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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz
1
© 2008 Chung Tai Educational Press. All rights reserved.
Linear Equations in Two Unknowns
[[ T ime a l lowed: 35 minutesTime a l lowed: 35 minutes ]]
1. (a) Complete the following table for the equation y = 2x − 1.
x −2 −1 2 (4 marks)
y −1
(b) Draw the graph of the equation y = 2x − 1 from x = −2 to x = 2 on a rectangular coordinate plane. (4 marks)
O
2
1
−1−2−3
−5
3
5
y
−1−2 1 2x
4
−4
Name :
Class :
Marks :
Date :
( )
/100
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
2. Which of the following ordered pairs satisfy the equation 0253 =−+ yx ?
(−1, 1), (0, 0), )54 ,2( , )
57 ,3( − (16 marks)
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
3. If A(a, 3) and B(−2, b) are points on the graph of the equation 623 =− yx , find the values of a and b. (8 marks)
4. The figure shows the graph of the equation xy −= 63 from 3−=x to 7=x .
O
2
1
−1−2−3−4
3
4
y
−1−2−3 1 2 5 6 7x
3 4
A
B3y = 6 − x
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
(a) Write down the coordinates of points A and B. (4 marks) (b) Find the coordinates of the points at which the graph cuts the x-axis and the y-axis.
(4 marks) (c) If C(c, c) lies on the graph, find the coordinates of C. (4 marks) (d) If the graph is extended, will it pass through the following points?
(i) )3
13 ,8( −D (3 marks)
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
(ii) )34 ,10( −E (3 marks)
5. The following is a sequence of figures formed by toothpicks.
The 2nd figure The 3rd figureThe 1st figure
By observation, number of toothpicks in the 1st figure 1)1(3 += , number of toothpicks in the 2nd figure 1)2(3 += , number of toothpicks in the 3rd figure 1)3(3 += .
(a) Find the number of toothpicks in the 4th and 5th figures each. (2 marks) (b) Write an equation in x and y where y represents the number of toothpicks in the x th
figure. (2 marks)
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
(c) Draw the graph of the equation obtained in (b) from 1=x to 10=x on a rectangular coordinate plane. (4 marks)
O
2423
2526
y
1 2 3 4x
5 6 7 8 9 10
2728293031
21
171819202122
109
111213141516
345678
(d) From the graph obtained in (c), find the value of y when 8=x . (2 marks)
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
6. In the figure, the graph of the equation 03 =+− kyx passes through A(2, 9) and cuts the x-axis and the y-axis at points B and C respectively.
O
y
x
A (2, 9)
C
B
3x − y + k = 0
(a) Find the value of k. (4 marks) (b) Find the coordinates of B and C. (8 marks)
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
(c) Find the area of ΔBOC. (4 marks) 7. In the figure, ABC is a right-angled triangle and the coordinates of C are (3, 2). If
points A and B lie on the graph of the equation 042 =−+ yx ,
O
y
x
C (3, 2)
A
B
2x + y − 4 = 0
(a) find the coordinates of A and B. (8 marks) (b) find the area of ΔABC. (4 marks)
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
8. In a Mathematics test, 10 marks are given for each correct answer and 4 marks are deducted for each incorrect answer. It is known that Philip got 50 marks in the test.
(a) Let x and y be the number of correct answers and incorrect answers Philip got respectively. Set up an equation in x and y. (4 marks)
(b) It is known that x is an integer not greater than 10. Draw a suitable straight line on a
rectangular coordinate plane, and find all the possible number of correct answers and incorrect answers he got respectively. (8 marks)
－ End of Paper －
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
Solution
1. (a) x −2 −1 0 2 @1A = 4A
y −5 −3 −1 3
(b)
O
2
1
−1−2−3
−5
3
5
y
−1−2 1 2x
4
−4
y = 2x − 1
2. Substitute 1−=x and 1=y into 0253 =−+ yx ,
L.H.S.0
2)1(5)1(3=
−+−= 2M
R.H.S. 0=
L.H.S. = R.H.S. ∴ (−1, 1) satisfies the equation. 1A
Substitute 0=x and 0=y into 0253 =−+ yx ,
L.H.S.2
2)0(5)0(3−=
−+= 2M
R.H.S. 0=
L.H.S. ≠ R.H.S. ∴ (0, 0) does not satisfy the equation. 1A
3A
1A
1A
1A
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
Substitute 2=x and
54
=y into 0253 =−+ yx ,
L.H.S.
