2000 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. Express ${\frac {7}{19}}$ as a percentage, correct to 1 decimal place.
   1. 2.7%
   2. 3.7%
   3. 27.1%
   4. 36.8%
2. Express 398753 correct to three significant figures.
   1. 398000
   2. 398700
   3. 398800
   4. 399000
3. Simplify ${\frac {10}{\sqrt {32}}}$
   1. ${\frac {5}{4}}{\sqrt {2}}$
   2. ${\frac {4}{5}}{\sqrt {2}}$
   3. ${\frac {5}{16}}{\sqrt {2}}$
   4. ${\frac {16}{5}}{\sqrt {2}}$
4. Find the missing number in base seven addition: ${\begin{array}{r}4\;3\;2\;1_{7}\\1\;2\;3\;4_{7}\\+\ ****_{7}\\\hline 1\;2\;3\;4\;1_{7}\\\end{array}}$
   1. 3453
   2. 5556
   3. 6016
   4. 13453
5. What fraction must be subtracted from the sum of $2{\frac {1}{6}}$ and $2{\frac {7}{12}}$ to give $3{\frac {1}{4}}$?
   1. ${\frac {1}{2}}$
   2. ${\frac {1}{4}}$
   3. ${\frac {3}{4}}$
   4. ${\frac {5}{12}}$
6. Simplify $\left({\frac {16}{81}}\right)^{-{\frac {3}{4}}}\times \surd {\frac {100}{81}}$
   1. ${\frac {80}{243}}$
   2. ${\frac {20}{27}}$
   3. ${\frac {25}{6}}$
   4. ${\frac {15}{4}}$
7. Which number is a perfect cube?
   1. 350
   2. 504
   3. 950
   4. 1728
8. If $104_{x}=68$, find the value of $x$
   1. 5
   2. 7
   3. 8
   4. 9
9. The ages of three men are in ratio 3:4:5. If difference between the ages of the oldest and youngest is 18 years, find the sum of the ages of the three men.
   1. 45 years
   2. 72 years
   3. 108 years
   4. 216 years
10. Given that $109_{4}x=-3$, find $x$
    1. ${\frac {1}{81}}$
    2. ${\frac {1}{64}}$
    3. 64
    4. 81
11. Given that the logarithm of a number is $1.8732$, find correct to 2 significant figures, the square root of the number.
    1. 0.29
    2. 0.75
    3. 0.86
    4. 0.93
12. A car moving at an average speead of $30{\text{kmh}}^{-1}$. How long does it take to cover 200m in?
    1. 2.4 sec
    2. 24 sec
    3. 144 sec
    4. 240 sec
13. A man bought a television set on hire purchase for ₦$25,000$, out of which he paid ₦$10,000$. If he is allowed to pay the balance in eight equal instalments, find the value of each instalment.
    1. ₦$\,1,250$
    2. ₦$\,1,578$
    3. ₦$\,1,875$
    4. ₦$\,3,125$
A tree is $8\,{\text{km}}$ due south of a building. Kofi is standing $8\,{\text{km}}$ west of the tree. Use this information to answer questions 14 and 15
14. How far is Kofi from the building?
    1. $4{\sqrt {2}}\,{\text{km}}$
    2. $8\,{\text{km}}$
    3. $8{\sqrt {2}}\,{\text{km}}$
    4. $16\,{\text{km}}$
15. Find the bearing of Kofi from the building.
    1. $315^{\circ }$
    2. $270^{\circ }$
    3. $225^{\circ }$
    4. $135^{\circ }$
16. Which of the following bearings is equivalent to $S50^{\circ }W$?
    1. $040^{\circ }$
    2. $130^{\circ }$
    3. $220^{\circ }$
    4. $230^{\circ }$
17. In the diagram, AB is a vertical pole and BC is horizontal. If $|AC|=10\,{\text{m}}$ and $|BC|=5\,{\text{m}}$, calculate the angle of depression of C from A.
    1. $63^{\circ }$
    2. $60^{\circ }$
    3. $45^{\circ }$
    4. $27^{\circ }$
The bar chart shows the distribution of marks scored by a group of students in a test.
