<li>If y varies directly as the square root of (x + 1) and y = 6 when x = 3. find x when y = 9.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>8</li>
<li>Option b</li>
<li>7</li>
<li>Option c</li>
<li>6</li>
<li>Option d</li>
<li>5</li> </ol>
</ol>
</li>
</li>
<li>Question 34
<li>The graph of the relation y = x² + 2x + k passes through the point (2,0). Find the value of k.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>0</li>
<li>Option b</li>
<li>−2</li>
<li>Option c</li>
<li>−4</li>
<li>Option d</li>
<li>−8
</ol>
The pie chart shows the distribution of 600 Mathematics textbooks for Arts, Business, Science and Technical classes.[[File:WA2013 MATH P1Q035.jpg|center|thumb]]''Use it to answer questions '''35''' and '''36.'''''</li> </ol>
</li>
</li>
<li>Question 35
<li>How many textbooks are for the Technical class?
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>100</li>
<li>Option b</li>
<li>150</li>
<li>Option c</li>
<li>200</li>
<li>Option d</li>
<li>250</li> </ol>
</ol>
</li>
</li>
<li>Question 36
<li>What percentage of the total number of textbooks belongs to science?
<ol type="a">
<ol type="a">
<li>Option a</li>
<li><math>12\tfrac{1}{2}%</math></li>
<li>Option b</li>
<li><math>20\tfrac{5}{6}%</math></li>
<li>Option c</li>
<li>25%</li>
<li>Option d</li>
<li><math>41\tfrac{2}{3}%</math></li> </ol>
</ol>
</li>
</li>
<li>Question 37
<li>[[File:WA2013 MATH P1Q037.jpg|center|thumb]]In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of <math>\ang</math>RVS.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>36</li>
<li>Option b</li>
<li>54</li>
<li>Option c</li>
<li>60</li>
<li>Option d</li>
<li>72</li> </ol>
</ol>
</li>
</li>
<li>Question 38
<li>What is the locus of the point X which moves relative to two fixed points P and M on a plane such that <math>\ang</math>PXM = 30°?
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>The bisector of the straight line joining P and M</li>
<li>Option b</li>
<li>An arc of a circle with <math>\overrightarrow{PM}</math> as a chord</li>
<li>Option c</li>
<li>The bisector of angle PXM</li>
<li>Option d</li>
<li>A circle centre X and radius PM.</li> </ol>
</ol>
</li>
</li>
<li>Question 39
<li>[[File:WA2013 MATH P1Q039.jpg|center|thumb]]In the diagram, PQ is a straight line. Calculate the value of the angle labelled 2y.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>130°</li>
<li>Option b</li>
<li>120°</li>
<li>Option c</li>
<li>110°</li>
<li>Option d</li>
<li>100°</li> </ol>
</ol>
</li>
</li>
<li>Question 40
<li>When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>11</li>
<li>Option b</li>
<li><math>\tfrac{15}{2}</math></li>
<li>Option c</li>
<li>5</li>
<li>Option d</li>
<li><math>\tfrac{5}{2}</math></li> </ol>
</ol>
</li>
</li>
<li>Question 41
<li>Express <math>\tfrac{2}{x+3}-\tfrac{1}{x-2}</math> as a simple fraction.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li><math>\tfrac{x-7}{x^2+x-6}</math></li>
<li>Option b</li>
<li><math>\tfrac{x-1}{x^2+x-6}</math></li>
<li>Option c</li>
<li><math>\tfrac{x -2}{x^2+x-6}</math></li>
<li>Option d</li>
<li><math>\tfrac{x+7}{x^2+x-6}</math></li> </ol>
</ol>
</li>
</li>
<li>Question 42
<li>An interior angle of a regular polygon is 5 times '''each''' exterior angle. How many sides has the polygon?
