Question 9:
(a) Complete the table in the answer space for the equation y = 8 – 3x – 2x² by writing down the values of y when x = –4 and x = 2.

(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 5 – 8x – 2x² for –5 ≤ x ≤ 3 and –27 ≤ y ≤ 9.

(c) From your graph, find
(i) the value of y when x = –2.5,
(ii) the positive value of x when y = –16.

(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation 8 – 3x – 2x² = 0 for –5 ≤ x ≤ 3 and –27 ≤ y ≤ 9.

Answer:

x	–5	–4	–3.5	–2	–1	0	1	2	3
y	–27	r	–6	6	9	8	3	s	–19

Calculate the value of r and s.


Solution:
(a)
y = 8 – 3x – 2x²  
when x = –4,
r = 8 – 3(–4) – 2 (–4)²
= 8 + 12 – 32 = –12

when x = 2,
s = 8 – 3(2) – 2(2)²
= 8 – 6 – 8 = –6


(b)



(c)
(i) From the graph, when x = –2.5, y = 2.5
(ii) From the graph, when y = –16, positive value of x = 2.8


(d)
y = 8 – 3x – 2x² ----- (1)
0 = 5 – 8x – 2x²  ----- (2)
(1) – (2) : y = 3 + 5x → y = 5x +3
The suitable straight line is y = 5x +3.

Determine the x-coordinates of the two points of intersection of the curve y = 8 – 3x – 2x² and the straight line y = 5x +3.

x	–5	0
y = 5x + 3	22	3

From the graph, x = –4.5, 0.55.

Question 8:
(a) Complete the table in the answer space for the equation y = x³ – 4x – 10 by writing down the values of y when x = –1 and x = 3.

(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 units on the y-axis, draw the graph of y = x³ – 4x – 10 for –3 ≤ x ≤ 4 and –25 ≤ y ≤ 38.

(c) From your graph, find
(i) the value of y when x = 2.2,
(ii) the value of x when y = 15.

(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation x³ – 12x – 5 = 0 for –3 ≤ x ≤ 4 and –25 ≤ y ≤ 38.

Answer:

x	–3	–2	–1	0	1	2	3	3.5	4
y	–25	–10		–10	–13	–10		18.9	38

Solution:
(a)
y = x³ – 4x – 10  
when x = –1,
y = (–1)³ – 4(–1) – 10
= –7

when x = 3,
y = (3)³ – 4(3) – 10
= 5

(b)




(c)
(i) From the graph, when x = 2.2, y = –8
(ii) From the graph, when y = 15, x = 3.4


(d)
y = x³ – 4x – 10 ----- (1)
0 = x³ – 12x – 5 ----- (2)
(1) – (2) : y = 8x – 5

The suitable straight line is y = 8x–5. Determine the x-coordinates of the two points of intersection of the curve y = x³ – 4x – 10 and the straight line y = 8x –5.

x	0	2
y = 8x – 5	–5	–11

From the graph, x = –0.45, 3.7.

Question 7:

x	–3	–2	–1	0	1	2	3	3.5	4
y	19	3	r	1	3	–1	s	–31.4	–51

Solution:

x	0	4
y = –10x + 10	10	–30

Question 3:
On the graph in the answer space, shade the region which satisfies all three inequalities y ≥ x – 2, y > –3x + 6 and y ≤ 4.

Answer:


Solution:

Question 4:
On the graph in the answer space, shade the region which satisfies all three inequalities y > x – 2, y ≤ –x + 6 and x ≥ 1.

Answer:


Solution:

Question 5 (3 marks):
On the graph in the answer space, shade the region which satisfies all three inequalities y ≥ –3x + 6, y > x + 1 and y ≤ 5.

Answer:


Solution:

Question 1:
On the graph in the answer space, shade the region which satisfies all three inequalities y > –2x + 8, y ≥ x + 1 and y ≤ 7.

Answer:



Solution:

Question 2:
On the graph in the answer space, shade the region which satisfies all three inequalities 2x + y ≥ 2, x + y < 6 and y ≥ 1.

Answer:



Solution: