Sign In

Mathematics for IGCSE & O level - Graphs Of Functions (Section 5)

1
What would be a good approach to graphically solve the equation x^2 - 2x - 3 = 0?
Answer
(B)
Sketch the parabola
2
In a graph for y = x^2 -5x +6. The values that you draw a line to solve the equation?
Answer
(D)
y = 5
3
What is calculated when finding the gradient of the curve?
Answer
(B)
The slope or steepness of the curve at a certain point.
4
In graphing y=x^2 -3x+2, what helps in determining the shape of the graph?
Answer
(B)
The coefficients.
5
In the case of growth, what is the value of the multiplier 'a'?
Answer
(C)
Greater than 1
6
Which of the following is the general form of a reciprocal graph?
Answer
(C)
y = a/x
7
What does the phrase 'Estimating the gradient to a curve' refer to?
Answer
(C)
Approximating the slope of the curve at a point.
8
How many values of 'x' you can get on graph y = x^2 - x -6, if y = 0?
Answer
(B)
Two values
9
In a cubic equation of the form y = ax^3 + bx^2 + cx + d, what influences the general 'shape' of the curve?
Answer
(B)
The coefficient 'a'
10
In the equation P = 700 * 1.05^x, which number represents the percentage the population grows each year?
Answer
(B)
1.05
11
What characteristics do all equations of the form y = a/x share?
Answer
A
C
12
What is the value of 'a' if y = a*b^x and the graph represents a decay?
Answer
(B)
0 < a < 1
13
What feature differentiates a parabola from a hyperbola?
Answer
(C)
Shape.
14
In the equation y = a/x, what happens to the graph as x approaches zero (from the positive side)?
Answer
(B)
y approaches infinity.
15
What best describes the graph of y = -x^2 + 2x + 3?
Answer
(C)
An inverted U-shaped curve
16
If 'a' in the quadratic equation y=ax^2+bx+c is positive, what can be said about the graph?
Answer
(C)
The graph opens upwards.
17
In a graph of y = a/x, what is the impact on the curve of changing the value of 'a'?
Answer
(C)
Stretches or compresses the curve vertically.
18
In the context of the coffee cooling problem, what does the variable 't' most likely represent?
Answer
(B)
The time in minutes
19
What is the first step to draw a graph?
Answer
(B)
Create a table of values
20
Which of the following can be identified by finding the intersection points of two graphs?
Answer
(B)
The solution of a system of equations
21
Which of the following is NOT a characteristic of a cubic graph?
Answer
(B)
It passes through the origin.
22
Which feature is NOT typically found in a linear graph?
Answer
(C)
A turning point.
23
What does the graph of an exponential function describe?
Answer
(C)
A value that increases or decreases over time
24
What is the significance of the vertex of a parabola?
Answer
(C)
It is the maximum or minimum point of the graph.
25
If a is negative, what shape will the quadratic graph y = ax^2 + bx + c display?
Answer
(B)
An upside-down 'U' shape.
26
In the context of graphs, what do the solutions of an equation represent?
Answer
(D)
The roots of the equation.
27
What is the form of equation for exponential graphs?
Answer
(B)
y = k * a^x
28
If you are given the graph of a function, how can you solve an equation graphically?
Answer
(C)
By drawing a horizontal line at the value of y and finding intersection points.
29
Which of the following scenarios can be modeled using exponential curves?
Answer
A
B
C
30
How many separate branches do reciprocal graphs typically have?
Answer
(B)
Two
31
What is the best way to find the roots of a quadratic equation using a graph?
Answer
(C)
Find where the graph intersects the x-axis.
32
What is the standard form of a quadratic function that is represented as a parabola?
Answer
(B)
y = ax^2 + bx + c
33
Which component of a quadratic equation determines the location of the y-intercept?
Answer
(C)
The constant term
34
If the value of a car decreases by 15% per year, what formula represents the value?
Answer
(A)
V = 5000 * 0.85^t
35
When solving a quadratic equation graphically, where do you look for the solutions?
Answer
(C)
At the points where the curve crosses the x-axis.
36
What will be the value of y when y= x^2 + 2x - 3, and x is equal to -2?
Answer
(B)
-3
37
What is the general method to estimate the gradient of a curve at a point?
Answer
A
C
38
Which of the following describes the graph of y= x^2 - 6x + 9?
Answer
(B)
An upward-opening parabola.
39
What does a vertical asymptote on a graph represent?
Answer
(B)
A value the graph approaches but never reaches
40
Which type of graph has asymptotes?
Answer
(D)
Reciprocal graphs
41
What happens to the values of y when drawing the graph of x^2 and x values are increasing from the origin?
Answer
(C)
The value of y increases.
42
In estimating a gradient, what is calculated?
Answer
(D)
Increase in y / Increase in x
43
When would you know that the curve is increasing or decreasing over time?
Answer
(C)
By checking the multiplier
44
What is the purpose of completing a table of values before drawing a graph?
Answer
(B)
To assist in plotting the graph accurately.
45
Where is the x-intercept or y-intercept can be found for any graph?
Answer
(B)
By finding the points where graph crosses the y-axis.
46
What is the graphical interpretation of the solution to a system of equations?
Answer
(C)
The points where the lines intersect.
47
In the equation y = 20 + 60*0.9^x, what does the term '20' most likely represent?
Answer
(A)
Initial Temperature
48
What type of symmetry is typically observed in a parabola?
Answer
(D)
Symmetry about a vertical line through the vertex.
49
When estimating the gradient of a curve at a point, why is it important to draw the tangent carefully?
Answer
(B)
The tangent should create equal space on both sides of the curve
50
What method is used to estimate the gradient of a curve at a specific point?
Answer
(B)
Draw a tangent