 5. Line 2: 6x − 2x − 4y − y + 3 + 5. Line 3: 4x − 5y + 8 — Diagram 7

[2 marks] (a)Mei Ling's answer is wrong. In which line is her mistake? Explain the mistake.

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Line 1 [1]1
She changed only the sign of 2x. The − before the bracket changes every sign: −y becomes +y and +5 becomes −5 [1]1

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[2 marks] (b)Find the correct answer.

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6x − 4y + 3 − 2x + y − 5 [1]1
= 4x − 3y − 2 [1]1

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For the teacher: Evaluating, high difficulty, standard 5.2.1

Textbook p. 113

Diagram 8 shows the prices of a holiday package. Puan Aishah plans a holiday for a group of 6 people, with at least one adult. Her budget is RM2 000.

Holiday package poster: 3 days 2 nights, adult RM380, child (12 years and below) RM280 — Diagram 8

[1 mark] (a)Write an expression for the total cost, in RM, for a adults and c children.

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380a + 280c [1]1

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[2 marks] (b)Plan a group of 6 people that keeps within the budget. State the number of adults and children, and use your expression to show that the cost is not more than RM2 000.

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A valid plan with a + c = 6 and a = 1, 2 or 3 [1]1
Correct substitution and cost: a = 1, c = 5: 380(1) + 280(5) = RM1 780; a = 2, c = 4: RM1 880; a = 3, c = 3: RM1 980 [1]1

With 4 adults and 2 children the cost is 380(4) + 280(2) = RM2 080, which is over the budget. So at most 3 adults can go.

Tick each point you got.

For the teacher: Creating, high difficulty, standard 5.1.3

Textbook p. 104

Section A: objective questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Section B: structured questions

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20