18. How many students scored 4 marks and above?
    1. 15
    2. 11
    3. 10
    4. 7
19. How many students took the test?
    1. 38
    2. 22
    3. 15
    4. 11
20. Calculate the standard deviation of the following: $2,3,6,2,5,0,4,2$
    1. 1.5
    2. 1.7
    3. 1.8
    4. 1.9
21. The probabilities that Kodjo and Adoga passed an examination are ${\frac {3}{4}}$ and ${\frac {3}{5}}$ respectively. Find the probability of both boys failing the examination.
    1. ${\frac {1}{10}}$
    2. ${\frac {3}{10}}$
    3. ${\frac {9}{20}}$
    4. ${\frac {2}{3}}$
22. Which of the following triangles are congruent?
    1. I and II only
    2. II and IV only
    3. I and II only
    4. II and III only
23. Which of the following statements is/are not true about a rectangle? I Each diagonal cuts the rectangle into two congruent triangles. II A rectangle has four lines of symmetry. III The diagonals intersect at right angles.
    1. I and II only
    2. III only
    3. II only
    4. II and III only
24. In the diagram, PQRS is a circle with centre O. POR is a diameter and $\angle PBQ=40^{\circ }$. Calculate $\angle OSR$.
    1. $30^{\circ }$
    2. $40^{\circ }$
    3. $45^{\circ }$
    4. $50^{\circ }$
25. Each side of a regular convex polygon subtends an angle of $30^{\circ }$ at its centre. Calculate each interior angle.
    1. $75^{\circ }$
    2. $150^{\circ }$
    3. $160^{\circ }$
    4. $168^{\circ }$
26. If the interior angles of a hexagon are $107^{\circ },2x^{\circ },150^{\circ },95^{\circ },(2x-15)^{\circ }$ and $123^{\circ }$, find $x$.
    1. $57{\frac {1}{2}}^{\circ }$
    2. $65^{\circ }$
    3. $106^{\circ }$
    4. $120^{\circ }$
27. In the diagram, POS and ROT are straight lines. OPQR is a parallelogram. $|OS|=|OT|$ and $\angle OST=50^{\circ }$. Calculate $\angle OPQ$.
