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Form 4 Mathematics imtixaanka qaranka 2024 iyo jawaabihiisa

Imtixaanka qaranka Fasalka 4aad ee 2024 ee Form 4 Mathematics, su'aal su'aal. Ku gal adigoo waqti leh sida imtixaanka dhabta ah, kadibna arag jawaabta iyo sharaxa su'aal kasta.

34 su'aalood, 100 dhibcood
120 daqiiqo

Gal imtixaankan

120 daqiiqo, 100 dhibcood. Su'aalaha doorashada waa laguu saxayaa; jawaabaha qoraalka adiga ayaa ku saxaya qodobada sixitaanka.

Akoon bilaash ah ayaa loo baahan yahay si aad u bilowdo, si jawaabahaaga iyo natiijooyinkaaga loo kaydiyo.

Tilmaamaha ardayga

Answer all questions in the ANSWER BOOKLET.

PART ONE: MULTIPLE CHOICE QUESTIONS (20 × 2 = 40 MARKS)

1
The algebraic expression for half of x is
- A.x+2
- B.x-2
- C.2x
- D.x/2
2 dhibcood
2
cot x · sin 2x · sec^2 x =
- A.0
- B.1
- C.2
- D.4
2 dhibcood
3
The value of angle C in the figure below (figure 1) is (right angle at B, angle A = 30°)
- A.50°
- B.40°
- C.60°
- D.70°
2 dhibcood
4
The expression cuberoot(16) × cuberoot(4) is equal
- A.16
- B.4
- C.3
- D.12
2 dhibcood
5
The number 20.003 has _____ significant digits
- A.2
- B.3
- C.4
- D.5
2 dhibcood
6
A Group of 250 students took a test. If 76% of them passed the test. How many students passed the exam?
- A.100
- B.190
- C.200
- D.60
2 dhibcood
7
If A = (2 3; 3 4) (a 2 by 2 matrix with first row 2, 3 and second row 3, 4), then det(A) =
- A.1
- B.9
- C.-1
- D.8
2 dhibcood
8
Find the area of the rectangle below (Fig. 2), whose sides are (3+√2) cm and (3-√2) cm.
- A.9 cm^2
- B.2 cm^2
- C.7 cm^2
- D.5 cm^2
2 dhibcood
9
The factorization of a^3 - 8 is:
- A.(a+2)(a^2-2a+4)
- B.(a+2)(a^2+4a+4)
- C.(a-2)(a^2-2a+4)
- D.(a-2)(a^2+2a+4)
2 dhibcood
10
The Mean of four numbers is 7, three of the numbers are 4,6 and 10. The fourth number is:
- A.10
- B.4
- C.6
- D.8
2 dhibcood
11
integral of 2/x dx =
- A.ln x + c
- B.2 ln x + c
- C.ln 2x + c
- D.ln(2/x) + c
2 dhibcood
12
If z = 3 + 4i then the magnitude of z, |z| =
- A.3
- B.4
- C.5
- D.7
2 dhibcood
13
The lim as x→-1 of x^3 + x^2 + x + 1 =
- A.0
- B.1
- C.2
- D.3
2 dhibcood
14
The derivative of y = x cos x is
- A.y' = cos x - x sin x
- B.y' = x cos x
- C.y' = x sin x
- D.y' = cos x + x sin x
2 dhibcood
15
The 6th term of a Geometric series is 486 and the 7th term is 1458. Find the common ratio.
- A.1
- B.2
- C.3
- D.4
2 dhibcood
16
The value of sin(π - x) is:
- A.cos x
- B.sin x
- C.sec x
- D.tan x
2 dhibcood
17
lim as h→0 of (f(x+h) - f(x))/h =
- A.f(x)
- B.f'(x)
- C.f(a)
- D.f'(a)
2 dhibcood
18
From a class of 25 students 4 are selected to work on a special assignment. In how many different ways can the 4 students be selected?
- A.6375600
- B.12650
- C.13800
- D.303600
2 dhibcood
19
If P(A) = 0.53, P(B) = 0.36, and P(A ∪ B) = 0.74, then P(A ∩ B) =
- A.0.47
- B.0.64
- C.0.15
- D.0.26
2 dhibcood
20
The value of 1/i^7 is equal to
- A.i
- B.-i
- C.1
- D.-1
2 dhibcood

PART TWO: MATCH COLUMN A WITH COLUMN B (10 MARKS)

M1
Match Column A with Column B. If f(s) = s^2 + 3s - 2, then f(-2) = Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M2
Match Column A with Column B. The integral of constant k with respect to x is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M3
Match Column A with Column B. 2(i)^58 = Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M4
Match Column A with Column B. P(A') can not be higher than Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M5
Match Column A with Column B. 6 cos(π/2 - x) sec(π/2 - x) = Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M6
Match Column A with Column B. The number of rows of the matrix (1 2 0 0; 1 1 3 0; 0 2 1 4) is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M7
Match Column A with Column B. There are 16 students in a class. If the ratio of boys to Girls is 3:5. Then the number of girls in the class is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M8
Match Column A with Column B. lim as x→0 of (1 - cos x)/x Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M9
Match Column A with Column B. The magnitude of the vector (9, 12) is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood
M10
Match Column A with Column B. The distance between (-1,3) and (3,3) is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
1 dhibcood

PART THREE: STRUCTURED QUESTIONS (50 MARKS)

T1
Trigonometry: Find the value of x that satisfies cot x = tan 65° [4 Marks]
4 dhibcood
T2
Trigonometry: Show that cos 3x = 4cos^3 x - 3 cos x [5 Marks]
5 dhibcood
C1
Complex Number: Use De Moivre's theorem to calculate the value of 1/(1 - i)^6 [4 Marks]
4 dhibcood
C2
Complex Number: Show that [(1 + i)/(1 - i)]^4 + [(1 - i)/(1 + i)]^4 = 2. Hint: Multiply each part by its conjugate and then simplify by applying the power. [5 Marks]
5 dhibcood

Imtixaanka waxaa diyaarisay Federal Ministry of Education, Culture and Higher Education (MoECHE), Somalia. Waxaa lagu wadaagay bilaash si ardaydu ugu diyaargaroobaan. Jawaabaha iyo sharaxyada waxaa qoray macallimiinta Sheerxirfad.

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