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Ibeere 1 Ìròyìn
Differentiate \( \frac{x}{\cos x} \) with respect to x
Ibeere 2 Ìròyìn
Ibeere 3 Ìròyìn
If \(y = 243(4x + 5)^{-2}\), find \(\frac{dy}{dx}\) when \(x = 1\).
Ibeere 4 Ìròyìn
A bag contains 16 red balls and 20 blue balls only. How many white balls must be added to the bag so that the probability of randomly picking a red ball is equal to \( \frac{2}{5} \)
Ibeere 5 Ìròyìn
Let \( \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \) p = \( \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} \) Q = \( \begin{pmatrix} u & 4 + u \\ -2v & v \end{pmatrix} \) be 2 x 2 matrices such that PQ = 1. Find (u, v)
Ibeere 6 Ìròyìn
The determinant of matrix \(\begin{pmatrix} x & 1 & 0 \\ 1-x & 2 & 3 \\ 1 & 1+x & 4 \end{pmatrix}\) in terms of x is
Ibeere 7 Ìròyìn
Evaluate \( \int_{2}^{\pi} (\sec^2 x - \tan^2 x)\,dx \)
Ibeere 8 Ìròyìn
Find the value of k if \( \frac{k}{\sqrt{3}+\sqrt{2}} = k\sqrt{3-2} \)
Ibeere 9 Ìròyìn
Ibeere 10 Ìròyìn
TQ is tangent to circle XYTR, \( \angle YXT = 32^\circ \), \( \angle RTQ = 40^\circ \). Find \( \angle YTR \)
< TWR = < TXR = 40∘ (Angles in the same segments)
< YXR = 40∘ + 32∘ = 72∘
< YXR + < YTR = 180∘ (Supplementary)
72∘ + < YTR = 180∘
< YTR = 180∘ - 72∘
= 108∘
Ibeere 11 Ìròyìn
If \(b^3 = a^{-2}\) and \(c^{\frac{1}{3}} = a^{\frac{1}{2}}b\), express c in terms of a
Ibeere 12 Ìròyìn
For what value of \(x\) does \(6\sin(2x - 25)^\circ\) attain its maximum value in the range \(0^\circ \le x \le 180^\circ\)
Ibeere 13 Ìròyìn
Evaluate \[ \frac{1}{0.03} \div \frac{1}{0.024} \]⁻¹ correct to 2 decimal places
Ibeere 16 Ìròyìn
Solve for the equation \( \sqrt{x} - \sqrt{(x - 2)} - 1 = 0 \)
Ibeere 17 Ìròyìn
Ibeere 18 Ìròyìn
%%
In the diagram, QTR is a straight line and < PQT = \(30^\circ\). find the sin of < PTR
1520=sinx
sin x = 1520=34
N.B x = < PRQ
Ibeere 19 Ìròyìn
Ibeere 20 Ìròyìn
A chord of a circle radius \( \sqrt{3}\,\mathrm{cm} \) subtends an angle of \(60^\circ\) on the circumference of he circle. Find the length of the chord
Awọn alaye Idahun
Ibeere 21 Ìròyìn
If x is a positive real number, find the range of values for which \( \frac{1}{3x} + \frac{1}{2} > \frac{1}{4x} \)
= x < 0, x < 16 = x < 16 (solution)
Case 2 (+, +) = x > 0, 6x -1 > 0 = x > 0, x > 16
Combining solutions in cases(1) and (2)
= x > 0, x < 16
= 0 < x < 16
Ibeere 22 Ìròyìn
Make \( \frac{a}{x} \) the subject of formula \( \frac{x+1}{x-a} \)
Ibeere 23 Ìròyìn
Awọn alaye Idahun
Ibeere 25 Ìròyìn
Ibeere 26 Ìròyìn
In the diagram above; O is the centre of the circle and |BD| = |DC|. If ∠DCB = 35o, find ∠BAO.
Awọn alaye Idahun
Ibeere 27 Ìròyìn
Ibeere 28 Ìròyìn
| Average hourly earnings(N) | 5−9 | 10−14 | 15−19 | 20−24 |
| No. of workers | 17 | 32 | 25 | 24 |
Estimate the mode of the above frequency distribution
Ibeere 29 Ìròyìn
Ibeere 31 Ìròyìn
Express in partial fractions \( \frac{11+2}{6x^2-x-1} \)
Ibeere 32 Ìròyìn
Ibeere 33 Ìròyìn
Ibeere 34 Ìròyìn
Ibeere 35 Ìròyìn
Given that \( \log_{4}(y - 1) + \log_{4}\left(\frac{1}{2}x\right) = 1 \) and \( \log_{2}(y + 1) + \log_{2}x = 2 \), solve for x and y respectively
Ibeere 36 Ìròyìn
The binary operation \( \oplus \) is defined by \( x \ast y = xy - y - x \) for all real values \( x \) and \( y \). If \( x \ast 3 = 2 \ast \), find \( x \)
Ibeere 37 Ìròyìn
If 10112 + x7 = 2510, solve for X.
10112 + x7 = 2510 = 10112 = 1 x 23 + 0 x 22 + 1 x 21 + 1 x 2o
= 8 + 0 + 2 + 1
= 1110
x7 = 2510 - 1110
= 1410
71472R00R2
X = 207
Ibeere 38 Ìròyìn
In the figure, PQST is a parallelogram and TSR is a straight line. If the area of \( \triangle \)QRS is 20cm2, find the area of the trapezium PQRT.
= 12 x 8 x h = 4h
h = 204
= 5cm
A△ (PQTS) = L x H
A△ PQRT = A△ QSR + A△ PQTS
20 + 50 = 70cm2
ALTERNATIVE METHOD
A△ PQRT = 12 x 5 x 28
= 70cm2
Ibeere 39 Ìròyìn
Ibeere 40 Ìròyìn
Ibeere 41 Ìròyìn
In the venn diagram, the shaded region is
Ibeere 42 Ìròyìn
In a recent zonal championship games involving 10 teams, teams X and Y were given probabilities \( \frac{2}{5} \) and \( \frac{1}{3} \) respectively of winning the gold in the football event. What is the probability that either team will win the gold?
Ibeere 43 Ìròyìn
Ibeere 44 Ìròyìn
Ibeere 45 Ìròyìn
The bar chart shows the distribution of marks scored by 60 pupils in a test in which the maximum score was 10. If the pass mark was 5, what percentage of the pupils failed the test?
= 25
5 of pupils who fail = 2560 x 100%
= 41.70%
Ibeere 46 Ìròyìn
Ibeere 47 Ìròyìn
The pie chart shows the monthly expenditure pf a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is ₦7200?
Ibeere 48 Ìròyìn
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