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>15</li>
<li>Option b</li>
<li>12</li>
<li>Option c</li>
<li>9</li>
<li>Option d</li>
<li>6</li> </ol>
</ol>
</li>
</li>
<li>Question 43
<li>[[File:WA2013 MATH P1Q043.jpg|center|thumb]]In the diagram, <math>\overrightarrow{ST}// \overrightarrow{PQ}</math> reflex angle SRQ = 198° and <math>\ang</math>RQP = 72°. Find the value of y.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>18°</li>
<li>Option b</li>
<li>54°</li>
<li>Option c</li>
<li>92°</li>
<li>Option d</li>
<li>108°</li> </ol>
</ol>
</li>
</li>
<li>Question 44
<li>[[File:WA2013 MATH P1Q044.jpg|center|thumb]]Using the Venn diagram, find n(X<math>\cap</math>Y').
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>2</li>
<li>Option b</li>
<li>3</li>
<li>Option c</li>
<li>4</li>
<li>Option d</li>
<li>6</li> </ol>
</ol>
</li>
</li>
<li>Question 45
<li>Given that P = x² + 4x − 2. Q = 2x and Q − P = 2, find x.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>−2</li>
<li>Option b</li>
<li>−1</li>
<li>Option c</li>
<li>1</li>
<li>Option d</li>
<li>2</li> </ol>
</ol>
</li>
</li>
<li>Question 46
<li>A pyramid has a rectangular base with dimensions 12 m by 8 m. If its height is 14 m, calculate the volume.
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>344 m²</li>
<li>Option b</li>
<li>448 m²</li>
<li>Option c</li>
<li>632 m²</li>
<li>Option d</li>
<li>840 m²</li> </ol>
</ol>
</li>
</li>
<li>Question 47
<li>The slant height of a cone is 5 cm and the radius of its base is 3 cm. Find, correct to the nearest whole number, the volume of the cone. [Take π = <math>\tfrac{22}{7}</math>]
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>48 cm³</li>
<li>Option b</li>
<li>47 cm³</li>
<li>Option c</li>
<li>38 cm³</li>
<li>Option d</li>
<li>13 cm³</li> </ol>
</ol>
</li>
</li>
<li>Question 48
<li>The distance between two towns is 50 km. It is represented on a map by 5 cm. find the scale used.
<li>An open cone with base radius 28 cm and perpendicular height 96 cm was stretched to form a sector of a circle. Calculate the area of the sector. [Take π = <math>\tfrac{22}{7}</math>].
<ol type="a">
<ol type="a">
<li>Option a</li>
<li>8800 cm²</li>
<li>Option b</li>
<li>8448 cm²</li>
<li>Option c</li>
<li>4400 cm²</li>
<li>Option d</li>
<li>4224 cm²</li> </ol>
</ol>
</li>
</li>
</ol>
</ol>
Line 393:
Line 376:
==== Section A ====
==== Section A ====
<ol>
<ol>
<li>Question 1
<li><ol type="a">
<ol type="a">
<li>Simplify without using tables or calculator, <math>\tfrac{\tfrac{3}{4}(3\tfrac{3}{8}+1\tfrac{2}{6})}{2\tfrac{1}{4}-1\tfrac{1}{4}}</math> </li>
<li>Sub-question a
<li>Given that log<sub>10</sub>2 = 0.3010 and log<sub>10</sub>3 = 0.4771, evaluate correct to 2 significant figures and without using tables or calculator, log<sub>10</sub>1.125. </li> </ol>
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question b
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question c
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question d
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question e
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question f
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
</ol>
</li>
</li>
<li>Question 2
<li><ol type="a">
<ol type="a">
<li>Solve: 7x </li>
<li>Sub-question a
<li>Salem, Sunday and Shaka shared a sum of ₦1,100.00.For every ₦2.00 that Salem gets, Sunday gets 50 kobo and for every ₦4.00 Sunday gets, Shaka gets ₦2.oo. Find Shaka's share. </li> </ol>
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question b
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question c
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question d
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question e
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question f
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
</ol>
</li>
</li>
<li>Question 3
<li><ol type="a">
<ol type="a">
<li>The present ages of a father and his son are in the ratio 10 : 3. If the son is 15 years old now, in how many years will the ratio of their ages be </li>
<li>Sub-question a
<li>The arithmetic mean of x, y and z is 6 while that of x, y, z, t, u, v and w is 9. Calculate the arithmetic mean of t, u, v and w. </li> </ol>
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question b
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question c
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question d
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question e
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question f
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
</ol>
</li>
</li>
<li>Question 4
<li>The area of a circle is 154 cm². It is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. Calculate the perimeter of the third sector. [Take π = <math>\tfrac{22}{7}</math>] </li>
<li>A boy 1.2 m tall, stands 6 m away from the foot of a vertical lamp pole 4.2 m long. If the lamp is at the tip of the pole.
