myUASARevision for UASA
More
My progress
Mathematics questions, chapter 6
Nama / NameKelas / ClassTarikh / Date

Linear equations

40 marks. Use Practice to check each answer as you go, or Exam to answer everything first. Do not use a calculator. Show your working for Section B.

Section A: objective questions

12 marks
Choose the correct answer.
1

Question 1

Which of the following is a linear equation in one variable?
Show answerHide answer
C
2(m − 3) = 10 has one variable, m, with power 1. 3x + 2 = 4y has two variables, k² has power 2, and 5a − 4 has no equals sign, so it is an expression, not an equation.
For the teacher: Remembering, low difficulty, standard 6.1.1
Textbook p. 125
2

Question 2

Three times a number, minus 4, is 20. Let the number be x. Which equation shows this?
Show answerHide answer
B
First multiply the number by 3 to get 3x, then subtract 4: 3x − 4 = 20. 3(x − 4) subtracts 4 before multiplying, and 4 − 3x subtracts in the wrong order.
For the teacher: Understanding, low difficulty, standard 6.1.2
Textbook p. 126
3

Question 3

Diagram 1 shows a level balance. Each box has a mass of x balls. Find the value of x.
Level balance: 3 boxes marked x and 3 balls on the left pan, 21 balls on the right pan
Diagram 1
Show answerHide answer
A
3x + 3 = 21. Take 3 balls from both sides: 3x = 18. Divide both sides by 3: x = 6. 8 comes from adding 3 instead of subtracting, 18 forgets to divide by 3, and 4 divides before subtracting.
For the teacher: Applying, low difficulty, standard 6.1.3
Textbook p. 128
4

Question 4

Diagram 2 shows the operations on a number x. Use backtracking to find x.
x, times 4, minus 6, gives 18
Diagram 2
Show answerHide answer
D
Undo in reverse order: 18 + 6 = 24, then 24 ÷ 4 = 6. Check: 6 × 4 − 6 = 18 ✓. 3 comes from 18 − 6 (the wrong inverse), 10.5 is 18 ÷ 4 + 6 (wrong order), and 78 is 18 × 4 + 6 (the operations were not reversed).
For the teacher: Applying, low difficulty, standard 6.1.3
Textbook p. 128
5

Question 5

Solve 2x − 43 = 6.
Show answerHide answer
C
Multiply both sides by 3: 2x − 4 = 18. Add 4: 2x = 22. Divide by 2: x = 11. 3 comes from dividing 6 by 3 instead of multiplying, 7 from subtracting 4 instead of adding, and 22 forgets to divide by 2.
For the teacher: Applying, medium difficulty, standard 6.1.3
Textbook p. 129
6

Question 6

Solve 3(x − 2) = x + 8.
Show answerHide answer
A
Expand: 3x − 6 = x + 8. Then 3x − x = 8 + 6, so 2x = 14 and x = 7. 5 comes from writing 3x − 2 (not multiplying the 2), 3.5 from adding the x terms (4x = 14), and 14 forgets to divide by 2.
For the teacher: Applying, medium difficulty, standard 6.1.3
Textbook p. 129
7

Question 7

Which of the following is a linear equation in two variables?
Show answerHide answer
B
4p − q = 7 has two variables, each with power 1. xy multiplies two variables, 2(k + 3) = 5k has only one variable, and x² has power 2.
For the teacher: Remembering, low difficulty, standard 6.2.1
Textbook p. 132
8

Question 8

Which ordered pair is a solution of 3x + y = 11?
Show answerHide answer
D
For (3, 2): 3(3) + 2 = 11 ✓. (2, 3) gives 9 (the values are swapped), (4, 2) gives 14 and (1, 7) gives 10.
For the teacher: Understanding, low difficulty, standard 6.2.3
Textbook p. 134
9

Question 9

Diagram 3 shows the graph of a linear equation in two variables. Which equation does it represent?
Straight line through the points (0, 3), (2, 5) and (4, 7)
Diagram 3
Show answerHide answer
C
Every point has y 3 more than x: (0, 3), (2, 5), (4, 7). Test (2, 5): 2 − 5 = −3 ✓. In the other equations, (2, 5) gives 7, −3 ≠ 3 and 9.
For the teacher: Understanding, medium difficulty, standard 6.2.4
Textbook p. 136
10

Question 10

Diagram 4 shows the graphs of x − y = −1 and x − y = 2. What type of solution do these simultaneous linear equations have?
Two parallel straight lines, x − y = −1 and x − y = 2
Diagram 4
Show answerHide answer
B
The lines are parallel, so they never meet. There is no point on both lines, so there is no solution.
For the teacher: Understanding, low difficulty, standard 6.3.1
Textbook p. 139
11

Question 11

Diagram 5 shows the graphs of x + y = 5 and x − y = 1. What is the solution of the simultaneous equations?
Graphs of x + y = 5 and x − y = 1 on a grid; the lines cross at one point
Diagram 5
Show answerHide answer
A
The lines meet at (3, 2), so x = 3 and y = 2. Check: 3 + 2 = 5 ✓ and 3 − 2 = 1 ✓. (2, 3) swaps the values; (5, 0) and (1, 0) are where each line crosses the x-axis.
For the teacher: Applying, medium difficulty, standard 6.3.2
Textbook p. 140
12