    1. $160^{\circ }$
    2. $140^{\circ }$
    3. $120^{\circ }$
    4. $100^{\circ }$
28. Given that $x=-{\frac {1}{2}}$ and $y=4$, evaluate $3x^{2}y+xy^{2}$.
    1. $-5$
    2. $-1$
    3. $4$
    4. $11$
29. Given that $27^{\left(1+x\right)}=9$, find $x$.
    1. $-3$
    2. $-{\frac {1}{3}}$
    3. $3$
    4. $2$
30. Given that $(2x+7)$ is a factor of $2x^{2}+3x-14$, find the other factor.
    1. $x+2$
    2. $2-x$
    3. $x-2$
    4. $x+1$
31. Given that $(2x+7)$ is a factor of $2x^{2}+3x-14$, find the other factor.
    1. $x+2$
    2. $2-x$
    3. $x-2$
    4. $x+1$
32. Simplify ${\frac {1}{x-3}}\;\;\;{\frac {3(x-1)}{x^{2}-9}}$
    1. ${\frac {x-1}{x-3}}$
    2. ${\frac {-2}{x+3}}$
    3. ${\frac {x-1}{x+3}}$
    4. ${\frac {4x}{2-9}}$
33. Which of the following number line represents the inequality $2\leq x<9$?
34. Form an inequality for a distance $d$ metres which is more than 18m but not more than 23m.
    1. $18<d\leq 23$
    2. $18\leq d<23$
    3. $18\leq d\leq 23$
    4. $d<18$ or $d>23$
35. Find the equation whose roots are -8 and 5.
    1. $x^{2}+13x+40=0$
    2. $x^{2}-13x-40=0$
    3. $x^{2}-3x+40=0$
    4. $x^{2}+3x-40=0$
36. Make $t$ the subject of the formula ${\sqrt {\frac {t-p}{r}}}$
    1. ${\frac {rk^{2}+p}{m^{2}}}$
    2. ${\frac {rk^{2}+pm^{2}}{m^{2}}}$
    3. ${\frac {rk^{2}-p}{m^{2}}}$
    4. ${\frac {rk^{2}-p^{2}}{m^{2}}}$
37. Solve the equation $3y^{2}=27y$
    1. $y=0$ or $3$
    2. $y=0$ or $9$
    3. $y=-3$ or $3$
    4. $y=3$ or $9$
38. Find the value of $x$ such that the expression ${\frac {1}{x}}+{\frac {4}{3x}}-{\frac {5}{6x}}+1$ equals zero
    1. ${\frac {1}{6}}$
    2. ${\frac {1}{4}}$
    3. ${\frac {-3}{2}}$
    4. ${\frac {-7}{6}}$
39. Given that $p$ varies directly as $q$ while $q$ varies inversely as $r$, which statement is true?
    1. $r$ varies directly as $p$
    2. $p$ varies inversely as $r$
    3. $p$ varies directly as $r$
    4. $q$ varies inversely as $p$
40. In the diagram, PQS is a circle with center O. RST is a tangent at S and $\angle SOP=96^{\circ }$. Find $\angle PST$.
    1. $42^{\circ }$
    2. $48^{\circ }$
    3. $60^{\circ }$
    4. $66^{\circ }$
41. A bicycle wheel of radius 42 cm is rolled over a distance of 66 metres. How many revolutions does it make? ($\pi ={\frac {22}{7}}$)
    1. 2.5
    2. 5
    3. 25
    4. 50
42. The height of a pyramid on a square base is 15cm. If the volume is 80cm³, find the area of the square base.
    1. 8cm²
    2. 9.6cm²
    3. 16cm²
    4. 25cm²
43. A tap leaks at the rate of 2cm³ per second. How long will it take to fill a container of 45 litres capacity? (1 litre = 1000 cm³)
    1. 8 hours
    2. 6 hours 15min
    3. 4 hrs 25min
    4. 3hrs
44. The lengths of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm², find the perpendicular distance between the sides.
    1. 5.0cm
    2. 6.9cm
    3. 10.0cm
    4. 20.0cm
45. The arc of a circle 50cm long subtends an angle of 75° at the center of the circle. Find, correct to 3 significant figures, the radius of the circle. [$\pi ={\frac {22}{7}}$].
    1. 8.74cm
    2. 38.2cm
    3. 61.2cm
    4. 76.4cm
46. In the diagram, |PQ| = |PS| and |RQ| = |RS|. Which statement is true?
    1. $\angle QPS=\angle QRS$
    2. |PO| = |RO|
    3. OR ∥ PS
    4. $\angle PQR=\angle PSR$
47. The area of a circle is 38.5cm². Find its diameter ($\pi ={\frac {22}{7}}$).
    1. 22cm
    2. 14cm
    3. 7cm
    4. 6cm
48. Find the volume (in cm³) of the solid.
    1. 100 cm³
    2. 150cm³
    3. 175cm³
    4. 250cm³
49. Solve the equation $3+5x-2x^{2}=0$
    1. $-{\frac {1}{2}}$, -3
    2. 2, 3
    3. -2, 3
    4. $-{\frac {1}{2}}$, 3
50. If the simple interest on ₦2,000 after 9 months is ₦60, at what rate per annum is the interest charged?
    1. 2${\frac {1}{4}}$%
    2. 4%
    3. 5%
    4. 6%

Theory

Section A

1. 1. Evaluate and express in standard form: ${\frac {4.56\times 3.6}{0.12}}$
   2. Without using mathematical tables or calculator, evaluate $(73.8)^{2}-(26.2)^{2}$
   3. Simplify ${\sqrt {1{\frac {19}{81}}}}$ expressing your answer in the form ${\frac {a}{b}}$ where a and b are positive integers.
2. 1. Given $\cos x=0.7431$, 0° < x < 90°, use tables to find the values of:
      1. $2\sin x$
      2. $\tan {\frac {x}{2}}$
   2. The interior angles of a pentagon are in ratio 2:3:4:4:5. Find the value of the largest angle.
3. 1. Given $y=ax^{2}-bx-12$, find values of x when $a=1$, $b=2$, $y=3$
   2. Solve: ${\sqrt {x^{2}+1}}={\frac {5}{4}}$, find the positive value of x.
4. Using ruler and compasses only:
   1. Construct ΔPQR such that $|PQ|=7cm$, $|PR|=6cm$, $\angle PQR=60^{\circ }$
   2. Locate point M, the mid-point of PQ
   3. Measure $\angle RMO$
5. The pie chart shows the distribution of marks scored by 200 pupils in a test.
   1. How many pupils scored:
      1. between 41 and 50 marks?
