Podcast
Questions and Answers
When expanding $(2x - 3)^3$ using the binomial theorem, which of the following represents the coefficient of the $x$ term?
When expanding $(2x - 3)^3$ using the binomial theorem, which of the following represents the coefficient of the $x$ term?
- -108 (correct)
- -54
- 54
- 108
Consider the binomial expansion of $(1 + x)^5$. What is the sum of the coefficients of the first three terms?
Consider the binomial expansion of $(1 + x)^5$. What is the sum of the coefficients of the first three terms?
- 10
- 15
- 16
- 11 (correct)
Using the binomial expansion, which of the following is the closest approximation of $(1.1)^3$ to 3 decimal places?
Using the binomial expansion, which of the following is the closest approximation of $(1.1)^3$ to 3 decimal places?
- 1.330
- 1.332
- 1.321
- 1.331 (correct)
Given $\sin(\theta) = \frac{\sqrt{3}}{2}$ and $0^\circ \leq \theta < 360^\circ$, what are all possible values of $\theta$?
Given $\sin(\theta) = \frac{\sqrt{3}}{2}$ and $0^\circ \leq \theta < 360^\circ$, what are all possible values of $\theta$?
If vectors $\mathbf{a} = 2\hat{i} + 3\hat{j}$ and $\mathbf{b} = \hat{i} - 4\hat{j}$, what is the result of the scalar product $\mathbf{a} \cdot \mathbf{b}$?
If vectors $\mathbf{a} = 2\hat{i} + 3\hat{j}$ and $\mathbf{b} = \hat{i} - 4\hat{j}$, what is the result of the scalar product $\mathbf{a} \cdot \mathbf{b}$?
If the expression $4x(2x - 5) + 3(5x^2 - 2x)$ is simplified, what is the coefficient of the $x$ term?
If the expression $4x(2x - 5) + 3(5x^2 - 2x)$ is simplified, what is the coefficient of the $x$ term?
Which of the following represents the correct factorization of the quadratic expression $x^2 + 7x + 10$?
Which of the following represents the correct factorization of the quadratic expression $x^2 + 7x + 10$?
After expanding and simplifying $(x - 3)(x + 2)$, what is the constant term?
After expanding and simplifying $(x - 3)(x + 2)$, what is the constant term?
For what values of $x$ does the quadratic equation $x^2 - 5x + 6 = 0$ hold true?
For what values of $x$ does the quadratic equation $x^2 - 5x + 6 = 0$ hold true?
Given the roots of a quadratic equation $ax^2 + bx + c = 0$ are $x = 2$ and $x = -3$, and assuming $a = 1$, what is the value of $b$?
Given the roots of a quadratic equation $ax^2 + bx + c = 0$ are $x = 2$ and $x = -3$, and assuming $a = 1$, what is the value of $b$?
What is the solution set for the quadratic inequality $x^2 - 4x - 5 < 0$?
What is the solution set for the quadratic inequality $x^2 - 4x - 5 < 0$?
What value of $x$ satisfies the equation $2x + 3 = 4x - 7$?
What value of $x$ satisfies the equation $2x + 3 = 4x - 7$?
Which inequality represents the solution to $3x - 5 \geq 7x + 1$?
Which inequality represents the solution to $3x - 5 \geq 7x + 1$?
Flashcards
Binomial Theorem
Binomial Theorem
A method to expand expressions of the form (a + b)^n.
Binomial Approximation
Binomial Approximation
An approximation using the first few terms of its binomial expansion; accurate when x is small.
Angle
(\theta) in Trigonometry
Angle (\theta) in Trigonometry
The angle formed by a point on the unit circle, measured counterclockwise from the positive x-axis.
Pythagorean Identity
Pythagorean Identity
Signup and view all the flashcards
Magnitude of a
Vector
Magnitude of a Vector
Signup and view all the flashcards
What does it mean to ‘simplify’?
What does it mean to ‘simplify’?
Signup and view all the flashcards
What is 'factorizing'?
What is 'factorizing'?
Signup and view all the flashcards
What is 'expanding'?
What is 'expanding'?
Signup and view all the flashcards
What are the roots of a quadratic equation?
What are the roots of a quadratic equation?
Signup and view all the flashcards
What is the 'gradient' of a line?
What is the 'gradient' of a line?
Signup and view all the flashcards
What is the y-intercept?
What is the y-intercept?
Signup and view all the flashcards
Circle Equation
Circle Equation
Signup and view all the flashcards
Completing the Square
Completing the Square
Signup and view all the flashcards
Study Notes
- These are practice questions for Edexcel AS Level Mathematics (Pure Year 1).
- The paper covers topics from Chapters 1-9 and Chapter 11.
Section A: Algebraic Expressions (Chapter 1)
- Simplify expressions by expanding and combining like terms.
- Factorize quadratic expressions into the product of two binomials.
- Expand and simplify the product of two binomials.
Section B: Quadratics (Chapter 2)
- Solve quadratic equations by factoring, completing the square, or using the quadratic formula.
- Determine the quadratic equation given its roots.
- Solve quadratic inequalities by finding critical values and testing intervals.
Section C: Equations and Inequalities (Chapter 3)
- Solve linear equations by isolating the variable.
- Solve linear inequalities, remembering to reverse the inequality sign when multiplying or dividing by a negative number.
- Solve systems of linear equations using substitution or elimination methods.
Section D: Graphs and Transformations (Chapter 4)
- Sketch quadratic graphs, identifying the vertex, x-intercepts, and y-intercept.
- Describe transformations of graphs, including translations and reflections.
- Find the coordinates of the vertex of a quadratic function.
Section E: Straight Line Graphs (Chapter 5)
- Find the gradient of a line given two points on the line.
- Determine the y-intercept of a line from its equation.
- Find the coordinates of the point where a line crosses the x-axis.
- Find the equation of a line given its gradient and a point on the line.
Section F: Circles (Chapter 6)
- Determine the center and radius of a circle from its equation in the form (x - a)^2 + (y - b)^2 = r^2.
- Find the coordinates of the points where a circle intersects the x-axis by setting y = 0 in the circle's equation.
- Find the equation of a circle given its center and a point on the circle.
Section G: Algebraic Methods (Chapter 7)
- Solve equations involving fractions.
- Express a quadratic expression in the completed square form a(x + b)^2 + c.
Section H: Binomial Expansion (Chapter 8)
- Expand binomial expressions using the binomial theorem.
- Find specific terms in a binomial expansion.
- Approximate values using binomial expansion.
Section I: Trigonometric Ratios (Chapter 9)
- Solve trigonometric equations for angles within a specified range.
- Prove trigonometric identities.
- Find the exact values of trigonometric ratios for specific angles.
Section J: Vectors (Chapter 11)
- Find the magnitude of a vector.
- Determine the scalar product (dot product) of two vectors.
- Find the vector between two points given their position vectors.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
