Year_9_Term_2_Test_-_Revision_List

Week Commencing: 24th February 2025

• Test Information:

  • Duration: 45 minutes

  • Type: Calculator paper

Year 9 Term 2 Test - Revision List

Types of Number and Sequences

• Key Concepts & Links:

  • [Dr Frost Link]

  • Prime Factor Decomposition

  • Highest Common Factor (HCF)

  • Lowest Common Multiple (LCM)

  • Sequences:

    • Nth Term

    • Quadratic Nth Term

Working with Circles

• Key Concepts & Links:

  • [Dr Frost Link]

  • Circles & Parts of Circles

  • Surface Area

  • Volume

  • Basic Angles Facts

  • Circle Theorems

Indices and Roots

• Key Concepts & Links:

  • [Dr Frost Link]

  • Powers and Roots

  • Laws of Indices

  • Negative and Fractional Indices

  • Standard Form:

    • Converting Standard Form

    • Calculations

Gradients and Lines

• Key Concepts & Links:

  • [Dr Frost Link]

  • Drawing Linear Graphs

  • Gradients

  • Equation of a Line: y = mx + c (also with rearranging)

  • Perpendicular Lines

Solving Equations and Inequalities

• Key Concepts & Links:

  • [Dr Frost Link]

  • Solving one-step/two-step equations including brackets

  • Solving Inequalities (including negatives)

  • Rearranging equations

  • Equations and inequalities with unknowns on both sides

Congruence, Similarity and Enlargement

• Key Concepts & Links:

  • [Dr Frost Link]

  • Understanding Positive Scale Factor Enlargement

Additional Revision Activities/Links

Similar Shapes and Congruence

• Key Concepts:

  • Similar Shapes and Area

  • Similar Shapes and Volume

  • Angles in Parallel Lines

  • Constructing Triangles and Congruence Proof

Trigonometry

• Key Concepts & Links:

  • [Dr Frost Link]

  • Bearings

  • Pythagoras' Theorem

  • Trigonometric Ratios:

    • Sine Rule

    • Cosine Rule

    • Area of a Triangle

    • 3D Trigonometry

Revision Links:

• Similar Shapes PDF

• Questions on Similar Shapes: Link

• Answers on Similar Shapes: Link

• Questions on Area and Volume: Link

• Answers on Area and Volume: Link

• Linear Inequalities: Link

• Forming and Solving Equations - Questions: Link

• Forming and Solving Equations - Answers: Link

• Gradients and Lines Interactive: Link

• Enlargements Advanced: Link

• Rearranging Formulae (Basic): Link

• Rearranging Formulae (Intermediate): Link

Mathematical Formulas

Arithmetic Series

• Formula: Sum to n terms, S = [2a + (n-1)d]

• Area of trapezium = (\frac{(a + b)h}{2})

Quadratic Equation

• Solutions of ax² + bx + c = 0 are given by:

  • (-b ± √{b² - 4ac}/2a)

Trigonometry

• In triangle ABC:

  • Sine Rule: (\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C})

  • Cosine Rule: (a² = b² + c² - 2bc\cdot cos A)

  • Area of triangle: (\frac{1}{2}ab \cdot sin C)

Volume and Surface Area

• Volume of cone: (\frac{1}{3} \pi r²h)

• Curved surface area of cone: (\pi r l)

• Volume of prism: Area of cross section x length

• Volume of cylinder: (\pi r²h)

• Curved surface area of cylinder: (2\pi rh)

• Volume of sphere: (\frac{4}{3}\pi r³)

• Surface area of sphere: (4\pi r²)

Study Guide for Key Topics

1. Types of Number and Sequences

• Prime Factor Decomposition: Break down numbers into their prime components.

• Highest Common Factor (HCF): The largest number that divides two or more numbers.

• Lowest Common Multiple (LCM): The smallest multiple common to two or more numbers.

• Sequences: Understand Nth terms and identify quadratic sequences.

2. Working with Circles

• Parts of Circles: Learn terminology (radius, diameter, circumference).

• Surface Area and Volume: Master formulas for cylinders and cones.

• Circle Theorems: Explore fundamental properties of angles and segments in circles.

3. Indices and Roots

• Laws of Indices: Rules for manipulating powers and roots.

• Standard Form: Convert between standard form and decimal; perform calculations.

4. Gradients and Lines

• Graphing: Draw linear graphs and calculate gradients.

• Equations of Lines: Understand the formula y = mx + c and its applications.

5. Solving Equations and Inequalities

• Types of Equations: Solve one-step and two-step equations, including those with brackets.

• Inequalities: Solve and represent inequalities on a number line.

6. Congruence, Similarity, and Enlargement

• Congruence: Identify congruent shapes and their properties.

• Similarity: Learn how area and volume scale with similar shapes.

7. Trigonometry

• Basic Theorems: Understand Pythagoras' Theorem and sine/cosine rules.

• Bearings: Study angles and directions using bearings in navigation.

8. Formulas to Remember

• Arithmetic Series Formula: S = [2a + (n-1)d]

• Quadratic Equation Solutions: (-b ± √{b² - 4ac})/2a

• Volume & Surface Area Formulas: Include cone, cylinder, and sphere formulas.

Additional Revision Activities & Resources

• Utilize provided links for practice questions and interactive activities to reinforce understanding across all topics included.

Detailed Study Guide for Key Topics

1. Types of Number and Sequences

• Prime Factor Decomposition: This process involves breaking down a number into its prime factors, which are the building blocks of all integers. For instance, to decompose 60, you can express it as 2 × 2 × 3 × 5. This helps in simplifying fractions and finding the HCF and LCM.

