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Math Revision: Index Laws, Surds, Quadratic Equations, Completing Square, Functions, Simul, Exams of Mathematics

Brunel University London Mathematics

A comprehensive revision of various mathematical concepts, including index laws, negative and fractional indices, surds, rationalizing denominators, solving quadratic equations, completing the square, functions, quadratic graphs, simultaneous equations, inequalities, quadratic inequalities, inequalities on graphs, regions, cubic graphs, reciprocal graphs, points of intersection, and translating graphs. It includes questions and answers for each topic, making it an excellent resource for students studying mathematics.

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2023/2024

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Excel AS and A Level Mathematics

(PURE) Year 1 - All Chapters Revision

Questions and answers

1. Chapter 1.1 - Index Laws*: What is a base? - Correct Answers The

number having the power applied to it

2. *Chapter 1.1 - Index Laws*: What is an index, power or exponent? -

Correct Answers The operation being applied to the base

3. *Chapter 1.1 - Index Laws*: What is the result when multiplying the

same bases of different powers? - Correct Answers You add the

powers

4. E.g. am x an = amen

5. *Chapter 1.1 - Index Laws*: What is the result when dividing the

same base of different powers? - Correct Answers You subtract the

powers

6. E.g. am / an = amen

7. *Chapter 1.1 - Index Laws*: What is the result when applying a power

to a base with a power already? - Correct Answers You multiply the

powers

8. E.g. (am)^n = am

9. *Chapter 1.1 - Index Laws*: What is having two bases in a bracket

with a power applied also equivalent to? - Correct Answers The

individual bases to the power on their own

10. E.g. (ab)^n = (an)*ban)

Partial preview of the text

Download Math Revision: Index Laws, Surds, Quadratic Equations, Completing Square, Functions, Simul and more Exams Mathematics in PDF only on Docsity!

Excel AS and A Level Mathematics

(PURE) Year 1 - All Chapters Revision

Questions and answers

Chapter 1.1 - Index Laws*: What is a base? - Correct Answers The number having the power applied to it
Chapter 1.1 - Index Laws: What is an index, power or exponent? - Correct Answers The operation being applied to the base
Chapter 1.1 - Index Laws: What is the result when multiplying the same bases of different powers? - Correct Answers You add the powers
E.g. am x an = amen
Chapter 1.1 - Index Laws: What is the result when dividing the same base of different powers? - Correct Answers You subtract the powers
E.g. am / an = amen
Chapter 1.1 - Index Laws: What is the result when applying a power to a base with a power already? - Correct Answers You multiply the powers
E.g. (am)^n = am
Chapter 1.1 - Index Laws: What is having two bases in a bracket with a power applied also equivalent to? - Correct Answers The individual bases to the power on their own
E.g. (ab)^n = (an)*ban)

Chapter 1.2 - Expanding Brackets: To find the product of two expressions, you.... - Correct Answers ...Multiply each term in one expression by each term in the other expression
Chapter 1.2 - Expanding Brackets: How do we expand brackets? - Correct Answers
Chapter 1.3 - Factorizing: What is a product of factors? - Correct Answers The multipliers used to achieve the final answer
Chapter 1.3 - Factorizing: What is factorizing? - Correct Answers The opposite of expanding brackets
Chapter 1.3 - Factorizing: A quadratic expression has the form... - Correct Answers ax^2 + box + c
Where a, b and c are real values and a does not equal 0
Chapter 1.3 - Factorizing: How do we factories a quadratic expression? - Correct Answers - Find two factors of ac that add up to b
- Rewrite the b term as a sum of these row factors
- Factories each pair of terms
- Take out the common factor
x^2 - y^2 = (x + y)(x - y)
Chapter 1.4 - Negative and Fractional Indices: Indices can be.... - Correct Answers negative numbers or fractions
Chapter 1.4 - Negative and Fractional Indices: What is the result of applying a fractional power with numerator 1 to a base? - Correct Answers The denominator is the root power
E.g. a^(1/m) = m[root]a
Chapter 1.4 - Negative and Fractional Indices: What is the result of applying a fractional power with numerator n to a base? -