<ol type="a">
<ol type="a">
<li>Sub-question a
<li>represent this information in a diagram. </li>
<li>calculate the:
<ol type="i">
<ol type="i">
<li>Sub-question i</li>
<li>length of the shadow of the boy cast by the lamp</li>
<li>Sub-question ii</li>
<li>angle of deviation of the lamp from the boy, correct to the nearest degree.</li> </ol>
<li>Sub-question iii</li>
</li> </ol>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question b
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question c
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question d
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question e
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question f
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
</ol>
</li>
<li>Question 5
<ol type="a">
<li>Sub-question a
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question b
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question c
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question d
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question e
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question f
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
</ol>
</li>
</li>
</ol>
</ol>
Line 687:
Line 402:
==== Section B ====
==== Section B ====
<ol start=6>
<ol start=6>
<li>Question 6
<li><ol type="a">
<ol type="a">
<li>Two positive whole numbers P and q are such that P is greater than q and their sums is equal to three times their difference.
<li>Aman sold 100 articles at 25 for ₦66.00 and made a gain of 32%. Calculate his gain or loss per cent if he sold them at 20 for ₦50.00. </li> </ol>
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question c
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question d
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question e
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question f
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
</ol>
</li>
</li>
<li>Question 7
<li><ol type="a">
<ol type="a">
<li>Copy and complete the table of values for the relation y = 3x² – 5x – 7. </li>
<li>Sub-question a
<li>Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 3x² – 5x – 7 for –3 ≤ x ≤ 4. </li>
<li>From your graph:
<ol type="i">
<ol type="i">
<li>Sub-question i</li>
<li>find the roots of the equation 3x² – 5x – 7 = 0;</li>
<li>Sub-question ii</li>
<li>estimate the minimum value of y;</li>
<li>Sub-question iii</li>
<li>calculate the gradient of the curve at the point x = 2.</li> </ol>
<li>Sub-question iv</li>
</li> </ol>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question b
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question c
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question d
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question e
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
<li>Sub-question f
<ol type="i">
<li>Sub-question i</li>
<li>Sub-question ii</li>
<li>Sub-question iii</li>
<li>Sub-question iv</li>
<li>Sub-question v</li>
</ol>
</li>
</ol>
</li>
</li>
<li>Question 8
<li>Question 8
Revision as of 21:38, 7 September 2024
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Objective Test Questions
Multiply 2.7 × Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^{-4}}
by 6.3 × and leave your answer in standard form.
1.7 × Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^3}
1.70 × Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^3}
1.701 × Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^3}
17.01 × Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^3}
If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 9^{(2-x)} = 3}
, find x.
1
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{2}}
2
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{2}}
In what number base is the addition 465 + 24 + 225 = 1050?
Ten
Nine
Eight
Seven
Simplify: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1\tfrac{7}{8}\times2\tfrac{2}{5}}{6\tfrac{3}{4} \div \tfrac{3}{4}}}
9
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4\frac{1}{2}}
2
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}
If Un = n(n2 + 1), evaluate U5 - U4.
18
56
62
80
If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \surd50 -K\surd8=\tfrac{2}{\surd2}}
-2
-1
1
2
A sales boy gave a change of ₦68 instead of ₦72. Calculate his percentage error.
