s1 Math Ch12easa

1

120Supplement

12.14New Trend Mathematics S1B Junior Form Supplementary Exercises

Chapter 12 Linear Equations in Two Unknowns12.15

Chapter 12 Linear Equations in Two

UnknownsWarm-up Exercise

1.If x(3, find the value of each of the following expressions.

(a)5x(2(b)

2.If y((4, find the value of each of the following expressions.

(a)2(7(y)(b)

3.Substitute the following pairs of given values in brackets [] into the corresponding algebraic expressions, and find the values of the expressions.

(a)x(2y[x(1, y(2](b)3(x(1)(5y[x((2, y(1]

4.Solve the following equations.

(a)13(5(2x(b)2(3x)(1(5(x(2)(9

5.(a)Write down the coordinates of pointsA to E as shown in the figure.

(b)Mark the following points on the rectangular coordinate plane.

A((3,1), B(4,2), C(0,1), D(2,(1), E((1,(2), F(1,(3)

[A copy of the following figure is provided in the Appendix.]

Build-up Exercise

[This part provides two extra sets of questions for each exercise in the textbook, namely Elementary Set and Advanced Set. You may choose to complete any ONE set according to your need.]Exercise 12A((((((((((((((( Elementary Set (((((((((((((((Level 1

1.Determine whether each of the following is a linear equation in two unknowns. If yes, put a ( in the box; otherwise put a (.

(a)4y(8(b)5x(3y(7

(c)x2(4x(3(d)5a(7(b

(e)3x(1(0

2.When x(1, find the corresponding value of y for each of the following linear equations in two unknowns.

(a)y(x(1(b)y(3x(2(c)y(4(5x

(d)y((2x(5(e)2y(6(3x

3.When y(2, find the corresponding value of x for each of the following linear equations in two unknowns.

(a)y(x(2(b)y(2x(1(c)y((3x(4

(d)2y((3(x(e)(3y((4(5x

4.When x((2, find the corresponding value of y for each of the following linear equations in two unknowns.

(a)x(y(3(b)2x(y(5(c)3x(2y(2(0

(d)(4x(5y((7(e)(6x(4(2y

5.When y((4, find the corresponding value of x for each of the following linear equations in two unknowns.

(a)x(2y(3(b)3x(4y(5(c)

(d)3x(5y(2(0(e)2x(6y(5(0

6.Complete the tables according to the following equations.

(a)y(2xx210123

y

(b)y(3x(1x210123

y

(c)2x(y(1x20123

y

(d)x(2y(0x(0246

y

(e)y(3(x(1)x11234

y

7.Complete the tables according to the following equations.

(a)2y(xx

y(3(2(1012

(b)y(x(3x

y(4(3(2(101

(c)y(2x(1x

y(5(3(1135

(d)x(2y(3(0x

y012345

(e)

x

y(4(20246

8.Complete the tables according to the following equations and draw the graphs of the equations on a rectangular coordinate plane.

(a)y(x(2x012345

y

(b)2x(y(5(0x32(1012

y

(c)2(x(1)(y(0x101234

y

(d)

x03691215

y

(e)y(3x(2x1

0

1

y

9.(a)Use a table to show the integral values of x and the corresponding values of y for the

equation from x((2 to x(3.

(b)Draw the graph of the equation from x((2 to x(3 on a rectangular coordinate plane.10.(a)Use a table to show the integral values of x and the corresponding values of y for the equation 3x(2y(1 from x((1 to x(5.

(b)Draw the graph of the equation 3x(2y(1 from x((1 to x(5 on a rectangular coordinate plane.Level 2

11.(a)Use a table to show the integral values of x and the corresponding values of y for the

equation from x(0 to x(5.

(b)Draw the graph of the equation from x(0 to x(5 on a rectangular coordinate plane.

12.Draw the graph of each of the following equations on a rectangular coordinate plane.

(a)

(From x((2 to x(4)(b)

(From x((5 to x(1)

(c)

(From x((5 to x(1)(d)

(From x((4 to x(2)

(e)

(From x((3 to x(3)

((((((((((((((( Advanced Set (((((((((((((((Level 1

1.When x(2, find the corresponding value of y for each of the following linear equations in two unknowns.

(a)y(3(x(b)y(2x(3(c)y((3x(4

(d)y(10(2x(e)2y(4(5x

2.When y((3, find the corresponding value of x for each of the following linear equations in two unknowns.

(a)y(2(x(b)y(3x(2(c)y((2x(3

(d)3y(4(x(e)(2y((5(2x

3.Complete the tables according to the following equations.