      2. above 80 marks?
   2. What fraction of the pupils scored at most 50 marks?
   3. What is the modal class?

Section B

6. 1. The table above shows the number of limes and apples of the same size in a bag. If two of the fruits are picked at random, one at a time, without replacement, find the probability that:
      1. both are good limes
      2. both are bad fruits
      3. one is a good apple and the other a bad lime
   2. Solve: $\log _{3}(4x+1)-\log _{3}(3x-5)=2$
7. 1. A man earns ₦150,000 per annum. He is allowed a tax free pay of ₦40,000. If he pays 25 kobo in the naira as tax on his taxable income, how much has he left?
   2. A bookshop had 650 copies of a book for sale. The books were marked at ₦75 per copy in order to make a profit of 30%. A bookseller bought 300 copies at 5% discount. If the remaining copies are sold at ₦75 each, calculate the percentage profit the bookshop would make on the whole?
8. 1. Copy and complete the table of values for the relation $y=x^{2}-2x-5$
   2. Draw the graph of the relation $y=x^{2}-2x-5$ using a scale of 2cm to 1 unit on the x-axis and 2cm to 2 units on the y-axis
   3. Using the same axes, draw the graph of $y=2x-3$
   4. Obtain the equation in the form $ax^{2}+bx+c=0$ where a, b and c are integers, the equation which is satisfied by the x-coordinate of the points of intersection of the two graphs
   5. From your graphs, determine the roots of the equation obtained in (d) above
9. 1. The mean of 1, 2, $x$, 11, $y$, 14 is 8 and the median is 9. Find the values of $x$ and $y$
   2. In the diagram, MN || PQ. |LM| = 3cm and |LP| = 4cm. If the area of ΔLMN is 18cm2, find the area of quadrilateral MPQN.
10. 1. A surveyor walks 100m up a hill which slopes at an angle of $24^{\circ }$ to the horizontal. Calculate correct to the nearest metre, the height through which he rises
    2. In the diagram, ABC is an isosceles triangle, $|AB|=|AC|=5\,{\text{cm}}$ and $|BC|=8\,{\text{cm}}$. Calculate, correct to the nearest degree, $\angle BAC$
    3. Two boats 70 meters apart and on opposite sides of a light-house. The angles of elevation of the top of the light-house from the two boats are $71.6^{\circ }$ and $45^{\circ }$. Find the height of the light-house. [Take $\tan 71.6^{\circ }=3$]
11. 1. A cylindrical well of radius 1 metre is dug out to a depth of 8 metres.
       1. calculate, in $m^{3}$, the volume of soil dug out
       2. If the soil is used to raise the level of rectanglular floor of a room 4m by 12m, calculate, correct to the nearest cm, the thickness of the new layer of soil. [Take $\pi ={\frac {22}{7}}$]
    2. The diagram shows a quadrilateral ABCD in which $\angle DAB$ is a right angle. $|AB|=3.3cm,|BC|=3.9cm,|CD|=5.2cm\;and\;|DA|=5.6cm.$
       1. find the length of $BD$
       2. Show that $\angle BCD=90^{\circ }$
12. 1. The first term of an Arithmetic progression (A,P) is 8. The ratio of the 7th term to the 9th term is 5:8. Calculate the common difference of the progression.
    2. A sphere of radius 2cm is of mass 11.2g. Find:
       1. the volume of the sphere
       2. the density of the sphere
       3. the mass of a sphere of the same material but with radius 3cm. [Take $\pi ={\frac {22}{7}}$]
13. <liTwo places X and Y on the equator are on longitudes 67°E and 123°E respectively.
    1. What is the distance between them along the equator?
    2. How far is X from the North Pole? [Take $\pi ={\frac {22}{7}}$ and radius of the Earth as 6400 km]
    1. In the diagram, POR is a circle centre O. N is the midpoint of chord PQ. $|PQ|=8\,{\text{cm}}$, $|ON|=3\,{\text{cm}}$, $\angle ONR=20^{\circ }$). Calculate the size of $\angle ORN$ to the nearest degree