Grade 9 Maths English

NATIONAL ASSESSMENT GEC 2024 GRADE 9 PILOT STUDY IN MATHEMATICS

General Test Information

  • Subject: Mathematics
  • Paper: 1
  • Marks: 75
  • Duration: 2 hours (Excluding 15 minutes reading time)
  • Pages: 23 (Excluding cover page)

Instructions for the Learner

  1. Reading Time: You will receive 15 minutes reading time before beginning the test.
  2. Instructions: Read all instructions and questions carefully.
  3. Answer Requirement: Answer all the questions.
  4. Answer Booklet: Use the answer booklet provided.
  5. Section A: Perform calculations before selecting the correct option.
  6. Section B: Show all necessary calculations.
  7. Calculator Use: Non-programmable scientific calculators are allowed unless stated otherwise.
  8. Diagrams: Diagrams are not necessarily drawn to scale; all lines should be considered straight unless indicated.
  9. Page Turning: Do not turn the page until instructed to do so.

SECTION A

Multiple Choice Questions

  1. Undefined Number: Which number is undefined?

    • A: 0 8
    • B: √8
    • C: βˆšβˆ’8 (correct answer)
    • D: 8 0 (1 mark)

  2. Highest Common Factor (HCF): Given numbers 125, 200, and 510. What is the HCF?

    • A: 10
    • B: 5 (correct answer)
    • C: 17
    • D: 2 (1 mark)

  3. Lowest Common Multiple (LCM): What is the LCM of 75, 450, and 1 800?

    • A: 1 800 (correct answer)
    • B: 30
    • C: 3 600
    • D: 75 (1 mark)

  4. Average Speed Relationship: Given time: 12, 9, 8, 6 and average speed: 60, 80, 90, 120. What is the relationship of average speed to time?

    • A: Rate
    • B: Ratio
    • C: Indirect proportion
    • D: Direct proportion (correct answer) (1 mark)

  5. Running Time Calculation: Thuto runs 6 km in 24 minutes. How long will it take him to run 10 km at a constant speed?

    • A: 1 4 hour
    • B: 2 5 hour
    • C: 2 3 hour
    • D: 5 2 hour (correct answer) (1 mark)

  6. Compound Interest Rate: Dibolelo bought shares for R5 300 and sold them for R11 291.45 after 17 years. What was the compound interest rate per annum?

    • A: 4.5 %
    • B: 4.4 % (correct answer)
    • C: 4.3 %
    • D: 4.1 % (1 mark)

  7. Commutative Property: Which expression demonstrates the commutative property?

    • A: (βˆ’π‘Ž + 𝑒) + (𝑏 βˆ’ 𝑔)
    • B: (βˆ’π‘Ž βˆ’ 𝑔) Γ— (𝑏 Γ— 𝑒)
    • C: (βˆ’π‘Ž Γ— 𝑒)(𝑏 Γ— βˆ’π‘”) (correct answer)
    • D: (βˆ’π‘Ž + 𝑏)(𝑒 βˆ’ 𝑔) (1 mark)

  8. Additive and Multiplicative Inverse: What are the additive inverse and multiplicative inverse of $ rac{1}{5}$?

    • A: βˆ’$ rac{1}{5}$ and βˆ’5
    • B: βˆ’$ rac{1}{5}$ and 5 (correct answer)
    • C: $ rac{1}{5}$ and βˆ’5
    • D: $ rac{1}{5}$ and 5 (1 mark)

  9. Simplification Problem: Simplify: 6 βˆ’ (3 βˆ’ 5) + 9 βˆ’ (βˆ’15) Γ· 3

    • A: 22
    • B: 12
    • C: 16
    • D: 20 (correct answer) (1 mark)

  10. Evaluating Expression: Evaluate: $5(3)(4) βˆ’ 5[3 βˆ’ 4(3)] βˆ’3 βˆ’ 2$. What is the value of the expression?

    • A: βˆ’21
    • B: 3 (correct answer)
    • C: βˆ’3
    • D: 27 (1 mark)