4%
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5\frac{5}{9}%}
5Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{15}{17}%}
7%
Four oranges sell for ₦x and three mangoes sell for ₦y. Olu bought 24 oranges and 12 mangoes. How much did he pay in terms of x and y?
₦(4x + 6y)
₦(6x + 4y)
₦(24x + 12y)
₦(12x + 24y)
Simplify: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{x^2-y^2}{(x + y)^2}+\frac{(x - y)^2}{3x + 3y}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{x - y}{3}}
x + y
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{x - y}}
x - y
Solve the inequality: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2x - 5}{2}<(2 - x)}
x > 0
x < Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tfrac{1}{4}}
x > Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\tfrac{1}{2}}
x < Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\tfrac{1}{4}}
If x = 64 and y = 27, calculate: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{x^{\tfrac{1}{2}} - y^{\tfrac{1}{3}}}{y - x^\tfrac{2}{5}}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\tfrac{1}{5}}
1
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tfrac{5}{11}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tfrac{11}{43}}
Which of the following lines represents the solution of the inequality 7x < 9x —4?
Option a
Option b
Option c
Option d
If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}
x + 2y = 3 and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{2}}
x - 2y = 1, find (x + y).
3
2
1
0
Given that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p^{\tfrac{1}{3}} = \frac{\sqrt[3]{q}}{r}}
, make q the subject of the equation.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q=p\sqrt{r}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q=p^{3}r}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q=pr^3}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q=pr^{\tfrac{1}{3}}}
In a diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle}
PQR =90°; find the perimeter of the polygon PQRST.
112cm
98cm
86cm
84cm
In the diagram, the height of a flagpole (TF) and the length of its shadow (FL) are in the ratio 6:8. Using K as a constant of proportionality, find the shortest distance between T and L.
7K units
10K units
12K units
14K units
A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\sqrt{21cm}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{42}}
cm
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\sqrt{19cm}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{21cm}}
A cube and a cuboid have the same base area. The volume of the cube is 64 cm³ while that of the cuboid is 80 cm³?.
2 cm
3 cm
5 cm
6 cm
In the diagram, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{VX}}
is a tangent to the circle UYW at W. If WY//UV, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ang}
UYW = 95° and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ang}
UWY = 46°, find Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ang}
UVW.
51°
49°
39°
34°
In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vartriangle}
ZYX Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \equiv}Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vartriangle}
OMN
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vartriangle}
YZX Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \equiv}Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vartriangle}
NOM
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vartriangle}
ZXY Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \equiv}MON
XYZ NOM
In the diagram, PQRS is a rhombus and PSQ = 35°. Calculate the size of PRQ.
65°
55°
45°
35°
Find the value of m in the diagram.
34°
27°
23°
17°
In the diagram, O is the centre of the circle, OM\\XZ and ZOM = 25°. Calculate XYZ.
50°
55°
60°
65°
If sin x = and cos x = 90°. find the value of (cos x − tan x).
An object is 6 m away from the base of a mast. The angle of depression of the object from the top of the mast is 50. Find, correct to 2 decimal places, the height of the mast.
8.60 m
7.51 m
7.15 m
1.19 m
The bearing of Y from X is 060° and the bearing of Z from Y is 060°. Find the bearing of X from Z.
300°
240°
180°
120°
Which of the following is not a probability of Mary scoring 85% in a mathematics test?
0.15
0.57
0.94
1.01Use this histogram to answer questions28and29
Estimate the mode of the distribution
51.5
52.5
53.5
54.5
What is the median class?
60.5 - 70.5
50.5 - 60.5
40.5 - 50.5
30.5 - 40.5
If 2logx = 6, find the value of x.
If P = {y: 2y ≥ 6} and Q = {y: y −3 ≤ 4}, where y is an integer, find .
{3,4}
{3,7}
{3,4,5,6,7}
{4,5,6}
Find the values of k in the equation 6k² = 5k + 6.
