Question 1(a): [1 mark]
For y = x^2, find the values of a, b, c, d, e from the table.
Answer type: Multiple answers type 1
ANSWER: a = 9 ; b = 4 ; c = 1 ; d = 0 ; e = 1
WORKING:
(-3)^2 = 9
(-2)^2 = 4
(-1)^2 = 1
(0)^2 = 0
(1)^2 = 1
Question 1(b): [1 mark]
What is the correct graph for y = x^2?
Answer type: Multiple choice type 1
A: A
B: B
C: C
D: D
ANSWER: A: A
Question 2(a): [1 mark]
For y = x^3 - 2x, find the values of a, b, c, d, e from the table.
Answer type: Multiple answer type 1
ANSWER: a = -4 ; b = 1 ; c = 0 ; d = -1 ; e = 4
WORKING:
(-2)^3 - 2(-2) = -4
(-1)^3 - 2(-1) = 1
(0)^3 - 2(0) = 0
(1)^3 - 2(1) = -1
(2)^3 - 2(2) = 4
Question 2(b): [1 mark]
What is the correct graph for y = x^3 - 2x?
Answer type: Multiple choice type 1
A: A
B: B
C: C
D: D
ANSWER: C: C
Question 3(a): [1 mark]
For A: y = x^2 - 1, -2 \leq x \leq 3, find the values of a, b, c, d, e, f from the table.
Answer type: Multiple answers type 1
ANSWER: a = 3 ; b = 0 ; c = -1 ; d = 0 ; e = 3 ; f = 8
WORKING:
(-2)^2 - 1 = 3
(-1)^2 - 1 = 0
(0)^2 - 1 = -1
(1)^2 - 1 = 0
(2)^2 - 1 = 3
(3)^2 - 1 = 8
Question 3(b): [1 mark]
For B: y = x^2 - x, -2 \leq x \leq 3, find the values of g, h, i, j, k, l from the table.
Answer type: Multiple answers type 1
ANSWER: g = 6 ; h = 2 ; i = 0 ; j = 0 ; k = 2 ; l = 6
WORKING:
(-2)^2 -(-2) = 6
(-1)^2 -(-1) = 2
(0)^2 -(0) = 0
(1)^2 -(1) = 0
(2)^2 -(2) = 2
(3)^2 -(3) = 6
Question 3(c): [1 mark]
Choose the correct statement below about the graph drawings.
Answer type: Multiple choice type 1
A: A is drawn correctly but B is drawn incorrectly.
B: B is drawn correctly but A is drawn incorrectly.
C: Both A and B are drawn correctly.
D: Both A and B are drawn incorrectly.
ANSWER: B: B is drawn correctly but A is drawn incorrectly.
WORKING: The graph drawn that is incorrect is y = x^2 + 1, but it should be y = x^2 - 1.
Question 4(a): [1 mark]
What is the difference between a sketch and a plot of a graph?
Answer type: Multiple choice type 1
A: A plot of a graph is more precise, using all the exact points. A sketch may use some of the known points that are then connected.
B: A sketch of a graph is more precise, using all the exact points. A plot may use some of the known points that are then connected.
C: There is no difference.
ANSWER: A plot of a graph is more precise, using all the exact points. A sketch may use some of the known points that are then connected.
Question 4(b): [6 marks]
There are 6 equations as follows:
A: y = x^3 + 2x^2
B: y = x^3
C: y = -x^3
D: y = x^2
E: y = x^2 + 2x
F: y = -x^2
and 6 graphs:
Match the graphs to the equations.
Answer type: Multiple answers type 1
ANSWER:
Graph 1 = D
Graph 2 = B
Graph 3 = A
Graph 4 = E
Graph 5 = F
Graph 6 = C
Question 5(a): [1 mark]
The values for y = -x^3 + 3x^2 for x from -1 to [/latex]3[/latex] can be seen in the table below.
Find the values of a, b, c, d, e from the table.
Answer type: Multiple answers type 1
ANSWER:
a = 4
b = 0
c = 2
d = 4
e = 0
WORKING:
-(-1)^3 + 3(-1)^2 = 4
-(0)^3 + 3(0)^2 = 0
-(1)^3 + 3(1)^2 = 2
-(2)^3 + 3(2)^2 = 4
-(3)^3 + 3(3)^2 = 0
Question 5(b): [2 marks]
What is the correct graph for y = -x^3 + 3x^2?
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A
Question 6(a): [1 mark]
The values for y = \dfrac{1}{2}(x^3 + x + 1), for x from -2 to [/latex]3[/latex] can be seen in the table below.
Find the values of a, b, c, d, e from the table.
Answer type: Multiple answers type 1
ANSWER:
a = -4.5
b = -0.5
c = 0.5
d = 1.5
e = 5.5
WORKING:
\dfrac{1}{2}( (-2)^3 + (-2) + 1) = -4.5
\dfrac{1}{2}( (-1)^3 + (-1) + 1) = -0.5
\dfrac{1}{2}( (0)^3 + (0) + 1) = 0.5
\dfrac{1}{2}( (1)^3 + (1) + 1) = 1.5
\dfrac{1}{2}( (2)^3 + (2) + 1) = 5.5
Question 6(b): [2 marks]
What is the correct graph for y = \dfrac{1}{2}(x^3 + x + 1)?
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A