  11. Simplification: Evaluate: $ rac{ ext{√}125}{3} - 32 + 0 + 1 - 4 + ext{√}121 - rac{ ext{√}64}{3}$

    • A: 1
    • B: $ rac{5}{3}$ (correct answer)
    • C: βˆ’$ rac{4}{3}$
    • D: βˆ’1 (1 mark)

  12. Expression Simplification: Simplify: $ ext{(} ext{√}27 rac{3}{2} + ext{√}50 rac{2}{42} βˆ’ ext{√}8 rac{3}{ ext{√}49} ext{)}^2$.

    • A: 16
    • B: 4
    • C: 1
    • D: 49 (correct answer) (1 mark)

  13. Exponent Simplification: Simplify: $3𝑛^3 Γ— 2𝑛^2$.

    • A: 6𝑛^5 (correct answer)
    • B: 5𝑛^5
    • C: 6𝑛^6
    • D: 5𝑛^6 (1 mark)

  14. Exploring Powers: Simplify: $(βˆ’2π‘₯^2𝑦)^3$.

    • A: $8π‘₯^6𝑦^3$
    • B: βˆ’$8π‘₯^6𝑦^3$ (correct answer)
    • C: βˆ’$8π‘₯^5𝑦^3$
    • D: $8π‘₯^5𝑦^3$ (1 mark)

  15. Exponent Evaluation: Evaluate: $2^{-2} Γ— 6^3 Γ— 3^{-2}$.

    • A: 6
    • B: $ rac{1}{36}$ (correct answer)
    • C: $ rac{1}{11}$
    • D: 5 (1 mark)

  16. Simplification with Variables: Simplify: $βˆ’3 ext{(π‘₯ βˆ’ } rac{1}{2} ext{𝑦}) βˆ’ 3 Γ— (π‘₯𝑦)^{βˆ’5}$.

    • A: $βˆ’ rac{1}{9}π‘₯^8𝑦^5$
    • B: $ rac{1}{9}π‘₯^8𝑦^5$ (correct answer)
    • C: $βˆ’3π‘₯^2𝑦^{11}$
    • D: $βˆ’3π‘₯^{βˆ’2}𝑦^{βˆ’11}$ (1 mark)

  17. Complex Function Simplification: Simplify: $ ext{(𝑦}^2 + rac{1}{𝑦} βˆ’ 2𝑦^2 imes 𝑦^2) βˆ’ 2$.

    • A: 4𝑦^4
    • B: 𝑦^{44}
    • C: βˆ’4𝑦^4 (correct answer)
    • D: βˆ’π‘¦^{44} (1 mark)

  18. Algebraic Expression Handling: Simplify: $ ext{√}4π‘₯^6𝑦^{βˆ’2} Γ— (π‘₯^2)^{βˆ’2} (2π‘₯)^{0} Γ— 𝑦^{βˆ’3}$.

    • A: $π‘₯𝑦^2/2$
    • B: $𝑦^2/2π‘₯$
    • C: $2π‘₯^{-1}𝑦^2$
    • D: $2𝑦^2π‘₯$ (correct answer) (1 mark)

  19. Identifying Patterns: Given sequence: $ rac{1}{2}; rac{3}{2}; rac{5}{2}; rac{7}{2}; ext{…}$. Which statement best describes the rule of the pattern?

    • A: Add 2 to the previous term to get the next term.
    • B: Add 1 to the previous term to get the next term.
    • C: Numerators are odd numbers. (correct answer)
    • D: Denominators are equal to 2.