If y varies directly as the square root of (x + 1) and y = 6 when x = 3. find x when y = 9.
8
7
6
5
The graph of the relation y = x² + 2x + k passes through the point (2,0). Find the value of k.
0
−2
−4
−8
The pie chart shows the distribution of 600 Mathematics textbooks for Arts, Business, Science and Technical classes.Use it to answer questions 35 and 36.
How many textbooks are for the Technical class?
100
150
200
250
What percentage of the total number of textbooks belongs to science?
25%
In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of RVS.
36
54
60
72
What is the locus of the point X which moves relative to two fixed points P and M on a plane such that PXM = 30°?
The bisector of the straight line joining P and M
An arc of a circle with as a chord
The bisector of angle PXM
A circle centre X and radius PM.
In the diagram, PQ is a straight line. Calculate the value of the angle labelled 2y.
130°
120°
110°
100°
When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number
11
5
Express as a simple fraction.
An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
15
12
9
6
In the diagram, reflex angle SRQ = 198° and RQP = 72°. Find the value of y.
18°
54°
92°
108°
Using the Venn diagram, find n(XY').
2
3
4
6
Given that P = x² + 4x − 2. Q = 2x and Q − P = 2, find x.
−2
−1
1
2
A pyramid has a rectangular base with dimensions 12 m by 8 m. If its height is 14 m, calculate the volume.
344 m²
448 m²
632 m²
840 m²
The slant height of a cone is 5 cm and the radius of its base is 3 cm. Find, correct to the nearest whole number, the volume of the cone. [Take π = ]
48 cm³
47 cm³
38 cm³
13 cm³
The distance between two towns is 50 km. It is represented on a map by 5 cm. find the scale used.
1 : 1,000,000
1 : 500,000
1 : 100,000
1 : 10,000
Given that (x + 2)(x² – 3x + 2) + 2(x + 2)(x – 1) = (x + 2)M, find M.
(x + 2)²
x(x + 2)
x² + 2
x² + x
An open cone with base radius 28 cm and perpendicular height 96 cm was stretched to form a sector of a circle. Calculate the area of the sector. [Take π = ].
8800 cm²
8448 cm²
4400 cm²
4224 cm²
Theory
Section A
Simplify without using tables or calculator,
Given that log102 = 0.3010 and log103 = 0.4771, evaluate correct to 2 significant figures and without using tables or calculator, log101.125.
Solve: 7x
Salem, Sunday and Shaka shared a sum of ₦1,100.00.For every ₦2.00 that Salem gets, Sunday gets 50 kobo and for every ₦4.00 Sunday gets, Shaka gets ₦2.oo. Find Shaka's share.
The present ages of a father and his son are in the ratio 10 : 3. If the son is 15 years old now, in how many years will the ratio of their ages be
The arithmetic mean of x, y and z is 6 while that of x, y, z, t, u, v and w is 9. Calculate the arithmetic mean of t, u, v and w.
The area of a circle is 154 cm². It is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. Calculate the perimeter of the third sector. [Take π = ]
A boy 1.2 m tall, stands 6 m away from the foot of a vertical lamp pole 4.2 m long. If the lamp is at the tip of the pole.
represent this information in a diagram.
calculate the:
length of the shadow of the boy cast by the lamp
angle of deviation of the lamp from the boy, correct to the nearest degree.
Section B
Two positive whole numbers P and q are such that P is greater than q and their sums is equal to three times their difference.
Express P in terms of q.
Hence, evaluate
Aman sold 100 articles at 25 for ₦66.00 and made a gain of 32%. Calculate his gain or loss per cent if he sold them at 20 for ₦50.00.
Copy and complete the table of values for the relation y = 3x² – 5x – 7.
Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 3x² – 5x – 7 for –3 ≤ x ≤ 4.
From your graph:
find the roots of the equation 3x² – 5x – 7 = 0;
estimate the minimum value of y;
calculate the gradient of the curve at the point x = 2.
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