(a)y(3xx210123

y

(b)y(2x(1x32(1012

y

(c)x(y(2x43(2(101

y

(d)5x(2y(0x(0246

y

(e)y(4(x(1)x43(2(101

y

4.Complete the tables according to the following equations.

(a)y((xx

y(3(2(1012

(b)y((x(5x

y(4(3(2(101

(c)x(y(1x

y(4(3(2(101

(d)2x(y(3x

y012345

(e)

x

y(4(20246

5.Complete the tables according to the following equations and draw the graphs of the equations on a rectangular coordinate plane.

(a)y(x(4x012345

y

(b)2x(y(3(0x210123

y

(c)3(x(1)(y(0x101234

y

(d)

x0510152025

y

(e)y(5x(4x1

0

1

y

6.(a)Use a table to show the integral values of x and the corresponding values of y for the

equation from x((2 to x(3.

(b)Draw the graph of the equation from x((2 to x(3 on a rectangular coordinate plane.

7.(a)Use a table to show the integral values of x and the corresponding values of y for the equation 2x(3y(1 from x((1 to x(5.

(b)Draw the graph of the equation 2x(3y(1 from x((1 to x(5 on a rectangular coordinate plane.Level 2

8.(a)Use a table to show the integral values of x and the corresponding values of y for the equation from x(0 to x(5.

(b)Draw the graph of the equation from x(0 to x(5 on a rectangular coordinate plane.

9.Draw the graph of each of the following equations on a rectangular coordinate plane.

(a)

(From x((2 to x(4)(b)

(From x((5 to x(1)

(c)

(From x((5 to x(1)(d)

(From x((4 to x(2)

(e)

(From x((3 to x(3)

10.Draw the graph of each of the following equations on a rectangular coordinate plane.

(a)

(From x((1 to x(4)(b)

(From x((2 to x(3)

(c)

(From x((3 to x(2)(d)

(From x((1 to x(4)

(e)

(From x((2 to x(3)

11.The following is a sequence of figures formed by dots.

(a)Complete the following table.Order of figure (x)1234

Number of dots (y)

(b)Write down the equation connecting x and y.

(c)Draw the graph of the equation obtained in (b) from x(1 to x(4 on a rectangular coordinate plane.

(d)From the graph obtained in (c), find the number of dots in the 6th figure.Exercise 12B

((((((((((((((( Elementary Set (((((((((((((((Level 1

1.Determine whether each of the following ordered pairs is a solution of the linear equation in two unknowns 2x(y(12. If yes, put a ( in the box; otherwise put a (.

(a)((2,16)(b)(0,6)

(c)(2,8)(d)

(e)(10,1)

2.Determine whether each of the following ordered pairs is a solution of the linear equation in two unknowns 2x(3y(7. If yes, put a ( in the box; otherwise put a (.

(a)(2,1)(b)((7,(7)

(c)(2,(1)(d)(5,1)

(e)((3,4)

3.Determine whether each of the following ordered pairs is a solution of the linear equation in two unknowns (x(4y(3(0. If yes, put a ( in the box; otherwise put a (.

(a)((7,(1)(b)(1,1)

(c)(5,3)(d)(3,1.5)

(e)(7,3.5)

4.Determine whether A(5,3) is on the graph of each of the following linear equations in two unknowns. If yes, put a ( in the box; otherwise put a (.

(a)

(b)y(4x(17

(c)x(11(2y(d)x(y(2

(e)3x(2y((9

5.Determine whether A((1,3) is on the graph of each of the following linear equations in two unknowns. If yes, put a ( in the box; otherwise put a (.

(a)x(2y(7(0(b)4x(3y(11

(c)5y((2x(13(d)3x(2y(9(0

(e)3x(7y(13

6.Determine whether A((2,(3) is on the graph of each of the following linear equations in two unknowns. If yes, put a ( in the box; otherwise put a (.

(a)(y(2x(5(b)y(x(1

(c)2x(3y(5(d)y((2x(7

(e)

7.The figure shows the graph of the equation 3x(2y(1.

(a)For points A to F, which points do not lie on the graph of the equation 3x(2y(1?

(b)Does each of the following points lie on the graph of the equation 3x(2y(1?

(i)(1,(1)

(ii)(3,(4)

(iii)((2,3)

(iv)((3,5)

(v)((5,7)

(vi)((6,9)

8.The figure shows the graph of the equation y(x(b.

(a)If P(p,0) is a point on the graph, find the value of p.

(b)If Q((1,q) is a point on the graph, find the value of q.

9.The figure shows the graph of the equation y(ax(3.

(a)When x(1, find from the graph the corresponding value of y.

(b)When y(1.8, find from the graph the corresponding value of x.

10.If A(a,(1) lies on the graph of the equation y((2x(3, find the value of a.