  20. Sequence Prediction: Given sequence: 0; 1; 1; 2; 3; 5;… what are the next two terms?

    • A: 8; 13
    • B: 7; 9
    • C: 6; 8
    • D: 7; 13 (correct answer) (1 mark)

  21. Identifying Patterns in Geometry: Which pattern represents pattern 4?

    • A: Option A
    • B: Option B
    • C: Option C
    • D: Option D (correct answer) (1 mark)

  22. Area Calculation: Jay makes a pattern with squares. What will the area of the 9th square be?

    • A: 324 cmΒ² (correct answer)
    • B: 256 cmΒ²
    • C: 81 cmΒ²
    • D: 18 cmΒ²

  23. Identifying Like Terms: Which of the following are like terms?

    • A: $2π‘π‘žπ‘Ÿ^2$ and $4𝑝^2π‘žπ‘Ÿ$
    • B: $βˆ’7π‘π‘ž^2$ and $βˆ’7π‘π‘Ÿ^2$
    • C: $5π‘π‘ž^2π‘Ÿ$ and $2π‘π‘žπ‘Ÿ^2$ (correct answer)
    • D: $βˆ’3π‘π‘ž^2π‘Ÿ$ and $5π‘π‘ž^2π‘Ÿ$ (1 mark)

  24. Finding Exponents: Given expression $βˆ’2π‘₯^3 + 3π‘₯^2 βˆ’ π‘₯ + 8$, what is the exponent of the term with the smallest coefficient?

    • A: 0
    • B: 1
    • C: 2
    • D: 3 (correct answer) (1 mark)

  25. Term Counting: How many terms are in the expression $βˆ’5π‘₯𝑦 Γ— π‘₯^5 βˆ’ 𝑦^2 3 + 5(π‘₯)$?

    • A: 6
    • B: 5
    • C: 4
    • D: 3 (correct answer) (1 mark)

  26. Simplification Challenge: Simplify: $βˆ’3𝑦(2𝑦^2 βˆ’ 4𝑦) βˆ’ 1$.

    • A: $βˆ’6𝑦^3 + 12𝑦^2 βˆ’ 1$ (correct answer)
    • B: $6𝑦^3 βˆ’ 12𝑦^2 βˆ’ 1$
    • C: $βˆ’6𝑦^3 + 12𝑦^2 + 3𝑦$
    • D: $6𝑦^3 βˆ’ 12𝑦^2 βˆ’ 3𝑦$ (1 mark)

  27. Multiple Expression Evaluation: Simplify: $15𝑦^3 βˆ’ 3𝑦(βˆ’π‘¦ + 2) + 6𝑦^2 3𝑦$.

    • A: $5𝑦^2 + 𝑦 βˆ’ 2$
    • B: $3𝑦^3 + 5𝑦^2 βˆ’ 2$
    • C: $11𝑦^2 + 𝑦 βˆ’ 2$ (correct answer)
    • D: $5𝑦^2 + 3𝑦 βˆ’ 2$ (1 mark)

  28. Radical Expression: Simplify: $ ext{√}(𝑦^8 + 9 imes rac{16}{𝑦^8})$.

    • A: $ rac{5𝑦^8}{4}$
    • B: $ rac{7𝑦^4}{4}$
    • C: $ rac{5𝑦^4}{4}$ (correct answer)
    • D: $ rac{7𝑦^8}{4}$. (1 mark)

  29. Product Evaluation: Given $(4π‘₯ - rac{1}{2})^2$, what is the product?

    • A: $16π‘₯^2 - rac{1}{4}$
    • B: $16π‘₯^2 - 4π‘₯ + rac{1}{4}$ (correct answer)
    • C: $16π‘₯^2 + rac{1}{4}$
    • D: $16π‘₯^2 - 4π‘₯ - rac{1}{4}$ (1 mark)

  30. Numerical Evaluation: For expression $9𝑝^2 βˆ’ 8π‘žπ‘Ÿ$, what is the numerical value if $𝑝 = βˆ’1$, $π‘ž = 0.125$, and $π‘Ÿ = rac{1}{2}$?

