Mathematics for IGCSE & O level - Graphs Of Functions (Section 6)
1
What is the most significant visual difference between the graphs of y = x^2 and y = x^3?
Answer
(B)
The symmetry.
2
What is the key to estimating the gradient of a curve at a point?
Answer
(B)
Drawing a tangent at that point
3
What type of function has graphs with two separate branches?
Answer
(B)
Reciprocal
4
What does the number '1.05' represents in the population equation?
Answer
(A)
Annual population growth
5
What is the shape of the graph of y = x^3?
Answer
(C)
An S-shaped curve
6
What graphical feature distinguishes quadratic and cubic graphs?
Answer
(B)
Number of turning points.
7
What shapes can a cubic graph take?
Answer
B
D
8
Which of the following are essential steps when drawing a graph to solve an equation?
Answer
A
B
C
9
In the formula for compound interest, D = 500 * 1.09^t, what does '500' represent?
Answer
(B)
The initial amount invested
10
Which of the following is/are an exponential function?
Answer
B
C
11
Which type of graph does the equation y = ax^3 + bx^2 + cx + d represent?
Answer
(D)
Cubic graphs
12
Which component of a quadratic equation determines the presence of a turning point?
Answer
(C)
The x^2 term.
13
If a graph represents the motion of an arrow shot upwards, which factors could be presented on the x-axis and y-axis?
Answer
(A)
X-axis: Time; Y-axis: Height.
14
What is the relationship between the gradient of a curve and the tangent line to the curve at a given point?
Answer
(B)
The gradient of the curve is the same as the gradient of the tangent
15
What is the visual representation of the solutions to a system of linear equations?
Answer
(C)
The point(s) of intersection of the lines.
16
What is a key characteristic used to distinguish different types of graphs?
Answer
(C)
The shape of the graph
17
In the function *y = a * b^x*, where *y* represents the value of a function and *x* the independent variable, which term represents the rate of change of the function?
Answer
(B)
b
18
What does the gradient of a straight line in a linear graph represent?
Answer
(A)
The rate of change of y with respect to x.
19
In the formula D=500 * 1.09^t, if Vivek withdrew the money when it reached $800, what would be the next step to calculate the time spent?
Answer
(B)
Draw a line at D=800 and see where it intersects the curve.
20
Which type of graph can be described by the equation y = ax + b?
Answer
(B)
Linear graph
21
What is the minimum number of points generally required to accurately draw a smooth curve for a function?
Answer
(C)
4
22
When sketching a quadratic graph, what are the key points you should usually find?
Answer
A
B
C
23
What is the purpose of plotting extra points to table values when graphing a reciprocal function?
Answer
(C)
To help draw the shape of the curve
24
In the equation of a quadratic graph, y = ax^2 + bx + c, what determines the direction the parabola opens?
Answer
(C)
The value of a
25
What is important to do before drawing a graph to solve an equation?