Question 12

Two pens and one ruler cost RM7.00. One pen and one ruler cost RM4.50. What is the price of one ruler?
Show answerHide answer
D
2p + r = 7 and p + r = 4.50. Subtract: p = 2.50. Then 2.50 + r = 4.50, so r = RM2.00. RM2.50 is the price of a pen, not the ruler.
For the teacher: Analysing, high difficulty, standard 6.3.3
Textbook p. 142

Section B: structured questions

28 marks
Answer all questions. Show your working.
13

Question 13

Aminah buys 3 kg of prawns at RMy per kilogram and vegetables for RM10. She pays RM64 altogether.
[1 mark] (a)Form a linear equation in one variable for this situation.
Show answerHide answer
Tick each point you got.
[1 mark] (b)Find the price of 1 kg of prawns.
Show answerHide answer
Tick each point you got.
[1 mark] (c)Write a situation for the equation x − 5 = 12, where x is Hafiz's age now.
Show answerHide answer
Tick each point you got.
For the teacher: Understanding, low difficulty, standard 6.1.2
Textbook p. 126
14

Question 14

Solve the equation 4x − 3 = 17 in two different ways.
Backtracking diagram: x, times 4, minus 3, gives 17. Below: 17 then two empty operation boxes then an empty box for x
Diagram 6
[2 marks] (a)Use the trial and improvement method. Start with x = 3 and show your trials in a table.
Show answerHide answer
Tick each point you got.
[2 marks] (b)Complete the backtracking diagram in Diagram 6 to find x.
Show answerHide answer
Tick each point you got.
For the teacher: Applying, medium difficulty, standard 6.1.3
Textbook p. 127
15

Question 15

Diagram 7 shows a rectangle. Its perimeter is 38 cm.
Rectangle with length (2x + 3) cm and width (x + 1) cm, perimeter 38 cm
Diagram 7
[2 marks] (a)Form an equation in x and solve it.
Show answerHide answer
Tick each point you got.
[2 marks] (b)Find the area of the rectangle.
Show answerHide answer
Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 6.1.4
Textbook p. 130
16

Question 16

Diagram 8 shows a triangle. The sum of the angles in a triangle is 180°.
Triangle with angles x°, (2x + 10)° and (x + 30)°
Diagram 8
[2 marks] (a)Find the value of x.
Show answerHide answer
Tick each point you got.
[1 mark] (b)Find the size of the largest angle.
Show answerHide answer
Tick each point you got.
For the teacher: Applying, medium difficulty, standard 6.1.4
Textbook p. 130
17

Question 17

Diagram 9 shows the graph of 2x + y = 4.
Straight line graph of 2x + y = 4 drawn on a grid from x = −1 to x = 3
Diagram 9
[2 marks] (a)Complete the table of values for 2x + y = 4.
x−10123
y4−2
Show answerHide answer
Tick each point you got.
[1 mark] (b)Use the graph to find the value of y when x = 1.5.
Show answerHide answer
Tick each point you got.
[1 mark] (c)Is (4, −4) a solution of 2x + y = 4? Show how you know.
Show answerHide answer
Tick each point you got.
For the teacher: Applying, medium difficulty, standard 6.2.4
Textbook p. 136
18

Question 18

Diagram 10 shows an incomplete receipt. A cup of teh tarik costs RM0.60 more than a piece of roti canai. Let the price of a cup of teh tarik be RMt and a piece of roti canai be RMr.
Receipt from Kedai Kopi Seri: 3 cups of teh tarik and 2 pieces of roti canai, prices missing, total RM8.30
Diagram 10
[2 marks] (a)Form two linear equations in t and r.
Show answerHide answer
Tick each point you got.
[2 marks] (b)Find the price of a cup of teh tarik and a piece of roti canai.
Show answerHide answer
Tick each point you got.
For the teacher: Analysing, high difficulty, standard 6.3.3
Textbook p. 145
19

Question 19

Ali solved 4(x − 3) = 2x + 6. Diagram 11 shows his working.
Ali's working: 4(x − 3) = 2x + 6; Line 1: 4x − 3 = 2x + 6; Line 2: 4x − 2x = 6 + 3; Line 3: 2x = 9; Line 4: x = 4.5
Diagram 11
[1 mark] (a)Ali's answer is wrong. In which line is his first mistake? Explain it.
Show answerHide answer
Tick each point you got.
[2 marks] (b)Solve the equation correctly and check your answer.
Show answerHide answer
Tick each point you got.
For the teacher: Evaluating, high difficulty, standard 6.1.3
Textbook p. 129
20

Question 20

Nurul wants to write a word problem for her friends. The answer must be: a burger costs RM4 and a drink costs RM1.
[2 marks] (a)Write a pair of simultaneous linear equations in b (price of a burger) and d (price of a drink) that has the solution b = 4, d = 1. Show that both equations are satisfied.
Show answerHide answer
Any pair works if the left sides are not multiples of each other and b = 4, d = 1 makes both true.
Tick each point you got.
[1 mark] (b)Write the word problem for your equations.
Show answerHide answer
Tick each point you got.
For the teacher: Creating, high difficulty, standard 6.3.3
Textbook p. 142