Sign In

Mathematics for IGCSE & O level - Graphs Of Functions (Section 4)

1
Which key concept relates to how exponential graphs can be used to interpret real-world phenomena?
Answer
(C)
Growth and Decay
2
What is used to work out the gradient of a curve?
Answer
(B)
Change in y / Change in x
3
When sketching the graph of a quadratic function, which of these is useful to find?
Answer
A
B
C
4
What graphical property changes as the constant 'c' is changed in a quadratic equation?
Answer
(C)
The y-intercept.
5
How many times does a quadratic graph intersect with the x-axis, generally?
Answer
(C)
Twice
6
In the context of graphs, which term can be used to find where a graph crosses the x-axis?
Answer
(C)
The roots
7
Which part of a graph shows the solutions of an equation?
Answer
(A)
The x-intercepts
8
What type of graphs are defined by equations of the form y = ax^2 + bx + c, where a, b, and c are constants, and a ≠ 0?
Answer
(C)
Quadratic graphs
9
What happens when 'a' is negative in the quadratic equation y = ax^2 + bx + c?
Answer
(B)
The graph opens downwards.
10
What is the shape and nature of the graph for the equation y = a/x?
Answer
(C)
It has two separate branches.
11
What is a key use of exponential graphs?
Answer
(A)
To represent growth and decay
12
Which of the following equations would best model the path of a ball thrown upwards?
Answer
(C)
y = -x^2 + 4x
13
How is the gradient of a curve estimated at a specific point?
Answer
(B)
By drawing a tangent to the curve at that point.
14
What is the key property of a quadratic graph represented by an equation in the form y = ax^2 + bx + c?
Answer
(B)
It is a curve with a 'U' or inverted 'U' shape.
15
Which is a characteristic of a hyperbola or reciprocal graph?
Answer
A
B
16
What is a characteristic of reciprocal functions?
Answer
(B)
They have graphs with two separate branches.
17
What is the significance of the x-intercepts on a graph?
Answer
(B)
They represent the roots/solutions of the equation.
18
Which of the following types of graphs can be used to solve a quadratic equation?
Answer
A
D
19
What is used in an exponential function to describe the degree of change, for example, growth or decay?
Answer
(B)
The multiplier
20
The process of identifying roots on the graph usually requires...
Answer
(C)
Finding points where the curve intersects the x-axis
21
If the coefficient of x^2 in a quadratic equation is negative, what is the general shape of the graph?
Answer
(B)
An upside-down 'U' shape.
22
If you are trying to estimate the temperature of the coffee after a certain time, which variable is used to show the time?
Answer
(D)
t
23
When drawing a reciprocal graph, why is it useful to consider both positive and negative values of x?
Answer
(C)
To show the two separate branches of the graph
24
In a quadratic equation, what is the term 'c' when the equation is expressed as y = ax^2 + bx + c?
Answer
(B)
The y-intercept
25
What does the vertical asymptote represent in a reciprocal graph?
Answer
(B)
The line the graph approaches but never touches
26
Which of these is described as an exponential graph?
Answer
(C)
y = ka^x
27
How are the solutions to a quadratic equation visually represented on a graph?
Answer
(B)
By the x-intercepts
28
What is true about the graph of y = x^2?
Answer
(B)
It's an upward-opening parabola with the vertex at the origin.
29
What is the maximum number of turning points a cubic graph can have?
Answer
(C)
2
30
If the graph of a quadratic equation does not intersect the x-axis, how many real solutions does it have?
Answer
(C)
Zero
31
In the coffee problem, if Irina leaves the coffee for 4 minutes, and then drinks it. What is the temperature then?
Answer
(D)
72.2
32
In the equation y = a/x, the graph will not intersect the axes. Why?
Answer
(A)
Because the x-axis and y-axis are both asymptotes.
33
In the compound interest formula D = 500 * 1.09^t, which value represents the percentage?
Answer
(B)
1.09
34
When estimating the gradient of a curve, how do you find increase in x and y?
Answer
(D)
By using the points on the tangent
35
In the equation y=2x^3-1, what shape graph can you derive?
Answer
(B)
An S-shaped curve.
36
Which of the following equations will produce a graph with a symmetrical 'U' shape?
Answer
(C)
y = x^2
37
What do exponential graphs represent?
Answer
A
B
38
Which of the following could be an appropriate scale for a graph displaying the equation y=2x^3?
Answer
A
C
39
What is the most immediate visual characteristic of a reciprocal graph?
Answer
(B)
It approaches, but never touches, an asymptote.
40
What happens if you are asked to sketch y = 1/x, but x = 0?
Answer
(B)
It's undefined
41
The x values where the curve cut the axis are:
Answer
(A)
X-intercept
42
In the equation of a graph, what information does the turning point provide?
Answer
(A)
The minimum or maximum value of the function
43
If an exponential function represents decay, which of the following is true about the multiplier?
Answer
(C)
The multiplier is less than 1.
44
When drawing a tangent line to estimate a gradient, what is the best approach for choosing points to calculate the gradient?
Answer
(B)
Choosing points that make the x increase an easy number.
45
What can you determine by knowing the roots of a quadratic equation?
Answer
(B)
Where the graph crosses the x-axis.
46
What kind of symmetry does a graph of y = a/x exhibit?
Answer
(C)
Symmetry about the origin.
47
In the context of compound interest, what does the initial amount of money invested represent in the exponential function?
Answer
(B)
The principal
48
When is the y-intercept found?
Answer
(A)
When x=0.
49
What is the primary reason for completing a table of values before plotting a graph?
Answer
(C)
To provide coordinates for plotting points.
50
Which of the following is true about the gradient of a straight line?
Answer
(B)
It is constant