8
2)54(5)2(3
=
−+= 2M
R.H.S. 0= L.H.S. ≠ R.H.S.
∴ )54 ,2( does not satisfy the equation. 1A
Substitute 3=x and
57
−=y into 0253 =−+ yx ,
L.H.S.
0
2)57(5)3(3
=
−−+= 2M
R.H.S. 0= L.H.S. = R.H.S.
∴ )57 ,3( − satisfies the equation. 1A
3. Substitute ax = and 3=y into 623 =− yx ,
41236)3(23
=
=
=−
aa
a
2M
Substitute 2−=x and by = into 623 =− yx ,
6
12262)2(3
−=
=−
=−−
bbb
2M
4. (a) Coordinates of point A )3 ,3( −= 2A
Coordinates of point B )1 ,3( = 2A
(b) Coordinates of the point at which the graph cuts the x-axis )0 ,6( = 2A
Coordinates of the point at which the graph cuts the y-axis )2 ,0( = 2A
1A
1A
2A
2A
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
(c) Substitute cx = and cy = into xy −= 63 ,
236463
=
=
−=
c
ccc
2M
∴ Coordinates of C )23 ,
23( = 2A
(d) (i) Substitute 8−=x and
313
=y into xy −= 63 ,
L.H.S.
13
)313(3
=
= 1A
R.H.S.14
)8(6=
−−= 1A
L.H.S. ≠ R.H.S.
∴ The graph does not pass through D )3
13 ,8( − . 1A
(ii) Substitute 10=x and
34
−=y into xy −= 63 ,
L.H.S.
4
)34(3
−=
−= 1A
R.H.S.4106
−=
−= 1A
L.H.S. = R.H.S.
∴ The graph passes through )34 ,10( −E . 1A
5. (a) Number of toothpicks in the 4th figure
131)4(3
=
+=
1A
Number of toothpicks in the 5th figure16
1)5(3=
+=
1A
(b) 13 += xy 2A
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
(c)
O
2423
2526
y
1 2 3 4x
5 6 7 8 9 10
2728293031
21
171819202122
109
111213141516
345678
y = 3x + 1
(d) From the graph, 25=y when 8=x . 2A
6. (a) Substitute 2=x and 9=y into 03 =+− kyx ,
309609)2(3
=
=+−
=+−
kkk
2M
(b) Substitute 0=y into 033 =+− yx ,
1330303
−=
−=
=+−
xx
x
2M
∴ Coordinates of B )0 ,1( −= 2A
1A
3A
2A
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
Substitute 0=x into 033 =+− yx ,
303)0(3
=
=+−
yy
2M
∴ Coordinates of C )3 ,0( = 2A
(c) Area of ΔBOC OCOB ××=21 2M
3121
××= square units
23
= square units 2A
7. (a) Substitute 3=x into 042 =−+ yx ,
204)3(2−=
=−+
yy
2M
∴ Coordinates of A )2 ,3( −= 2A
Substitute 2=y into 042 =−+ yx ,
10422
=
=−+
xx
2M
∴ Coordinates of B )2 ,1( = 2A
(b) Area of ΔABC ACBC ××=21 2M
)]2(2[)13(21
−−×−×= square units
4221
××= square units
4= square units 2A
8. (a) 50410 =− yx 2M 2525 =− yx 2A
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New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11
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© 2008 Chung Tai Educational Press. All rights reserved.
(b) 2525 =− yx
x 5 7 9
y 0 5 10
O
6
5
9
10
12
13
11
y
1 2 3 4x
4
3
2
1
7
8
5 6 7 8 9 10
5x − 2y = 25
The number of questions must be a non-negative integer. ∴ x and y must be non-negative integers. 1M
According to the graph, only 5=x , 0=y ; 7=x , 5=y and 9=x , 10=y satisfy the above condition.
∴ Philip got 5 correct answers and 0 incorrect answer,
7 correct answers and 5 incorrect answers or
9 correct answers and 10 incorrect answers. 3A
1A
3A
