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?
2
In a graph for y = x^2 -5x +6. The values that you draw a line to solve the equation?
3
What is calculated when finding the gradient of the curve?
Одговорити(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?
5
In the case of growth, what is the value of the multiplier 'a'?
6
Which of the following is the general form of a reciprocal graph?
7
What does the phrase 'Estimating the gradient to a curve' refer to?
Одговорити(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?
9
In a cubic equation of the form y = ax^3 + bx^2 + cx + d, what influences the general 'shape' of the curve?
10
In the equation P = 700 * 1.05^x, which number represents the percentage the population grows each year?
11
What characteristics do all equations of the form y = a/x share?
12
What is the value of 'a' if y = a*b^x and the graph represents a decay?
13
What feature differentiates a parabola from a hyperbola?
14
In the equation y = a/x, what happens to the graph as x approaches zero (from the positive side)?
15
What best describes the graph of y = -x^2 + 2x + 3?
Одговорити(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?
17
In a graph of y = a/x, what is the impact on the curve of changing the value of 'a'?
Одговорити(C)
Stretches or compresses the curve vertically.
18
In the context of the coffee cooling problem, what does the variable 't' most likely represent?
19
What is the first step to draw a graph?
20
Which of the following can be identified by finding the intersection points of two graphs?
Одговорити(B)
The solution of a system of equations
21
Which of the following is NOT a characteristic of a cubic graph?
Одговорити(B)
It passes through the origin.
22
Which feature is NOT typically found in a linear graph?
23
What does the graph of an exponential function describe?
Одговорити(C)
A value that increases or decreases over time
24
What is the significance of the vertex of a parabola?
Одговорити(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?
Одговорити(B)
An upside-down 'U' shape.
26
In the context of graphs, what do the solutions of an equation represent?
Одговорити(D)
The roots of the equation.
27
What is the form of equation for exponential graphs?
28
If you are given the graph of a function, how can you solve an equation graphically?
Одговорити(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?
30
How many separate branches do reciprocal graphs typically have?
31
What is the best way to find the roots of a quadratic equation using a graph?
Одговорити(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?
33
Which component of a quadratic equation determines the location of the y-intercept?
34
If the value of a car decreases by 15% per year, what formula represents the value?
35
When solving a quadratic equation graphically, where do you look for the solutions?
Одговорити(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?
37
What is the general method to estimate the gradient of a curve at a point?
38
Which of the following describes the graph of y= x^2 - 6x + 9?
Одговорити(B)
An upward-opening parabola.
39
What does a vertical asymptote on a graph represent?
Одговорити(B)
A value the graph approaches but never reaches
40
Which type of graph has asymptotes?
41
What happens to the values of y when drawing the graph of x^2 and x values are increasing from the origin?
Одговорити(C)
The value of y increases.
42
In estimating a gradient, what is calculated?
Одговорити(D)
Increase in y / Increase in x
43
When would you know that the curve is increasing or decreasing over time?
Одговорити(C)
By checking the multiplier
44
What is the purpose of completing a table of values before drawing a graph?
Одговорити(B)
To assist in plotting the graph accurately.
45
Where is the x-intercept or y-intercept can be found for any graph?
Одговорити(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?
Одговорити(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?
48
What type of symmetry is typically observed in a parabola?
Одговорити(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?
Одговорити(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?
