Podcast Beta
Questions and Answers
To simplify an algebraic fraction, we need to find the ______ factor of the numerator and the denominator.
highest common
When expanding brackets, we need to multiply each term in the first bracket by each term in the ______ bracket.
second
A quadratic sequence has a general term of the form 𝑎𝑛² + 𝑏𝑛 + 𝑐, where 𝑎, 𝑏, and 𝑐 are ______.
constants
To solve a quadratic equation, we can use the ______ formula: 𝑥 = (-𝑏 ± √(𝑏² - 4𝑎𝑐)) / 2𝑎.
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In a right-angled triangle, Pythagoras' Theorem states that the square of the ______ is equal to the sum of the squares of the other two sides.
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If 𝑦 is directly proportional to 𝑥 and 𝑦 = 8 when 𝑥 = 2, find 𝑦 when 𝑥 = ______
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The reciprocal of 4 is ______
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A triangle with sides 9 cm, 12 cm, and 15 cm is a ______-angled triangle according to Pythagoras' Theorem
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The equation of a line parallel to 𝑦 = 3𝑥 + 1 passing through the point (2, 4) is ______
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The sum of two consecutive even numbers is always ______
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Study Notes
Algebraic Fractions
- Simplify fractions by cancelling out common factors, such as 3𝑥² - 12 / 6𝑥² = 1/2
Simplifying Algebraic Expressions
- Combine like terms, such as 4𝑥 + 2𝑥² - 3𝑥 + 7 = 2𝑥² + 𝑥 + 7
Expanding Brackets
- Expand and simplify expressions, such as (2𝑥 + 3)(𝑥 - 4) = 2𝑥² - 5𝑥 - 12
Transformations
- Describe transformations that map one triangle to another, such as a enlargement by a scale factor of 2
Quadratic nth Term
- Find the nth term of a quadratic sequence, such as 2, 6, 12, 20, … = 𝑛² + 𝑛
Solving Quadratics
- Solve quadratic equations, such as 𝑥² - 5𝑥 + 6 = 0, using factorization or the quadratic formula
Index Laws
- Simplify expressions using the index laws, such as (2³ ⋅ 2⁴) / 2⁵ = 2²
Bearings
- Calculate the distance traveled east, such as 100 km on a bearing of 070°, using trigonometry
Compound Percentages
- Calculate the value of an investment after multiple years, such as 5% per year for 3 years, using the formula 𝐴 = 𝑃(1 + 𝑟/100)ⁿ
Pythagoras' Theorem
- Find the length of the hypotenuse of a right-angled triangle, such as a triangle with legs of 5 cm and 12 cm
Angles in Polygons
- Calculate the sum of the interior angles of a polygon, such as a hexagon with (6 - 2) × 180° = 720°
Finding the Gradient
- Find the gradient of a line, such as a line passing through the points (2, 3) and (6, 11), using the formula 𝑚 = (𝑦₂ - 𝑦₁) / (𝑥₂ - 𝑥₁)
Rearranging Formulae
- Rearrange formulas to solve for a specific variable, such as 𝐴 = 3𝐵 + 2𝐶, to solve for 𝐶
Probability Tree Diagrams
- Draw a probability tree diagram and find the probability of an event, such as drawing two red balls from a bag with 3 red and 2 blue balls
Bounds
- Find the upper and lower bounds of a number, such as 5.62 rounded to two decimal places, with bounds 5.615 and 5.625
Forming and Solving Equations
- Form an equation and solve for a variable, such as the sum of 𝑥 and twice 𝑥 is equal to 15, to solve for 𝑥
Exchange Rates
- Calculate the exchange rate, such as £1 equivalent to $1.25, to find the value of £50 in dollars
Distance-Time Graphs
- Interpret a distance-time graph to find the speed of an object, such as an object traveling 150 meters in 30 seconds, with a speed of 5 meters per second
Surds
- Simplify surds, such as 50⁵⁰, to its simplest form
Ratio
- Calculate the ratio of boys to girls in a school, such as 3:5, to find the number of boys given the number of girls
Direct Proportion
- Find the value of 𝑦 when 𝑥 is directly proportional to 𝑥, such as 𝑦 = 8 when 𝑥 = 2, to find 𝑦 when 𝑥 = 5
Calculator Skills
- Use a calculator to evaluate expressions, such as 2³ × 5 - 49, to get the correct answer
Area of 2D Shapes
- Calculate the area of a rectangle, such as a rectangle with length 8 cm and width 5 cm, with an area of 40 cm²
Reciprocals
- Find the reciprocal of a number, such as 4, to get 1/4
Non-Calculator Section Estimation and Substitution
- Estimate the value of a number, such as 50⁵⁰, using approximations or substitution
Scatter Graphs
- Describe the correlation shown in a scatter graph, such as a positive correlation with an upward-sloping line
Conditional Probability
- Find the conditional probability of an event, such as 𝑃(𝐵|𝐴), given the probability of two events 𝐴 and 𝐵
Reverse Percentages
- Calculate the original price of an item, such as an item with a 20% discount and a price of £80, to find the original price
Mean
- Calculate the mean of a set of numbers, such as 4, 8, 6, 10, and 2, to get the average value
Multiplying Decimals
- Multiply decimals, such as 3.6 × 2.4, to get the correct answer
Standard Form
- Write a number in standard form, such as 4500, to get 4.5 × 10³
Inverse Proportion
- Find the value of 𝑦 when 𝑦 is inversely proportional to 𝑥, such as 𝑦 = 10 when 𝑥 = 5, to find 𝑦 when 𝑥 = 2
Parallel Line Equations
- Write the equation of a line parallel to a given line, such as 𝑦 = 3𝑥 + 1, passing through a given point, such as (2, 4)
Pythagoras' Theorem
- Confirm whether a triangle is a right-angled triangle, such as a triangle with sides 9 cm, 12 cm, and 15 cm, using Pythagoras' theorem
Ratio Problem Solving
- Divide a quantity in a given ratio, such as £180 in the ratio 2:3:4, to find the share of each part
Algebraic Proof
- Prove algebraic identities, such as the sum of two consecutive even numbers is divisible by 4
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Description
A quiz covering various algebra topics such as simplifying algebraic fractions and expressions, expanding brackets, transformations, and quadratic sequences.