Chapter 1.6 - Rationalizing Denominators: If a fraction has a surd in the denominator, it is sometimes useful to... - Correct Answers rearrange it so that the denominator is a rational number
This is called rationalizing the denominator
Chapter 1.6 - Rationalizing Denominators: For fractions in the form 1/[root]a, we... - Correct Answers multiply the numerator and denominator by [root]a
Chapter 1.6 - Rationalizing Denominators: For fractions in the form 1/(a + [root]b), we.... - Correct Answers Multiply the numerator and denominator by a - [root]b
Chapter 1.6 - Rationalizing Denominators: For fractions in the form 1/(a = [root]b), we... - Correct Answers Multiply the numerator and denominator by a + [root]b
Chapter 2.1 - Solving Quadratic Equations: A quadratic equation can be written in the form.... - Correct Answers ax^2 + box"
- c = 0
Where a, b and c are real constants and a does not equal 0
Chapter 2.1 - Solving Quadratic Equations: Quadratic equations can have _________________ solutions - Correct Answers one, two or no real solutions
Chapter 2.1 - Solving Quadratic Equations: To solve a quadratic equation by factorizing... - Correct Answers - Write the equation in the form of ax^2 + box" + c = 0
- Factories the left-hand side
- Set each factor equal to 0 and solve to find the values of x
Chapter 2.1 - Solving Quadratic Equations: Sometimes, equations cannot be factories easily. So the quadratic formula is used. - Correct Answers The solutions to the equation ax^2 + box" + c = 0 are given by the formula:

Chapter 2.2 - Completing the square: It is frequently useful to rewrite quadratic expressions by completing the square.
The general formula is.... - Correct Answers x^2 + box = (x + b/2)^2 - (b/2)^
Chapter 2.2 - Completing the square: As a quadratic, the general formula is... - Correct Answers ax^2 + box + c = a(x + b/2a)^2 + (c - (b^2)/4a^2)
Chapter 2.3 - Functions: What is a function? - Correct Answers A mathematical relationship that maps each value of a set of inputs to a single output. The notation f(x) is used to represent a function of x.
Chapter 2.3 - Functions: What is the domain? - Correct Answers The set of possible inputs for a function
Chapter 2.3 - Functions: What is the range? - Correct Answers The set of possible outputs for a function
Chapter 2.3 - Functions: What is the roots of a function? - Correct Answers The values of x for which f(x) = 0
Chapter 2.4 - Quadratic Graphs: When f(x) = ax^2 + box + c, the graph of y = f(x) has a curved shape called a.... - Correct Answers Parabola
Chapter 2.4 - Quadratic Graphs: When drawing f(x) = ax^2 + box + c, what can be determined from the coefficient of x^2? - Correct Answers The overall shape of the graph
Chapter 2.4 - Quadratic Graphs: When drawing f(x) = ax^2 + box + c, if a is positive, the parabola will be... - Correct Answers a U-Shape
Chapter 2.4 - Quadratic Graphs: When drawing f(x) = ax^2 + box + c, if a is negative, the parabola will be... - Correct Answers an n-shape

If b^2 - 4ac < 0, then... - Correct Answers f(x) has no real root
Chapter 2.6 - Modelling with Quadratics: A mathematical model is a mathematical description of a real life situation. Mathematical models use the language and tools of mathematics to represent and explore real life patterns and relationships, and to predict what will happen next.
Models can be... - Correct Answers ...complicated or simple, and their results can be exact or approximate. Sometimes a model is only valid under certain circumstances, or for a limited range of inputs. You will learn more about how models involve simplifications and assumptions in Stats and Mechanics
Quadratic Functions can be used to model and explore a range of practical contexts, including projectile motion
Chapter 3.1 - Equations and Inequalities: Linear simultaneous equations in two unknowns have ______set of values that will make a pair of equations true at the same time - Correct Answers one
Chapter 3.1 - Linear Simultaneous Equations: Linear simultaneous equations can be solved by... - Correct Answers Elimination or Substitution
Chapter 3.2 - Quadratic Simultaneous Equations: To solve a linear and quadratic simultaneous equation, you can... - Correct Answers Rearrange the linear to make a single subject term to be substituted into the quadratic
Chapter 3.2 - Quadratic Simultaneous Equations: Simultaneous Equations with a linear and a quadratic can have up to ____ pairs of solutions - Correct Answers two
Chapter 3.3 - Simultaneous Equations on Graphs: How can we find the point on a graph that satisfies both equations? - Correct Answers Find the point of intersection

