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Ibeere 2 Ìròyìn
A binary operation \( \ast \) is defined on a set of real numbers by \(x \ast y = x^y\) for all real values of \(x\) and \(y\). If \(x \ast 2 = x\). Find the possible values of \(x\)
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Ibeere 3 Ìròyìn
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Ibeere 4 Ìròyìn
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Ibeere 5 Ìròyìn
From the figure, calculate TH in centimeters
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TH5+QH = tan 30∘
TH = (b + QH) tan 30∘
QH = 56 (5 + QH) 1√3
QH(1 - 1√3 ) = 5√3
QH = 5√3√3−1√3
= 5√3−1
Ibeere 6 Ìròyìn
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Ibeere 7 Ìròyìn
Simplify \( \frac{1}{p} - \frac{1}{q} + \frac{p}{q} - \frac{q}{p} \)
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Ibeere 8 Ìròyìn
| Class | Frequency |
| 1−5 | 2 |
| 6−10 | 4 |
| 11−15 | 5 |
| 16−20 | 2 |
| 21−25 | 3 |
| 26−30 | 2 |
| 31−35 | 1 |
| 36−40 | 1 |
Find the median of the observation in the table given.
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Ibeere 9 Ìròyìn
Solve without using tables \( \log_{5}(62.5) - \log_{5}\left(\frac{1}{2}\right) \)
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Ibeere 10 Ìròyìn
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Ibeere 12 Ìròyìn
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Ibeere 13 Ìròyìn
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Ibeere 14 Ìròyìn
| \(Weight(s)\) | \(0-10\) | \(10-20\) | \(20-30\) | \(40-50\) | |
| Number of coconuts | \(10\) | \(27\) | \(19\) | \(6\) | \(2\) |
Estimate the mode of the frequency distribution above.
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Ibeere 15 Ìròyìn
If \( \sqrt{x^2 + 9} = x + 1 \), solve for x
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Ibeere 16 Ìròyìn
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Ibeere 17 Ìròyìn
Calculate the length in cm. of the area of a circle of diameter 8cm which subtends an angle of \( \frac{1}{2} \)o at the centre of the circle
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Ibeere 18 Ìròyìn
In the diagram, O is the centre of the circle and POQ a diameter. If POR = \(96^\circ\), find the value of ORQ.
Awọn alaye Idahun
< ROQ = 180 - 86 = 84?
? OQR = Isosceles
R = Q
R + Q + 84 = 180(angle in a ? )
2R = 96 since R = Q
R = 48?
ORQ = 48?
Ibeere 19 Ìròyìn
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Ibeere 20 Ìròyìn
PQRST is a regular pentagon and PQVU is a rectangle with U and V lying on TS and SR respectively as shown in the diagram. Calculate TUP
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Ibeere 21 Ìròyìn
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Ibeere 22 Ìròyìn
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Ibeere 24 Ìròyìn
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Ibeere 26 Ìròyìn
The bar chart shows the distribution of marks in a class test. How many students took the test?
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Ibeere 27 Ìròyìn
In the diagram, PQRs is a circle with 0 as centre and PQ/RT. If RTS = \(32^\circ\). Find PSQ
Awọn alaye Idahun
< RTS = < PQS = 32∘ (Alternative angle)
< PSQ = 90 - < PSQ = 90∘ - 32∘
= 58∘
Ibeere 28 Ìròyìn
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Ibeere 29 Ìròyìn
Integrate 1−xx3 with respect to x
Ibeere 30 Ìròyìn
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Ibeere 31 Ìròyìn
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Ibeere 32 Ìròyìn
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Ibeere 33 Ìròyìn
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Ibeere 34 Ìròyìn
If x is negative, what is the range of values of x within which \( \frac{x+1}{3} > \frac{1}{X+3} \)
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= x > 0, x < -3, x < -4 = x < -3(solution only)
Case 3 (-, +, -) = x < 0, x > -3, x < -4 = x < -0, -4 < x < 3(solutions)
Case 4 (-, -, +) = x < 0, x + 3 < 0, x + 4 > 0
= x < 0, x < -5, x > -4 = x < -0, -4 < x < -3(solution)
combining the solutions -4 < x < -3
Ibeere 35 Ìròyìn
If \(9\left(x - \frac{1}{2}\right)^3x^2\)
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Ibeere 36 Ìròyìn
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Ibeere 37 Ìròyìn
The shaded portion in the Venn diagram is
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Ibeere 38 Ìròyìn
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Ibeere 39 Ìròyìn
In the figure, the line segment ST is tangent to two circles at S and T. O and Q are the centres of the circles with OS = 5cm. QT = 2cm and OR = 14cm. Find ST
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SQ2 = 142 - 52
196 - 25 = 171
ST2 + TQ2 = SQ2
ST2 + 22 = 171
ST2 = 171 - 4
= 167
ST = √167
= 12.92 = 12.9cm
Ibeere 40 Ìròyìn
Evaluate \( \left(x + \frac{1}{x} + 1\right)^2 - \left(x + \frac{1}{x} + 1\right)^2 \)
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Ibeere 41 Ìròyìn
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Ibeere 42 Ìròyìn
Evaluate \( \frac{3524}{0.05} \) correct to 3 significant figures
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Ibeere 43 Ìròyìn
simplify \( \frac{1}{\sqrt{3}-2} - \frac{1}{\sqrt{3}+2} \)
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√3+2−√3+23−2√3+2√3−4
= 43−2
= 4−1
= -4
Ibeere 44 Ìròyìn
If \( \sin \theta = \cos \theta \), find \( \theta \) between 0o and 360o
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Ibeere 45 Ìròyìn
In the diagram above, |PQ| = |QR|, |PS| = |RS|, ∠PSR = 30o and ∠PQR = 80o. Find ∠SPQ.
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Ibeere 46 Ìròyìn
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Ibeere 47 Ìròyìn
Make x the subject of the relation \( \frac{1+ax}{1-ax}=\frac{p}{q} \)
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Ibeere 48 Ìròyìn
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Ibeere 49 Ìròyìn
In the diagram, \(QP // ST\): \(PQR = 34^\circ\) \(QRS = 73^\circ\) and \(RS = RT\). Find \(SRT\)
Awọn alaye Idahun
R = 180∘ - 107∘
< p = 180∘ - (107∘ - 34∘ )
108 - 141∘ = 39∘
Angle < S = 39∘ (corr. Ang.) But in △ SRT
< S = < T = 39∘
SRT = 180 - (39∘ + 39∘ )
= 180∘ - 78∘
= 102∘
Ibeere 50 Ìròyìn
The chances of three independent events X, Y, Z occurring are \( \frac{1}{2} \), \( \frac{2}{3} \), \( \frac{1}{4} \) respectively. What are the chances of Y and Z only occurring?
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