• Highest Common Factor (HCF): The HCF is the largest factor that two or more numbers share. For example, the HCF of 24 and 36 is 12. The HCF can be found using prime factorization or by listing the factors of each number and identifying the highest one.

• Lowest Common Multiple (LCM): The LCM is the smallest multiple that is shared between two or more numbers. For example, the LCM of 3 and 4 is 12. Calculating the LCM can be achieved through listing the multiples or applying the relation with HCF: LCM(a, b) = (a × b) / HCF(a, b).

• Sequences: In mathematics, a sequence is an ordered list of numbers. The Nth term of a linear sequence can be calculated using the formula a_n = a + (n - 1)d, where a is the first term and d is the common difference. For quadratic sequences, the relationship between the terms often involves square numbers and can be identified by finding patterns in the differences of consecutive terms.

2. Working with Circles

• Parts of Circles: Key terms include:

  • Radius: The distance from the center to any point on the circle.

  • Diameter: Twice the radius, the longest distance across the circle.

  • Circumference: The total distance around the circle, calculated using C = πd (where d is the diameter) or C = 2πr (where r is the radius).

• Surface Area and Volume:

  • Surface Area of a Cylinder: A = 2πr(h + r) where h is height. It includes the areas of the two circular bases and the rectangle that wraps around.

  • Volume of a Cylinder: V = πr²h, which calculates the capacity of the cylinder.

  • For Cones:

    • Surface Area: A = πr(l + r), where l is the slant height.

    • Volume: V = (1/3)πr²h, signifying a third of the volume of a cylinder of the same base and height.

• Circle Theorems: Include important properties such as the angle subtended by an arc at the center being double that subtended at the circumference and the cyclic quadrilateral theorem.

3. Indices and Roots

• Laws of Indices: Include the key rules:

  • a^m × a^n = a^(m+n)

  • a^m / a^n = a^(m-n)

  • (a^m)^n = a^(mn)

  • a^0 = 1 (for a ≠ 0)

• Standard Form: Converting standard form to decimal involves moving the decimal point to the right or left based on the exponent. For example, 3.2 × 10^4 = 32000. This form is particularly useful in handling very large or small numbers and performing calculations efficiently.

4. Gradients and Lines

• Graphing: The gradient (slope) of a line indicates its steepness. It can be calculated as:

  • Gradient (m) = (y2 - y1) / (x2 - x1).

• Equations of Lines: The straight-line equation is y = mx + c, where m denotes the gradient, and c is the y-intercept. Rearranging equations may include converting to the form Ax + By = C to find x-intercepts and plot lines effectively.

5. Solving Equations and Inequalities

• Types of Equations: To solve linear equations, operations such as addition, subtraction, multiplication, or division are employed to isolate the variable. For example, for 2x + 3 = 11, subtract 3 and divide by 2.

• Inequalities: When solving inequalities, if you multiply or divide by a negative number, you must reverse the inequality sign (e.g., if -x > -4, then x < 4). Representing these on a number line helps visualize solution sets.

6. Congruence, Similarity, and Enlargement

• Congruence: Shapes are congruent if they have the same size and shape. Properties include matching corresponding sides and angles. Transformations such as translations, rotations, and reflections preserve congruence.

• Similarity: Similar shapes maintain the same shape but differ in size. Ratios of corresponding sides are equal. For example, if two triangles have corresponding side lengths in the ratio 2:3, their areas will be in the ratio 4:9 respectively due to the area scaling with the square of the length ratio.

7. Trigonometry

• Basic Theorems:

  • Pythagorean Theorem: In a right-angled triangle, a² + b² = c², where c is the hypotenuse. This helps find the lengths of sides.

  • Sine Rule: For triangles, a/sin A = b/sin B = c/sin C helps relate the lengths of sides to their opposite angles.

  • Cosine Rule: a² = b² + c² - 2bc cos A provides a means to calculate one side of a triangle when the other sides and the included angle are known.

  • Area of Triangle: Given by A = (1/2)ab sin C, relating the sides and the included angle.

• Bearings: Used in navigation, bearings are measured in degrees clockwise from north. Understanding how to interpret angles and calculating distances using trigonometric relationships is vital in real-world applications.

8. Formulas to Remember

• Arithmetic Series Formula: S = [2a + (n-1)d], where S is the sum, a is the first term, d is the common difference, and n is the number of terms. This formula can find the total sum of a defined number of sequence terms efficiently.

• Quadratic Equation Solutions: The formula (-b ± √(b² - 4ac)) / 2a facilitates finding the roots of a quadratic equation of the form ax² + bx + c = 0.

• Volume & Surface Area Formulas: Including cone, cylinder, and sphere formulas (as outlined above) are crucial for calculating relevant geometric properties.

Additional Revision Activities & Resources

• Utilize provided links for practice questions and interactive activities to reinforce understanding across all topics included.

Additional Revision Links for Trigonometry and All Topics

1. Trigonometry Revision Links

• Khan Academy - Trigonometry: A comprehensive resource with instructional videos and exercises covering sine, cosine, tangent, and more. Visit Khan Academy Trigonometry

• Math is Fun - Trigonometry: Offers explanations and examples on key trigonometry concepts. Visit Math is Fun - Trigonometry

• Mathway - Trigonometry Problems Solver: A tool to solve trigonometric problems. Visit Mathway

2. General Revision Links for All Topics

• BBC Bitesize - Maths: Engaging lessons and quizzes across various mathematical topics. Visit BBC Bitesize Maths

• Dr Frost Maths: Interactive resources and links that cover a variety of key mathematical concepts, including exam revision. Visit Dr Frost Maths

• IXL Math: Extensive practice problems across all topics with instant feedback. Visit IXL Math