Mwala_Learn Pre-NECTA

Objectives: Mwala_Learn Pre-NECTA

Mwala_Learn Pre-NECTA Exams Series 1

Mwala_Learn Pre-NECTA Exams

Series 1 - Form 1 to 4

SECTION A (60 Marks)

Answer all questions in this section.

1.(a) Numbers (Form I Syllabus)

Simplify: 2^3 × 2^5 ÷ 2^4

2.(a) Exponents and Radicals (Form II Syllabus)

Solve: √(49) + ³√(27)

3.(a) Sets (Form II Syllabus)

Let A = {1,2,3,4} and B = {3,4,5}. Find A ∪ B and A ∩ B.

4.(a) Vectors (Form IV Syllabus)

Draw the vector A = 3i + 4j using Canvas:

5.(a) Areas and Perimeters (Form I & IV Syllabuses)

Calculate the area of a rectangle with length 10 cm and width 5 cm.

6.(a) Units (Form I Syllabus)

Convert 5 km into meters.

7.(a) Ratio, Profit and Loss (Form I Syllabus)

A shopkeeper buys a pen at 100 TZS and sells it at 120 TZS. Calculate the profit percentage.

8. Sequence and Series (Form III Syllabus)

Find the sum of the first 10 terms of the arithmetic series: 2, 5, 8, ...

9.(a) Trigonometry (Form II & IV Syllabuses)

Find sin 30°, cos 60°, and tan 45°.

10.(a) Algebra (Form I & II Syllabus)

Solve for x: 2x + 5 = 15

11.(a) Statistics (Form II & III Syllabuses)

Find the mean of the numbers: 4, 8, 6, 10, 12

12.(a) Three Dimensional Figures (Form IV Syllabus)

Draw a cuboid with length 100px, width 60px, height 40px using Canvas:

SECTION B (40 Marks)

Answer all questions in this section.

13.(a) Matrices and Transformations (Form IV Syllabus)

Let A = [[1,2],[3,4]] and B = [[0,1],[1,0]]. Find A + B.

14.(a) Relations (Form III Syllabus)

Define a relation R on set {1,2,3} such that R = {(1,2),(2,3)}. Is R reflexive?

14.(c) Linear Programming (Form IV Syllabus)

Maximize Z = 3x + 4y subject to x + y ≤ 5, x ≥ 0, y ≥ 0.

Mwala_Learn Pre-NECTA Exams Series 1 - Answers

Mwala_Learn Pre-NECTA Exams

Series 1 - Form 1 to 4 Answers

SECTION A (60 Marks) - Answers

1.(a) Numbers

Question: Simplify 2^3 × 2^5 ÷ 2^4

Solution:

  1. Use the law of exponents: a^m × a^n = a^(m+n) and a^m ÷ a^n = a^(m-n)
  2. 2^3 × 2^5 ÷ 2^4 = 2^(3+5-4) = 2^4
  3. 2^4 = 16

Answer: 16

2.(a) Exponents and Radicals

Question: Solve √(49) + ³√(27)

Solution:

  1. √(49) = 7
  2. ³√(27) = 3
  3. Add the results: 7 + 3 = 10

Answer: 10

3.(a) Sets

Question: Let A = {1,2,3,4} and B = {3,4,5}. Find A ∪ B and A ∩ B.

Solution:

  1. Union (A ∪ B) = all elements in A or B: {1,2,3,4,5}
  2. Intersection (A ∩ B) = elements in both A and B: {3,4}

Answer: A ∪ B = {1,2,3,4,5}, A ∩ B = {3,4}

4.(a) Vectors

Question: Draw the vector A = 3i + 4j

Solution: Scale 1 unit = 20px

Vector A is shown in green above

5.(a) Areas and Perimeters

Question: Calculate area of rectangle length 10 cm, width 5 cm

Solution:

  1. Area = length × width
  2. Area = 10 × 5 = 50 cm²

Answer: 50 cm²

6.(a) Units

Question: Convert 5 km into meters

Solution:

  1. 1 km = 1000 m
  2. 5 km = 5 × 1000 = 5000 m

Answer: 5000 meters

7.(a) Ratio, Profit and Loss

Question: Buy at 100 TZS, sell at 120 TZS. Profit %?

Solution:

  1. Profit = Selling price - Cost price = 120 - 100 = 20 TZS
  2. Profit % = (Profit / Cost price) × 100 = (20/100) × 100 = 20%

Answer: 20%

8. Sequence and Series

Question: Sum of first 10 terms of 2,5,8,...

Solution:

  1. Arithmetic series formula: S_n = n/2 [2a + (n-1)d]
  2. a = 2, d = 3, n = 10
  3. S_10 = 10/2 [2×2 + (10-1)×3] = 5 [4 + 27] = 5 × 31 = 155

Answer: 155

9.(a) Trigonometry

Question: Find sin 30°, cos 60°, tan 45°

Solution:

  1. sin 30° = 1/2
  2. cos 60° = 1/2
  3. tan 45° = 1

Answer: sin30°=1/2, cos60°=1/2, tan45°=1

10.(a) Algebra

Question: Solve 2x + 5 = 15

Solution:

  1. 2x = 15 - 5 = 10
  2. x = 10 / 2 = 5

Answer: x = 5

11.(a) Statistics

Question: Find mean of 4,8,6,10,12

Solution:

  1. Mean = (4 + 8 + 6 + 10 + 12) / 5 = 40 / 5 = 8

Answer: 8

12.(a) Three Dimensional Figures

Question: Draw a cuboid with length 100px, width 60px, height 40px

Cuboid drawn in red and black above

SECTION B (40 Marks) - Answers

13.(a) Matrices and Transformations

Question: A = [[1,2],[3,4]], B=[[0,1],[1,0]]. Find A + B

Solution:

A + B = [[1+0, 2+1], [3+1, 4+0]] = [[1,3],[4,4]]

Answer: [[1,3],[4,4]]

14.(a) Relations

Question: R = {(1,2),(2,3)} on {1,2,3}. Is R reflexive?

Solution: Reflexive requires (1,1),(2,2),(3,3) ∈ R. They are not.

Answer: No, R is not reflexive

14.(c) Linear Programming

Maximize Z = 3x + 4y subject to x+y ≤ 5, x≥0, y≥0

Solution:

  1. Feasible region: (0,0),(5,0),(0,5),(x+y=5)
  2. Evaluate Z:
    • (0,0): Z=0
    • (5,0): Z=15
    • (0,5): Z=20

Answer: Maximum Z = 20 at (0,5)

Reference Book: N/A

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