JAMB UTME - Mathematics - 2009
Frage 1 Bericht
The cumulative frequency curve above shoes the distribution of the scores of 50 students in an examination. Find the 36th percentile scores
Antwortdetails
Frage 2 Bericht
Antwortdetails
Frage 3 Bericht
If \(y = 3 \cos 4x\), \(\frac{dy}{dx}\) equals
Antwortdetails
Frage 4 Bericht
In the figure above, TS//XY and XY = TY,
Antwortdetails
< TYZ = 94∘
n∘ = 180 - (94∘ + 34∘ )
= 180∘ - 128∘
= 52∘
Frage 5 Bericht
Antwortdetails
52x - 1 x 5x + 1 = 125
53x - 1 = 5-2
3x - 1= -2
3x = -1
therefore, x = -13
Frage 6 Bericht
If \( p = \begin{pmatrix} x + 3 & x + 2 \\ x + 1 & x - 1 \end{pmatrix} \) evaluate x if \(|p| = -10\)
Antwortdetails
|P| = (x + 3)(x - 1) - (x + 2)(x + 1)
x2 + 2x - 3 - (x2 + 3x + 2)
x2 + 2x - 3 - x2 - 3x - 2
-x - 5 = -10
-x = -10 + 5
x = 5
Frage 7 Bericht
Antwortdetails
Frage 8 Bericht
If \(m * n = n-(m + 2)\) for any real numbers m and n, find the value of \(3 * (-5)\)
Antwortdetails
= n - (m + 2)
3 ∗ (-5) = -5 - (3 + 2)
= -5 - 5
= -10
Frage 9 Bericht
| Marks | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| No. of students | 3 | 4 | 1 | 0 | 4 | 5 | 2 | 1 |
The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.
Antwortdetails
= 35
Frage 10 Bericht
Evaluate \( \int \sec^2 \theta \, d\theta \)
Frage 11 Bericht
If s = (2 + 3t)(5t - 4), find \( \frac{dy}{dx} \) when t = \( \frac{4}{5} \) sec
Antwortdetails
= 10t - 8 + 15t2 - 12t
dsdt = 15t2 - 2t - 8
= 30t - 2 ; t = 45
= 30t - 2
= 30 x 45 - 2 → 24 - 2
= 22 sec
Frage 12 Bericht
I.S∩T∩W=S II. S∪T∪W=S
III. T∩W=S
If S⊂T⊂W, which of the above statements are true?
Antwortdetails
S∪T∪W = W (imply W is a universal set for S and T) T∩W = S imply all the elements of S are in T and W)
S ⊂ T ⊂ W
∴ I, II, and III
Frage 13 Bericht
Antwortdetails
Frage 14 Bericht
A student spent \( \frac{1}{5} \) of his allowances on books, \( \frac{1}{3} \) of the remainder on food and kept the rest for contingences. What fraction was kept?
Antwortdetails
spent 13 of 45 on food
45 x 13 = 415
therefore, 45 - 415
= 12−415
= 815
Frage 15 Bericht
Antwortdetails
= -5 - (3+2)
= -5-5
= -10
Frage 16 Bericht
Antwortdetails
x2 + 25 = 169
x2 = 144
x = √ 144
= 12
Length of the chord AB = 2x
2*12= 24cm
Frage 17 Bericht
A binary operation \(plus\) defined on the set of integers is such that m \(plus\) n = n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0.
Antwortdetails
Frage 18 Bericht
Antwortdetails
Frage 19 Bericht
| No. of days | 1 | 2 | 3 | 4 | 5 | 6 |
| No. of students | 20 | \(2x\) | 60 | 40 | \(x\) | 50 |
The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term
Antwortdetails
3x = 260 - 170
3x = 90 → x = 30
therefore, 20 + 2x + 60 + 40
= 180
Frage 20 Bericht
Simplify \( \frac{5+\sqrt{7}}{3+\sqrt{7}} \)
Antwortdetails
Frage 22 Bericht
Antwortdetails
Imply x = 4/3 and - 3/5
3x = 4 and 5x = -3
∴3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x – 20x – 12 = 0 By expansion
15x2 - 11x – 12 = 0
Frage 23 Bericht
A cliff on the bank of a river is 300 meter high. if the angle of depression of a point on the opposite side of the river is \(60^\circ\), find the width of the river.
Antwortdetails
We can solve this problem using trigonometry. Let's draw a diagram of the situation:
A /| / | / | h = 300 m / | ----------- x B
Where point A is the top of the cliff, point B is the unknown point on the opposite side of the river, and x is the width of the river.
We know that the angle of depression from A to B is 60 degrees. This means that the angle of elevation from B to A is also 60 degrees.