11.If B((2,b) lies on the graph of the equation 2x(5y(1, find the value of b.

12.If both A(a,0) and B(0,b) lie on the graph of the equation 3x(4y(2(0, find the values of a and b.

13.If ((3,6) lies on the graph of the equation ax(y(0, find the value of a.

14.If (5,(4) lies on the graph of the equation x(by(0, find the value of b.

15.If ((2,8) lies on the graph of the equation 2x(y(c, find the value of c.Level 216.(a)Draw the graph of the equation y(2x(1 from x((3 to x(4 on a rectangular coordinate plane.

(b)(i)Does (1,5) lie on the graph?

(ii)If H(h,h(3) is a point on the graph, find the value of h.17.(a)Draw the graph of the equation 3x(y(5(0 from x((2 to x(4 on a rectangular coordinate plane.

(b)Does each of the following points lie on the graph of the equation 3x(y(5(0?

(i)((3,14)(ii)(5,3)

(iii)(0.5,3.5)(iv)(3.5,0.5)

(v)(2.5,(2.5)(vi)((2.5,2.5)

(c)Write down the coordinates of the points at which the graph cuts the x-axis and the y-axis.

18.If both (0,1) and lie on the graph of the equation y(ax(b, find the values of a and b.((((((((((((((( Advanced Set (((((((((((((((Level 1

1.The following figure shows the graph of the equation 2x(3y(1.

(a)For points A to F, which points do not lie on the graph of the equation 2x(3y(1?

(b)Does each of the following points lie on the graph of the equation 2x(3y(1?

(i)(1,(1)(ii)(2,(1)

(iii)

(iv)((4,3)

(v)((6,4)(vi)(5,5)

2.The figure shows the graph of the equation y((x(b.

(a)If P(p,0) is a point on the graph, find the value of p.

(b)If Q(4,q) is a point on the graph, find the value of q.

3.The figure shows the graph of the equation y(ax(2.

(a)When x(0.5, find from the graph the corresponding value of y.

(b)When y(1.4, find from the graph the corresponding value of x.

4.If A(a,3) lies on the graph of the equation y((2x(4, find the value of a.

5.If lies on the graph of the equation 3x(5y(1, find the value of b.

6.If both A(a,0) and B(0,b) lie on the graph of the equation 3x(4y(5(0, find the values of a and b.

7.If ((2,(3) lies on the graph of the equation ax(y(0, find the value of a.

8.If ((4,3) lies on the graph of the equation 3x(by(0, find the value of b.

9.If (5,(2) lies on the graph of the equation 3y(c(4x, find the value of c.Level 210.(a)Draw the graph of the equation y(2x(1 from x((3 to x(4 on a rectangular coordinate plane.

(b)(i)Does (2,4) lie on the graph?

(ii)If H(h,h(2) is a point on the graph, find the value of h.

11.(a)Draw the graph of the equation 2x(y(4(0 from x((4 to x(3 on a rectangular coordinate plane.

(b)Does each of the following points lie on the graph of the equation 2x(y(4(0?

(i)((5,(6)(ii)((2,(3)

(iii)((1,2)(iv)(1,5)

(v)(2,8)(vi)(3,10)

(c)Write down the coordinates of the points at which the graph cuts the x-axis and the y-axis.

12.Find the coordinates of the points at which each of the following graphs cuts the x-axis and the y-axis.

(a)y(4x(2(b)3x(4y(5(0(c)2x(5y((3

13.Find the coordinates of the points at which each of the following graphs cuts the x-axis and the y-axis.

(a)

(b)

(c)

14.If both and (0,2) lie on the graph of the equation y(ax(b, find the values of a and b.

15.It is known that the cost of each standard ticket of a space museum is $10 and that of each concessionary ticket is $5. Mr.Chan bought the same number of standard tickets and concessionary tickets at $90. How many standard tickets and concessionary tickets did Mr.Chan buy respectively?

16.In (ABC, AB(8cm, BC((x(2y)cm and AC((2x(y)cm.

(a)If the perimeter of the triangle is 20cm, write down the equation representing the relation between x and y.

(b)Draw the graph of the equation obtained in (a) from x(0 to x(4 on a rectangular coordinate plane.

(c)It is known that ABC is an isosceles triangle where AC(BC. Find the values of x and y.17.(a)Draw the graphs of the equations x(y(2, x(y(1 and x(y((1 from x((3 to x(2 on the same rectangular coordinate plane.

(b)(i)Write down the coordinates of the points at which each of the graphs of the above three equations cuts the x-axis and the y-axis.

(ii)Can A(0,1) satisfy the above three equations at the same time?

