Question 1
Perform the following calculations

(i)	(7)+(-14)	(ii)	(-8)+(9)
(iii)	(-4)-(13)	(iv)	(-5)-(-17)
(v)	(-9)×(11)	(vi)	(-11)×(-11)
(vii)	(-32)¸(8)	(viii)	(-12)¸(-6)

Question 2
Simplify the following algebraic inequalities

(i)	5 < 2x +15	(ii)	x-25 > 7
(iii)	7x + 12 < 12x -3	(iv)	-9x -17 > 9x +1
(v)	3x -29 < 7x+11	(vi)	-11x -12 < 19x +8

Question 3
Show, step, by step, how the expression on the left-hand side simplifies to that on the right.

(i)	3x+4x+7(2x-3) = 21x-21
(ii)	4x2 + 7x+2x(4x-5) = 12x2 - 3x
(iii)	2x(y+2) - 2y(x+2) = 4x-4y
(iv)	(x+2)(y-2) +(x-3)(y+2) = 2xy -y -10
(v)	(x+2)(x+2) - (x-2)(x-2) = 8x
(vi)	(x+2)(x+2) - x(x+2) = 2x+4

Question 4
Perform the following calculations:

(i)	(2/3) (5/7)	(ii)	(-2/3) (7/5)
(iii)	(3) (2/5)	(iv)	(6/7) ([9/ 13])
(v)	(2/3) ¸([5/ 11])	(vi)	(5) ¸(-3/4)
(vii)	(7/3) ¸(8)	(viii)	(-2/3) ¸(1/5)

Question 5
Show, step, by step, how the expression on the left-hand side simplifies to that on the right. Use cancellation where possible.
(i)

Question 6
Show, step, by step, how the expression on the left-hand side simplifies to that on the right.
(i)

Question 7
Given the following lines:

(i)	y = x+2
(ii)	y = -4x+3
(iii)	y = 0.5x -2
(iv)	2y = 6x +4

(a) Write down the slope, x intercept and yintercept for each line.
(b) Calculate the values of y when x = -2,0,2,4,6.
(c) Plot each line over the interval x = -2 to x = 6.

Question 8
Write each of the following in slope intercept form:

(i)	2y-5x+10 = 0	(ii)	0.2y +0.4x = 2
(iii)	2x+3y-1 = 0	(iv)	4x+3y-2 = 0

Question 9
Find the equation of each line described by the following:

(i)	Slope = 2, y-intercept = 0	(ii)	Slope = -2, y-intercept = 0
(iii)	Slope = 1, y-intercept = -2	(iv)	Slope = -1, y-intercept = 2

Question 10
In each case, find if the two lines given intersect, and if so find the point (or points) of intersection:

(i)	2x+y = 5	5x+4y = 11
(ii)	x-5y = 11	3x-y = 5
(iii)	3x+2y = 6	6x+4y = 12
(iv)	x+7 = y	2x-3y+18 = 0

(v)	3x-7y = 12	5x-2y = 20
(vi)	3x-2y = 5	2x+5y = 12
(vii)	3x+2y = 11	2x+1 = 0
(viii)	x-3y = 5	2x-6y = 3

Question 11
Find the equation of the line joining the following points:

(i)	(2,3)	(1,7)
(ii)	(-2,1)	(1,6)
(iii)	(0,-4)	(-2,-5)
(iv)	(-1,4)	(-2,-1)
(v)	(0,4)	(-1,5)
(vi)	(2,0)	(0,-4)

Answers

Question 2

(i)	-5 < x	(ii)	x > 32	(iii)	3 < x	(iv) -1 > x
(v)	-10 < x	(vi)	-2/3 < x

Question 4

(i)	[10/ 21]	(ii)	- [14/ 15]	(iii)	6/5 = 11/5	(iv)	[54/ 91]
(v)	[22/ 15] = 1[7/ 15]	(vi)	-[20/ 3] = -62/3	(vii)	[7/ 24]	(viii)	-[10/ 3] = - 31/3

Question 7
(i) Slope = 1, Intercepts: (0,2), (-2, 0); Points:(-2,0),(0,2),(2,4),(4,6),(6,8).
(ii) Slope = -4, Intercepts: (0,3),(³/₄,0); Points:(-2,11),(0,3),(2,-5),(4,-13),
(6,-21).
(iii) Slope = -¹/₂, Intercepts: (0,-2), (4, 0); Points:(-2,-3),(0,-2),(2,-1), (4,0),(6,1).
(iv) Slope = 3, Intercepts: (0,2), (-²/₃, 0); Points:(-2,-4),(0,2),(2,8),(4,14),(6,20).

Question 8

(i)	y = 5/2 x -5	(ii)	y = -2 x +10
(iii)	y = - 2/3 x +1/3	(iv)	y = -11/3 x +2/3

Question 9

(i)	y = 2x	(ii)	y = -2x
(iii)	y = x-2	(iv)	y = -x+2

Question 10

(i)	(3,-1)
(ii)	(1,-2)
(iii)	lines are the same, an infinite number of solutions exist.
(iv)	(-3,4)
(v)	(4,0)
(vi)	([49/ 19], [26/ 19])
(vii)	(-1/2, 61/4)
(viii)	lines are parallel, no solution exists

Question 11
(i) y = -4x+11
(ii) y = 1²/₃x + 4¹/₃
(iii)y = ¹/₂ x -4
(iv) y = 5x+9
(v) y = -x+4
(vi)y = 2x-4