Using trigonometry, we can set up the following equation:
tan(60) = h / x
where h is the height of the cliff and x is the width of the river. We can solve for x:
x = h / tan(60) x = 300 / √3 x = 100√3 meters
Therefore, the width of the river is 100√3 meters. Answer is correct.
Frage 24 Bericht
Find the range of values of \(x\) for which \(3x - 7 \le 0\) and \(x + 5 > 0\)
Antwortdetails
Frage 25 Bericht
Antwortdetails
∫(cos)-2 dθ,
let u = cos θ
∴∫u-2 = 1/u + c
∫cos θ = sin θ + c
∫sec-2θ = 1/u sin θ + c
= (sinθ / cosθ) + c
= Tan θ + c
Frage 26 Bericht
Find the value of \( \sin 45^\circ - \cos 30^\circ \)
Antwortdetails
Frage 27 Bericht
The histogram above represents the number of candidates that sat for Mathematics examination in a school. How many candidate scored more than 50 marks?
Antwortdetails
Frage 28 Bericht
Antwortdetails
Frage 29 Bericht
Antwortdetails
Frage 30 Bericht
Antwortdetails
Frage 31 Bericht
If \(P = \begin{bmatrix} x+3 & x+2 \\ x+1 & x-1 \end{bmatrix}\) evaluate x if \(|P| = -10\)
Antwortdetails
(x+3)(x-1) - {(x+1)(x+2)} = -10
x2 - x + 3x - 3 - {x2 + 2x + x + 2} = -10
x2 + 2x - 3 - {x2 + 3x + 2} = -10
-x - 5 = -10
-5 + 10 = x
5 = x
∴x = 5
Frage 32 Bericht
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3, \ldots\)
Antwortdetails
Frage 33 Bericht
Evaluate \(\frac{81.81+99.44}{20.09+36.16}\) correct to 3 significant figures.
Antwortdetails
Frage 34 Bericht
Antwortdetails
Let u = 2+3t ∴du/dt = 3
and v = 5t-4 ∴dv/dt = 5
dx/dt = Vdu/dt + Udv/dt
= (5t-4)3 + (2+3t)5
= 15t - 12 + 10 + 15t
= 30t - 2
= 30x4/5 - 2
= 24 - 2
= 22
Frage 35 Bericht
The probability of a student passing any examination is \( \frac{2}{3} \). If the student takes three examinations, what is the probability that he will not pass any of them?
Antwortdetails
Frage 36 Bericht
Antwortdetails
Frage 37 Bericht
Antwortdetails
Frage 38 Bericht
Simplify \(4\frac{3}{4} - 6\frac{1}{4}\)
Antwortdetails
194 - 254 ............(A)
215 - 54 .............(B)
Now work out the value of A and the value of B and then find the value AB
A = 194 - 254
= ?64
B = 215 x 520
= 10520
= 214
But then AB = -64
214 = -64 ÷ 214
= -64 x 421
= -2484
= -27
Frage 39 Bericht
i. \(S \cap T \cap W = S\)
ii. \(S \cup T \cup W = W\)
ii. \(T \cap W = S\)
If \(S \subset T \subset W\). Which of the above statements are true?
Antwortdetails
Frage 40 Bericht
A regular polygon has \(150^\circ\) as the size of each interior angle. How many sides does it have?
Antwortdetails
Frage 41 Bericht
Antwortdetails
Frage 42 Bericht
Antwortdetails
Frage 43 Bericht
Antwortdetails
x2 + 9 = 25
x2 = 25 – 9
x2 = 16
x = √ 16
= 4 cm
∴ The locus is a circle of radius 4 cm with the center 0
Frage 44 Bericht
Antwortdetails
Frage 45 Bericht
Find the infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3, ...\)
Antwortdetails
Frage 46 Bericht
Antwortdetails
Frage 47 Bericht
Antwortdetails
Frage 48 Bericht
Antwortdetails
Frage 49 Bericht
| No. of days | 1 | 2 | 3 | 4 | 5 | 6 |
| No. of students | 20 | x | 50 | 40 | 2x | 60 |
The distribution above shows the number of days a group of 260 students were absents from school in a particular term. How many students were absent for at least four days in the term
Antwortdetails
3X + 170 = 260
3X = 260 - 170
3x = 90
x = 30
Absent for at least 4 days
| 4 | 5 | 6 |
| 40 | 2x | 60 |
i.e 40 + 2x + 60 = 40 + (2 x 30) + 60
= 40 + 60 + 60
= 160
Frage 50 Bericht
Find the acute angle between the straight lines \(y = x\) and \(y = \sqrt{3x}\)
Antwortdetails
x2 = 3x
3x = 90o
x = 90o3 = 30o
