JAMB - Mathematics (2006)

1
The table above shows the scores of a group of students in a physics test. If the mode is m and the number of students who scored 4 or more is n, what is (n, m)?
Відповідь
(A)
(33, 4)
2
A final examination requires that a student answer any 4 out of 6 questions. In how many ways can this be done?
Відповідь
(A)
15
3
If the mean of five consecutive integers is 30, find the largest of the numbers
Відповідь
(C)
32
4
A bag contains 5 black, 4 white and x red marbles. If the probability of picking a red marble is 2/5, find the value of x
Відповідь
(D)
6
5
Find the variance of 2x, 2x-1 and 2x+1
Відповідь
(A)
2/3
6
The table above shows the distribution of recharge cards of four major GSM operators. What is the probability that a recharge card selected at random will be GTN or Qtel?
Відповідь
(C)
2/5
7
The pie chart above shows the expenditure of a family whose income is N30,000. If the expenditure on food is twice that on housing and that on school fees is twice that on transport, how much does the family spend on food?
Відповідь
(D)
N 12 500
8
For what value of n is \(^{n+1}C_3\) = 4(\(^nC_3\))?
Відповідь
(D)
3
9
The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.
Відповідь
(B)
y = x² + 7x - 18
10
Differentiate (x\(^2\) - \(\frac{1}{x}\))\(^2\) with respect to x
Відповідь
(C)
4x³ - 2 - ²/_x³
11
Find the value of x for which the function 3x\(^3\) - 9x\(^2\) is minimum
Відповідь
(B)
2
12
If ^dy/_dx = x + cos x, find y
Відповідь
(D)
^x²/₂ + sin x + c
13
Differentiate (cos θ - sin θ)\(^2\)
Відповідь
(A)
-2 cos 2θ
14
Evaluate \(\int_{-4}^0(1 - 2x)dx\)
Відповідь
(C)
20
15
simplify \(\frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{3}+\frac{\frac{2}{5}}{\frac{4}{5}}}\)
Відповідь
(D)
\(\frac{2}{15}\)
16
If m:n = 13:11, find m\(^2\) - n\(^2\) : (m + n)\(^2\)
Відповідь
(D)
1:12
17
Calculate the logarithm to base 9 of 3\(^{-4}\) x 9\(^2\) x (81)\(^{-1}\)
Відповідь
(C)
-2
18
If (K2)\(_6\) * 3\(_6\) = 3\(_5\)(K4)\(_5\), what is the value of k?
Відповідь
(D)
2
19
In a small village of 500 people, 350 speak the local language while 200 speak pidgin English. What percentage of the population speak both.
Відповідь
(B)
10%
20
Find the tax on an income of N20,000 if no tax is paid on the first N10,000 and tax is paid at N50 in N1000 on the next N5000 and at N55 in N1000 on the remainder
Відповідь
(D)
N525
21
Evaluate \(\frac{2}{6-5\sqrt{3}}\)
Відповідь
(C)
\(-\left(\frac{12}{39}+\frac{10\sqrt{3}}{39}\right)\)
22
Compute 110011₂ + 11111₂
Відповідь
(B)
1010010₂
23
Simplify \((25)^{\frac{-1}{2}} \times (27)^{\frac{1}{3}} + (121)^{\frac{-1}{2}} \times (625)^{\frac{-1}{4}}\)
Відповідь
(A)
³⁴/₅₅
24
Convert 2232\(_4\) to base six
Відповідь
(A)
450₆
25
In the diagram above, QR is the diameter of the semicircle QR. Find the area of the figure to the nearest whole number. [\(\pi = \frac{22}{7}\)]
Відповідь
(A)
89 cm²
26
If tan θ = ⁵/₄, find sin²θ - cos²θ.
Відповідь
(C)
⁹/₄₁
27
PQ and RS are two parallel lines. If the coordinates of P, Q, R, S are (1,q), (3,2), (3,4), (5,2q) respectively, find the value of q
Відповідь
(D)
2
28
In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find lYZl.
Відповідь
(B)
\(7\left(\frac{\sqrt{6}}{2}\right)\)
29
In the diagram above, find the value of x
Відповідь
(C)
45^o
30
In the diagram above, POQ is a diameter of the circle PQRS. If ∠PSR = 145°, find x°
Відповідь
(A)
55^o
31
What is the locus of points equidistant from the lines ax + by + c = 0?
Відповідь
(D)
A line ax + by +q = 0
32
PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS
Відповідь
(D)
60^o
33
If the locus of the points which are equidistant from point P and Q meets line PQ at point N, then PN equals
Відповідь
(A)
NQ
34
In the diagram above, PQ = 10 cm, PS = 8 cm and ∠PSR is 60^o while ∠SRQ is a right angle. Find SR
Відповідь
(A)
14 cm
35
The solution set of the shaded area above is
Відповідь
(D)
y ≤ x, y + x ≤ 4 and y ≥ 0
36
A binary operation \(\oplus\) defined on the set of real number is such that x\(\oplus\)y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6
Відповідь
(D)
⁹/₅
37
If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?
Відповідь
(B)
p varies inversely as r⁶
38
A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)
Відповідь
(A)
\(\frac{-8}{15}\)
39
Find the value of k if the expression kx³ + x² - 5x - 2 leaves a remainder 2 when it is divided by 2x + 1
Відповідь
(C)
-10
40
Solve the inequalities for which \(\frac{x+4}{3}-\frac{x-3}{2} < 4\)
Відповідь
(B)
x > -7
41
The cost of renovating a 6 m square room is N540. What is the cost of renovating a 9 m square room?
Відповідь
(D)
N810
42
The sum of the first n positive integers is
Відповідь
(D)
¹/₂ n(n+1)
43
If \(T = 2\pi \sqrt{\frac{l}{g}}\), make g the subject of the formula
Відповідь
(B)
(4π²l) / T²
44
If y = x\(^2\) - x - 12, find the range of values of x for which y \( \geq \) 0
Відповідь
(B)
x \( \leq \) -3 or x \( \geq \) 4
45
How many terms of the series 3, -6, +12, - 24, + ..... are needed to make a total of 1 - 2\(^8\)?
Відповідь
(D)
8