Second Term Examination Mathematics SS 1 Second Term Lesson Notes

SECOND TERM EXAMINATION

Subject: Mathematics
Class: SS1
Time:

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SECTION A: OBJECTIVE QUESTIONS

Instruction: Answer all questions in this section.

1. If V varies directly with T and V = 6 when T = 2, the formula connecting V and T is:
   a) V = 5T
   b) V = 8T
   c) V = 3T
   d) V = 4T

2. The height of a closed cylinder is equal to its radius r. Express the total surface area of the cylinder in terms of π and r:
   a) 2πr²
   b) 22πr²
   c) 32πr²
   d) 42πr²

3. A cone and a cylinder have equal heights and volumes. If r is the radius of the cylinder, what is the radius of the cone in terms of r?
   a) r
   b) 3r
   c) r/3
   d) 1/3 r

4. The slant height of a cone is twice its base radius r. Express the total surface area of the cone in terms of π and r:
   a) 2/3 πr²
   b) πr²
   c) 1 1/3 πr²
   d) 2πr²

5. What is the value of 5³ mod 4?
   a) 0
   b) 1
   c) 2
   d) 3

6. x varies inversely with y, and x = 9 when y = 8. Find x when y = 12:
   a) 6
   b) 10 2/3
   c) 11
   d) 13

Use the table below to answer questions 7 – 10

7. Which shoe size is the mode?
   a) 36
   b) 37
   c) 38
   d) 39

8. The median shoe size is:
   a) 36
   b) 37
   c) 38
   d) 39

9. The mean shoe size is:
   a) 36
   b) 37
   c) 38
   d) 40

10. The range of the shoe sizes is:
    a) 4
    b) 3
    c) 2
    d) 1

11. If (2x + 3) is a factor of 6x² + x – 12, the other factor is:
    a) (x + 6)
    b) (2x – 3)
    c) (3x + 4)
    d) (3x – 4)

12. Find the roots of the equation x² + 12x – 28 = 0. The greater root is:
    a) -14
    b) -2
    c) 2
    d) 14

13. Increase ₦330 in the ratio 6:5
    a) ₦180
    b) ₦275
    c) ₦360
    d) ₦396

14. A girl walks 6km at a speed of 4.5 km/h. How many minutes does her journey take?
    a) 27
    b) 45
    c) 80
    d) 120

15. A rope 24m long is divided into three pieces in the ratio 2:1:5. The length of the shortest piece is:
    a) 3m
    b) 6m
    c) 8m
    d) 15m

16. What is the sum of the roots of the equation x² – 3x + 2 = 0?
    a) -3
    b) -1
    c) 2
    d) 3

17. 3cm on a map represents a distance of 60km. If the scale is expressed as 1:n, then n =
    a) 20
    b) 60
    c) 2000
    d) 6000

18. Evaluate (101.5)² – (100.5)²
    a) 1
    b) 2.02
    c) 20.02
    d) 202

19. Express the product of 0.06 and 0.09 in standard form:
    a) 5.4 × 10⁻³
    b) 5.4 × 10⁻²
    c) 5.4 × 10⁻¹
    d) 5.4 × 10²

20. Simplify 36¹/² × 64⁻¹/³ × 50
    a) 0
    b) 1/24
    c) 2/3
    d) 1 1/2

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SECTION B: THEORY QUESTIONS

(Answer any three questions only.)

1. The following data gives the lengths (cm) of 30 iron rods:
   45, 55, 65, 60, 61, 68, 59, 54, 64, 50, 68, 72, 68, 80, 67, 70, 62, 79, 64, 63, 71, 59, 64, 53, 57, 74, 55, 76, 67, 57.

   • Construct a frequency table using class intervals 45-49, 50-54, 55-59, etc.
   • Calculate the Mean, Median, and Mode.

2. Solve the equation x² – 2x – 3 = 0 graphically for x values from -2 to 5.

3a. Construct a table of modular subtraction for mod 7.
3b. The cost of producing a machine is ₦232,000, with materials, labor, and overheads in the ratio 7:9:2. Calculate the labor cost for producing 32 machines.

4a. Find the values of sin and tan if cos = 0.125 in the range 0°–90°.
4b. A post casts a shadow 6m longer when the sun’s elevation is 30° than when it is 60°. Find the height of the post.

5a. In a group of 120 students:

• 60 studied Mathematics
• 40 studied Physics
• 55 studied Chemistry
• 22 studied none of the three subjects
• 12 studied Physics & Mathematics only
• 8 studied Chemistry & Physics only
• 7 studied Mathematics & Chemistry only

Draw a Venn diagram illustrating this data.
5b. Find the number of students that studied all three subjects.