    • A: 4
    • B: 7 (correct answer)
    • C: 16
    • D: 20 (1 mark)

  31. Equation Factoring: Factorise: $25π‘Ž^2 βˆ’ 16𝑏^2$.

    • A: $(5π‘Ž βˆ’ 4𝑏)(5π‘Ž + 4𝑏)$ (correct answer)
    • B: $(5π‘Ž + 16𝑏)(5π‘Ž βˆ’ 16𝑏)$
    • C: $(25π‘Ž βˆ’ 4𝑏)(25π‘Ž + 4𝑏)$
    • D: $(25π‘Ž + 16𝑏)(25π‘Ž βˆ’ 16𝑏)$ (1 mark)

  32. Quadratic Factoring: Factorise: $𝑦^2 βˆ’ 11𝑦 + 28$.

    • A: $(𝑦 βˆ’ 4)(𝑦 + 7)$
    • B: $(𝑦 + 7)(𝑦 + 4)$
    • C: $(𝑦 βˆ’ 7)(𝑦 βˆ’ 4)$ (correct answer)
    • D: $(𝑦 + 4)(𝑦 βˆ’ 7)$ (1 mark)

  33. Expression Factoring: Factorise: $9𝑝^2 + 27𝑝 βˆ’ 90$.

    • A: $9(𝑝 + 5)(𝑝 + 2)$ (correct answer)
    • B: $9(𝑝 βˆ’ 2)(𝑝 + 5)$
    • C: $9(𝑝 βˆ’ 5)(𝑝 + 2)$
    • D: $9(𝑝 βˆ’ 2)(𝑝 βˆ’ 5)$ (1 mark)

  34. Polynomial Simplification: Simplify: $2π‘Ž^2 βˆ’ 10π‘Ž + 12π‘Ž(π‘Ž + 2) βˆ’ 3(π‘Ž + 2)$.

    • A: $2(π‘Ž + 3)π‘Ž βˆ’ 3$
    • B: $2(π‘Ž βˆ’ 3)π‘Ž + 3$
    • C: $2(π‘Ž βˆ’ 2)π‘Ž + 2$
    • D: $2(π‘Ž + 2)π‘Ž βˆ’ 2$ (correct answer) (1 mark)

  35. Fraction Simplification: Simplify: $48π‘Ÿ βˆ’ 3π‘Ÿ(𝑝 + π‘ž)^{2} 2 12π‘Ÿ + 3π‘π‘Ÿ + 3π‘žπ‘Ÿ$.

    • A: $4 βˆ’ 𝑝 + π‘ž$
    • B: $4 + 𝑝 βˆ’ π‘ž$
    • C: $4 βˆ’ 𝑝 βˆ’ π‘ž$ (correct answer)
    • D: $4 + 𝑝 + π‘ž$ (1 mark)

  36. Solving Equations: Given $βˆ’2 = βˆ’4π‘š$, what is the value of $π‘š$?

    • A: βˆ’12
    • B: 2 (correct answer)
    • C: βˆ’2
    • D: 12 (1 mark)

  37. Exponential Equation: $π‘Ž^7 = βˆ’2$, what is the value of $a$?

    • A: 14
    • B: βˆ’14 (correct answer)
    • C: βˆ’9
    • D: 9 (1 mark)

  38. Quadratic Solutions: Solve $(π‘₯ βˆ’ 4)^2 = 0$.

    • A: $π‘₯ = 4$ (correct answer)
    • B: $π‘₯ = βˆ’4$
    • C: $π‘₯ = 2$ or $π‘₯ = βˆ’2$
    • D: $π‘₯ = 0$ or $π‘₯ = 4$ (1 mark)

  39. Factoring Products: Solve $(π‘₯ βˆ’ 3)(1 - π‘₯) = 0$. What are the values of $π‘₯$?

    • A: $π‘₯ = 3$ or $π‘₯ = βˆ’1 (correct answer)
    • B: $π‘₯ = βˆ’3$ or $π‘₯ = 1$
    • C: $π‘₯ = 3$ or $π‘₯ = 1$
    • D: $π‘₯ = βˆ’3$ or $π‘₯ = βˆ’1$ (1 mark)

  40. Profit Calculation: Marius buys cell phones for $π‘₯$ rands and sells them, determining the selling price $𝑦$ by doubling the price he paid and then subtracting 3 rand. Which equation represents this scenario?

