Revision Exercise Sheet
1. Solve for x in the following equations:
(i) 2x=1 (ii) 2x+6=12 (iii) 3-x=7
(iv) 5(2x-4)=30 (v) 2
3=
x (vi) 2
23 =− xx
2. Express x in terms of y in each of the following cases:
(i) y=6x+12 (ii) 6x-12y = 18 (iii) 2x+8y=12
(iv) 42
5
1+= xy (v) 3
2
3+= x
y (vi) 2
6
1
3
2+= xy
3. Solve the following systems of simultaneous equations:
(i) y=3-2x (ii) 5x-2y = 11 (iii) 2x-5y=20
y=x 3x+3y = 15 2=3x-2.5y
(iv) 4P-3Q = 5 (v) x-y+z = 0 (vi) 2x+2y-5z = -5
2Q+2P = 20 2y-2z = 2 x-y+z = 3
-x+2y+2z = 29 -3x+y+2z = -2
4. Given the equations of the lines:
(a) y = 2+x
(b) y = 3-4x
(c) y = 0.5x-2
Plot each line over the interval x = -2 to x = 6
5. Given the equations of the following lines:
(a) 2y-5x+10 = 0
(b) x = 10-2y
(c) y+5x=15
(i) Write each of the equations in the form y = f(x)
(ii) Write down the slope and the intercept of each line
(iii) Write down the inverse of each function (i.e. x = g(y))
(iv) Sketch the graph of each line