(iii)Describe the properties of the graphs of the three equations.Chapter Test(Time allowed: 1 hour)

Section A (1) [ 3 marks each ]

1.According to the equation y(3x(4, complete the following table.x(20

y2

2.Does the ordered pair (1,4) satisfy the equation 2x(y(6?

3.If 2x(y(14 and x((2, find the value of y.

4.According to the equation 3x(2y(3(0, complete the following table.x(1

y(9(3

5.If A(a,0) is a point on the graph of the equation 2x(4y(10, find the value of a.

6.If B(0,b) is a point on the graph of the equation 7y(2x((14, find the value of b.Section A (2) [ 6 marks each ]

7.If both ordered pairs (m,m) and ((2,n) satisfy the equation y(3x(6, find the values of m and n.

8.In the figure, the graph of the equation y(4x(8 cuts the x-axis and y-axis at A and B respectively. Find the area of (AOB.

9.A transportation company owns light trucks and medium trucks. A light truck can carry 10boxes of goods and a medium truck can carry 25 boxes of goods. If x light trucks and y medium trucks together can just carry 95 boxes of goods, find the respective number of the two types of trucks.

10.(a)According to the equation y(2x, complete the following table.x(1012

y

(b)Draw the graph of the equation y(2x from x((1 to x(2 on a rectangular coordinate plane.Section B

11.In the figure, the graphs of the equations y(ax(1 and y(bx(5 intersect at C((2,3).

(a)Find the values of a and b.(4 marks)

(b)Find the coordinates of A and B.(6 marks)

(c)Hence find the area of the shaded region.

(3 marks)Multiple Choice Questions [ 3 marks each ]

12.Which of the following are linear equations in two unknowns?

I.y(4x

II.y(5(6x(7y

III.x2(3y(0

IV.3x(4(0

A.I and II only

B.I and IV only

C.II and III only

D.I, II and IV only

13.Which of the following ordered pairs can satisfy the equation 2y(3x(2?

I.(0,0)

II.(2,2)

III.

IV.((2,(2)

A.III only

B.IV only

C.I and II only

D.II and III only

14.The table below shows some solutions of a linear equation in two unknowns. Find the linear equation in two unknowns.x4681012

y79111315

A.y(2x

B.y(x(7

C.y(x(3

D.4y(7x

15.When x(5, find the corresponding value of y for the linear equation in two unknowns 3y(1(4x.

A.

B.4

C.7

D.

16.The table below shows some solutions of the equation y(x(1. Find the values of a and b.x(4(3a24

y(5(401b

A.a((2, b(2

B.a((2, b(3

C.a(1, b(2

D.a(1, b(3

17.For the ordered pair (4,0), which of the following linear equations in two unknowns does it satisfy?

I.y(4x

II.x(4y

III.3y(8(2x

IV.3y(8(2x

A.II only

B.III only

C.I and II only

D.III and IV only

18.The figure below shows the graph of the linear equation in two unknowns y(ax. Which of the following ordered pairs lies on the graph of y(ax?

A.(8,2)

B.(6,3)

C.(2,(4)

D.((5,(1)

19.Which of the following ordered pairs is a solution of the equation x(2y(3?

A.(1,1)

B.(1,(1)

C.(3,1)

D.(4,1)

20.Which of the following ordered pairs cannot satisfy the equation y(2x(5?

A.(5,17)

B.(4,13)

C.(2,9)

D.(1,7)

21.Which of the following points does not lie on the graph of the equation 2x(3y(5?

A.((2,(3)

B.(1,(1)

C.(2,0)

D.(7,3)

22.If P(2,p) lies on the graph of the equation y((2x(3, find the value of p.

A.(7

B.(1

C.0.5

D.7

23.If Q(q,(2) lies on the graph of the equation 3x(5y(28, find the value of q.

A.6

B.12

C.(6

D.(7

24.Which of the following equations has a graph passing through point (3,4)?

A.3x(4y

B.4x(3y

C.x(y(1(0

D.2x(y(10(0

25.If H(h,h(2) lies on the graph of the equation 5x(2y(8, then h(

A.2.

B.3.

C.4.

D.5.

26.If the graph of the equation x(ky(30 passes through P(12,9), then k(

A.(2.

B.(1.

C.2.

D.3.

Ex.12B Advanced Set

Ex.12B Advanced Set

Ex.12B Advanced Set

Ex.12A Advanced Set

Ex.12A Elementary Set

Ex.12A Elementary Set

Ex.12A Elementary Set

Ex.12B Elementary Set

Ex.12B Elementary Set

Ex.12A Advanced Set

Ex.12B Elementary Set

Ex.12A Advanced Set

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