Lesson I1
I1 Locating roots by change of sign Quiz: AQA Maths, Unit 9
20 questions
In partnership with Revision Ninja
Lesson I1, Locating roots by change of sign: 20 multiple choice questions for the AQA Maths (7357), Unit 9: Numerical methods, written with Revision Ninja.
Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.
The 20 questions
-
If a continuous function has opposite signs at interval endpoints, what exists between them?
- A maximum point
- At least one root
- Exactly one root
- No roots
-
Why can a sign-change method fail to detect a double root of f(x) = 0?
- No sign change
- Multiple y-intercepts
- Infinite gradient
- Discontinuous function
-
What condition must a function satisfy for a sign change to guarantee a root?
- Continuous
- Differentiable
- Increasing
- Linear
-
If f(a) and f(b) have the same sign, how many roots are in (a, b)?
- Exactly zero roots
- Exactly one root
- No definite conclusion
- Exactly two roots
-
Which interval must contain a root of x^3 - x - 1 = 0 by change of sign?
- (-1, 0)
- (2, 3)
- (0, 1)
- (1, 2)
-
Which of these intervals shows a change of sign for f(x) = x^2 - 3?
- (0, 1)
- (3, 4)
- (4, 5)
- (1, 2)
-
Which interval must contain a root of x^3 - 2x - 5 = 0?
- (2, 3)
- (-1, 0)
- (0, 1)
- (3, 4)
-
Which interval must contain a root of cos x - x = 0?
- (0, 1)
- (2, 3)
- (-1, 0)
- (1, 2)
-
Which interval must contain a root of ln x + x - 2 = 0?
- (0, 1)
- (3, 4)
- (1, 2)
- (2, 3)
-
Which interval must contain a root of x^3 - 4x + 1 = 0?
- (-1, 0)
- (3, 4)
- (0, 1)
- (1, 1.5)
-
Which intervals contain the positive root of x^2 - 2x - 1 = 0?
- (2, 3)
- (3, 4)
- (4, 5)
- (1, 2)
-
Why does sign change fail to guarantee a root for f(x) = 1/x on [-1, 1]?
- Function is non-differentiable
- Function is stationary
- Roots are complex
- Function is discontinuous
-
For f(x) = x^3 - 2 on [1, 2], what is the new interval after one bisection step?
- [0, 1]
- [1.5, 2]
- [1, 1.5]
- [1, 2.5]
-
The equation 1/x - 2 = 0 has a root in [0.25, 1]. What is the root?
- x = 2
- x = 1
- x = 0.25
- x = 0.5
-
Which interval must contain a root of x^3 - 7 = 0?
- (0, 1)
- (-2, -1)
- (2, 3)
- (1, 2)
-
Which interval must contain a root of x^2 - 2x - 1 = 0 for the negative root, using f(-1) = 2 and f(0) = -1?
- (0, 1)
- (-1, 0)
- (-2, -1)
- (1, 2)
-
For f(x) = x^3 - 2x - 1, which interval must contain a root?
- (-3, -2)
- (1, 2)
- (0, 1)
- (2, 3)
-
Which interval must contain a root of x^3 + x - 3 = 0?
- (-2, -1)
- (1, 2)
- (2, 3)
- (0, 1)
-
What does a sign change of a continuous function across an interval guarantee?
- At least one root
- No real solutions
- An asymptote
- A local maximum
-
Why can sign change fail to locate the root of f(x) = (x - 2)^2?
- It is complex
- It is undefined
- It is repeated
- It is discontinuous
Related quizzes
- Iterative methods and Newton-Raphson Quiz · I2 · 20 questions
- Numerical integration with the trapezium rule Quiz · I3 · 20 questions
- Numerical methods in context Quiz · I4 · 20 questions
- Mathematical proof, disproof and contradiction Quiz · A1 · 20 questions
- Indices and surds Quiz · B1-B2 · 20 questions
- Straight lines and gradients Quiz · C1 · 20 questions
- Binomial expansion Quiz · D1 · 20 questions
- Trigonometric definitions, sine and cosine rules, radians Quiz · E1 · 20 questions
- Exponential and natural logarithm functions and graphs Quiz · F1 · 20 questions
- Derivative as gradient, first principles and second derivatives Quiz · G1 · 20 questions