Grade 10 Mathematics Common Assessment Task March 2025 Notes

KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS COMMON ASSESSMENT TASK MARCH 2025

This document outlines the structure and content of a Grade 10 Mathematics Common Assessment Task, including the question types, instructions, and marking scheme, necessary for understanding and preparation.

General Information

• Marks: 75

• Time: 1½ hours

• Pages: This question paper consists of 5 pages in total.

Instructions and Information

1. Read the following instructions carefully before answering the questions.

2. This question paper consists of 3 questions.

3. Answer ALL the questions.

4. Number the answers correctly according to the numbering system used in this question paper.

5. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers.

6. Answers only will NOT necessarily be awarded full marks.

7. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.

8. If necessary, round off answers correct to TWO decimal places, unless stated otherwise.

9. Write neatly and legibly.

Question 1

1.1 Mathematical Concepts

• 1.1.1 If $x ext{ is in } ext{(0, 7, 9)}$, choose the value of $x$ from the given set that will make the expression $ext{√}(x-5)$ be:

  • Rational (1 mark)

  • Irrational (1 mark)

  • Non-real (1 mark)

1.2 Estimation of Square Roots

• Between which two consecutive integers does $ext{√}170$ lie? Show all working details without the use of a calculator. (2 marks)

1.3 Simplification Tasks

• 1.3.1 Simplify the following fully:

  • A) $(x-2y)(x^2+2xy+4y^2)$ (2 marks)

  • 1.3.2 Simplify $(5-4x)^2$ (2 marks)

  • 1.3.3 Simplify $rac{x^2-9}{x-3} imes(x+3)$ (5 marks)

  • 1.3.4 Simplify $rac{102x+34}{51-x}$ (4 marks)

1.4 Factorisation Tasks

• 1.4.1 Factorise the following expressions fully:

  • 2x²-18 (2 marks)

  • 1.4.2 Factorise 8 + 125a³ (3 marks)

  • 1.4.3 Factorise x³ - 2x² + 5x - 10 (3 marks)

1.5 Exponential Evaluation

• If $2^x = 3$, evaluate:

  • 1.5.1 $2$ (1 mark)

  • 1.5.2 $8x$ (2 marks)

  • 1.5.3 $16$ (3 marks)

Question 2

2.1 Solving Equations

• Solve for $x$ in the following equations:

  • 2.1.1 $3x(x-8)=0$ (2 marks)

  • 2.1.2 $7x^2 - 5x - 2 = 0$ (3 marks)

  • 2.1.3 $35x-4-729=0$ (3 marks)

  • 2.1.4 $2x^2 = 128$ (4 marks)

  • 2.1.5 $2^{(x+1)} + 21 = 20$ (5 marks)

2.2 Algebraic Identity Assessment

• If $(a^2+2a)^2 = (a^2-2a)^{10} + b$, calculate the value of b. (4 marks)

2.3 Inequality and Representation

• Given: -9 < -2x + 3 < 5

  • 2.3.1 Solve for $x$. (2 marks)

  • 2.3.2 Represent the solution of 2.3.1 on a number line. (2 marks)

2.4 Simultaneous Equations

• Solve for $x$ and $y$ simultaneously:

  • 2x - y = 17 (4 marks)

  • 4y + 3x = 9 (4 marks)

Question 3

3.1 Right-Angled Triangle Properties

• In the diagram below, triangle APQR is a right-angled triangle, where angle Q = 90°, P = 0, PQ = 5 units, and PR = 13 units.

  • 3.1.1 Determine the numerical value of:

  • (a) $QR$ (2 marks)

  • (b) $ext{cos}$ (1 mark)

  • (c) $ext{cot}$ (1 mark)

  • (d) $ext{sec} QRP$ (1 mark)

  • 3.1.2 Write down the trigonometric ratio that is equal to $rac{QR}{PR}$. (1 mark)

3.2 Evaluations

• If $A = 34^ ext{°}$ and $B = 53^ ext{°}$, use your calculator to evaluate the following (correct to TWO decimal places):

  • 3.2.1 $ext{cos}(B-A)$ (2 marks)

  • 3.2.2 $ext{sin}^2 B$ (2 marks)

3.3 Non-Calculator Determination

• Without using a calculator, determine the value of:

  • $ext{cosec} 45^ ext{°} imes ext{sin} 60^ ext{°}$ (5 marks)

  • $ext{sin} 45^ ext{°} imes ext{cos} 30^ ext{°}$ (5 marks)

Marking Guideline

• The marking guideline for each question breaks down the allocation of marks based on the accuracy and completeness of the solutions provided. Full marks are awarded for correct methodologies and answers, as shown in various examples within the marking guideline for each respective question.

Welcome to today's episode where we explore the Grade 10 Mathematics Common Assessment Task for the Kwazulu-Natal Province, Republic of South Africa, designed for March 2025. This assessment is structured to test various mathematical concepts and skills essential for students.

General Information

• Marks: 75

• Time: 1½ hours

• Pages: This question paper consists of 5 pages in total.

Instructions and Information

1. Read the following instructions carefully before answering the questions.

2. This question paper consists of 3 questions.

3. Answer ALL the questions.

4. Number the answers correctly according to the numbering system used in this question paper.

5. Clearly show ALL calculations, diagrams, graphs, etc., which you have used in determining your answers.

6. Answers only will NOT necessarily be awarded full marks.

7. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.

8. If necessary, round off answers correct to TWO decimal places, unless stated otherwise.

9. Write neatly and legibly.

Question Breakdown

• Question 1: Covers Mathematical Concepts, Estimation of Square Roots, Simplification Tasks, Factorisation Tasks, and Exponential Evaluation. Examples include simplifying expressions and estimating square roots.

• Question 2: Focuses on Solving Equations, Algebraic Identity Assessment, Inequality and Representation, and Simultaneous Equations. It touches on solving quadratic equations and evaluating algebraic expressions.

• Question 3: Explores Right-Angled Triangle Properties with trigonometric evaluations and non-calculator tasks for students.

Marking Guideline

The marking guideline for each question outlines the allocation of marks based on the accuracy and completeness of the solutions provided. Full marks are awarded for correct methodologies and answers, emphasizing understanding and problem-solving skills.

Thank you for tuning in! Remember to review these concepts regularly and practice as much as you can to excel in your mathematics understanding. Until next time!