New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11

10

© 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

New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11

11

© 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

New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11

12

© 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

New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11

13

© 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

New Trend Mathematics (2nd Edition) S1B - Chapter Quiz - Chapter 11

14

© 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

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