    • A: $𝑦 = (π‘₯ βˆ’ 3)^{2}$
    • B: $𝑦 = 2(π‘₯ βˆ’ 3)$
    • C: $𝑦 = π‘₯^{2} βˆ’ 3$
    • D: $𝑦 = 2π‘₯ βˆ’ 3$ (correct answer) (1 mark)

  41. Perimeter Problem: Given perimeter of a square as $P = 4(π‘₯ βˆ’ 1)$ and $P = 16$ cm, find the value of $π‘₯$.

    • A: 5
    • B: 21
    • C: 3 (correct answer)
    • D: 13 (1 mark)

  42. Equation Mapping: For $𝑦 = π‘₯^2 - 1$, given values: $π‘₯ = -2$, -1, 0, 1, 2, what ordered pair does NOT satisfy?

    • A: (βˆ’2; 3) (correct answer)
    • B: (0; βˆ’1)
    • C: (1; 1)
    • D: (2; 3) (1 mark)

  43. Quadratic Solutions Reference: Given equation $π‘₯^2 βˆ’ 3π‘₯ βˆ’ 18 = 0$, find values of $π‘₯$.

    • A: $π‘₯ = βˆ’6$ or $π‘₯ = βˆ’3$
    • B: $π‘₯ = 6$ or $π‘₯ = βˆ’3$ (correct answer)
    • C: $π‘₯ = βˆ’6$ or $π‘₯ = 3$
    • D: $π‘₯ = 6$ or $π‘₯ = 3$ (1 mark)

  44. Basic Algebra: Given the equation $2π‘š + 0.5 = 80$, what is the value of $π‘š$?

    • A: 1
    • B: βˆ’1
    • C: 2 (correct answer)
    • D: βˆ’3 (1 mark)

  45. Finding Roots: From $6π‘₯^3 βˆ’ π‘₯ = 4π‘₯^2$, find values of $π‘₯$.

    • A: 0 or $ rac{1}{4}$ (correct answer)
    • B: 3 or $ rac{1}{4}$
    • C: 0 or βˆ’$ rac{1}{4}$
    • D: 3 or βˆ’$ rac{1}{4}$ (1 mark)

  46. Consequent Number Product: The product of two consecutive even numbers is 120; find the numbers.

    • A: βˆ’30 and 4
    • B: 30 and 4 or βˆ’4 and βˆ’30
    • C: 10 and 12 or βˆ’10 and βˆ’12 (correct answer)
    • D: βˆ’10 and 12 (1 mark)

  47. Input/Output Mapping: Given Input $βˆ’1, 2, 5, 8$, Output is $b: βˆ’1, 2, 5$. What is the value of $b$?

    • A: βˆ’2
    • B: βˆ’4
    • C: 2
    • D: 4 (correct answer) (1 mark)

  48. Linear Function Evaluation: Given $𝑦 = -2π‘₯ βˆ’ 3$, output if input is $βˆ’5$?

    • A: βˆ’3
    • B: βˆ’5
    • C: 7 (correct answer)
    • D: 1 (1 mark)

  49. Flow Diagram Analysis: Identify the rule used in the flow diagram:

    • A: Multiply by βˆ’2
    • B: Multiply by βˆ’1
    • C: Multiply by βˆ’6
    • D: Multiply by βˆ’3 (correct answer) (1 mark)

  50. Graph Representation: Identify graph representing relationship between input $π‘₯$ and output $𝑦$ for given values.

    • A: Option A
    • B: Option B
    • C: Option C
    • D: Option D (correct answer) (1 mark)

  51. Value Definition: Input of $π‘₯$ gives output of $𝑦$. Determine value of $π‘Ž$.