Chapter 3.3 - Simultaneous Equations on Graphs: The graph of a linear and quadratic equation can either - Correct Answers - Intersect Twice
- Intersect Once
- Not Intersect at All
Chapter 3.3 - Simultaneous Equations on Graphs: After substituting, you can use the discriminant of... - Correct Answers ...the resulting quadratic equation to determine the number of intersections
Chapter 3.3 - Simultaneous Equations on Graphs: For a pair of simultaneous equations that produce a quadratic equation in the form ax^2 + box + c = 0:
What is the discriminant for two real solutions? - Correct Answers b^2 + 4ac > 0
Chapter 3.3 - Simultaneous Equations on Graphs: For a pair of simultaneous equations that produce a quadratic equation in the form ax^2 + box + c = 0:
What is the discriminant for one real solutions? - Correct Answers b^2 + 4ac = 0
Chapter 3.3 - Simultaneous Equations on Graphs: For a pair of simultaneous equations that produce a quadratic equation in the form ax^2 + box + c = 0:
What is the discriminant for no real solutions? - Correct Answers b^2 + 4ac = 0
Chapter 3.4 - Linear Inequalities: The solution of an inequality is... - Correct Answers ...the set of all real numbers x that make the inequality true
Chapter 3.4 - Linear Inequalities: You may sometimes need to find the set of values for which two inequalities are true together. Number lines can be useful to find your solution

Chapter 3.7 - Regions: If y(>/=)f(x) or y(</=)f(x), then the curve y=f(x) is... - Correct Answers included in the region and is represented by a solid line
Chapter 4.1 - Cubic Graphs: A cubic function has the form... - Correct Answers ax^3 + bx^2 + cx + d
With a, b, c and d are real numbers and a is non-zero
Chapter 4.1 - Cubic Graphs: What is the general shape of a cubic graph? - Correct Answers
Chapter 4.1 - Cubic Graphs: If p is a root of the function f(x), then the graph of y = f(x)... - Correct Answers touches or crosses the x-axis at the point (p,0)
Chapter 4.2 - Quartic Graphs: A quartic function has the form... - Correct Answers ax^4 + bx^3 + cx^2 + dx + e
Where a, b, c, d, and we are real numbers and a is non-zero
Chapter 4.2 - Quartic Graphs: What is the general shape of a quartic graph? - Correct Answers
Chapter 4.3 - Reciprocal Graphs: You can sketch graphs of reciprocal functions such as y = 1/y, y = 1/x^2, and y = -2/x by considering asymptotes.
The graphs of y = k/x and y = k/x^2 where k is a real constant, have asymptotes at... - Correct Answers x = 0 and y = 0
Chapter 4.3 - Reciprocal Graphs: What do the asymptote graphs look like? - Correct Answers
Chapter 4.4 - Points of intersection: The x-coordinates at the points of intersection of the curves with equations y = f(x) and y = g(x) are the solution to the equation... - Correct Answers f(x) = g(x)
Chapter 4.5 - Translating Graphs: - Correct Answers

Math Revision: Index Laws, Surds, Quadratic Equations, Completing Square, Functions, Simul, Exams of Mathematics

Related documents

Partial preview of the text

Download Math Revision: Index Laws, Surds, Quadratic Equations, Completing Square, Functions, Simul and more Exams Mathematics in PDF only on Docsity!

Excel AS and A Level Mathematics

(PURE) Year 1 - All Chapters Revision

Questions and answers