2013 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. Multiply 2.7 × $10^{-4}$ by 6.3 × $10^{6}$ and leave your answer in standard form.
   1. 1.7 × $10^{3}$
   2. 1.70 × $10^{3}$
   3. 1.701 × $10^{3}$
   4. 17.01 × $10^{3}$
2. If $9^{(2-x)}=3$, find x.
   1. 1
   2. ${\frac {3}{2}}$
   3. 2
   4. ${\frac {5}{2}}$
3. In what number base is the addition 465 + 24 + 225 = 1050?
   1. Ten
   2. Nine
   3. Eight
   4. Seven
4. Simplify: ${\frac {1{\tfrac {7}{8}}\times 2{\tfrac {2}{5}}}{6{\tfrac {3}{4}}\div {\tfrac {3}{4}}}}$
   1. 9
   2. $4{\frac {1}{2}}$
   3. 2
   4. ${\frac {1}{2}}$
5. If U_n = n(n² + 1), evaluate U₅ - U₄.
   1. 18
   2. 56
   3. 62
   4. 80
6. If $\surd 50-K\surd 8={\tfrac {2}{\surd 2}}$
   1. -2
   2. -1
   3. 1
   4. 2
7. A sales boy gave a change of ₦68 instead of ₦72. Calculate his percentage error.
   1. 4%
   2. $5{\frac {5}{9}}\%$
   3. 5${\frac {15}{17}}\%$
   4. 7%
8. 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?
   1. ₦(4x + 6y)
   2. ₦(6x + 4y)
   3. ₦(24x + 12y)
   4. ₦(12x + 24y)
9. Simplify: ${\frac {x^{2}-y^{2}}{(x+y)^{2}}}+{\frac {(x-y)^{2}}{3x+3y}}$
   1. ${\frac {x-y}{3}}$
   2. x + y
   3. ${\frac {3}{x-y}}$
   4. x - y
10. Solve the inequality: ${\frac {2x-5}{2}}<(2-x)$
    1. x > 0
    2. x < ${\tfrac {1}{4}}$
    3. x > $2{\tfrac {1}{2}}$
    4. x < $2{\tfrac {1}{4}}$
11. If x = 64 and y = 27, calculate: ${\frac {x^{\tfrac {1}{2}}-y^{\tfrac {1}{3}}}{y-x^{\tfrac {2}{5}}}}$
    1. $2{\tfrac {1}{5}}$
    2. 1
    3. ${\tfrac {5}{11}}$
    4. ${\tfrac {11}{43}}$
12. Which of the following lines represents the solution of the inequality 7x < 9x —4?
    1. Option a
    2. Option b
    3. Option c
    4. Option d
13. If ${\frac {1}{2}}$x + 2y = 3 and ${\frac {3}{2}}$x - 2y = 1, find (x + y).
    1. 3
    2. 2
    3. 1
    4. 0
14. Given that $p^{\tfrac {1}{3}}={\frac {\sqrt[{3}]{q}}{r}}$, make q the subject of the equation.
    1. $q=p{\sqrt {r}}$
    2. $q=p^{3}r$
    3. $q=pr^{3}$
    4. $q=pr^{\tfrac {1}{3}}$
15. In a diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and $\angle$PQR =90°; find the perimeter of the polygon PQRST.

    

    1. 112cm
    2. 98cm
    3. 86cm
    4. 84cm
16. 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.

    

    1. 7K units
    2. 10K units
    3. 12K units
    4. 14K units
17. A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord.
    1. $2{\sqrt {21cm}}$
    2. ${\sqrt {42}}$cm
    3. $2{\sqrt {19cm}}$
    4. ${\sqrt {21cm}}$
18. 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?.
    1. 2 cm
    2. 3 cm
    3. 5 cm
    4. 6 cm

19. 

    In the diagram, ${\overline {VX}}$ is a tangent to the circle UYW at W. If WY//UV, $\angle$UYW = 95° and $\angle$UWY = 46°, find $\angle$UVW.
    1. 51°
    2. 49°
    3. 39°
    4. 34°
20. In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?

    

    1. $\vartriangle$ZYX $\equiv$ $\vartriangle$OMN
    2. $\vartriangle$YZX $\equiv$ $\vartriangle$NOM
    3. $\vartriangle$ZXY $\equiv$ $\vartriangle$MON
    4. $\vartriangle$XYZ $\equiv$ $\vartriangle$NOM

21. 

    In the diagram, PQRS is a rhombus and $\angle$PSQ = 35°. Calculate the size of $\angle$PRQ.
    1. 65°
    2. 55°
    3. 45°
    4. 35°

22. 

    Find the value of m in the diagram.
    1. 34°
    2. 27°
    3. 23°
    4. 17°

23. 

    In the diagram, O is the centre of the circle, OM\\XZ and $\angle$ZOM = 25°. Calculate $\angle$XYZ.
    1. 50°
    2. 55°
    3. 60°
    4. 65°
24. If sin x = ${\tfrac {5}{13}}$ and 0°≤ x ≤ 90°. find the value of (cos x − tan x).
    1. ${\tfrac {7}{13}}$
    2. ${\tfrac {12}{13}}$
    3. ${\tfrac {79}{156}}$
    4. ${\tfrac {209}{156}}$
25. 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.
    1. 8.60 m
    2. 7.51 m
    3. 7.15 m
    4. 1.19 m
26. The bearing of Y from X is 060° and the bearing of Z from Y is 060°. Find the bearing of X from Z.
    1. 300°
    2. 240°
    3. 180°
    4. 120°
27. Which of the following is not a probability of Mary scoring 85% in a mathematics test?
    1. 0.15
    2. 0.57
    3. 0.94
    4. 1.01

    

    Use this histogram to answer questions 28 and 29
28. Estimate the mode of the distribution
    1. 51.5
    2. 52.5
    3. 53.5
    4. 54.5
29. What is the median class?
    1. 60.5 - 70.5
    2. 50.5 - 60.5
    3. 40.5 - 50.5
    4. 30.5 - 40.5
30. If 2log_x$(3{\tfrac {3}{8}})$ = 6, find the value of x.
    1. ${\tfrac {3}{2}}$
    2. ${\tfrac {4}{3}}$
    3. ${\tfrac {2}{3}}$
    4. ${\tfrac {1}{2}}$
31. If P = {y: 2y ≥ 6} and Q = {y: y −3 ≤ 4}, where y is an integer, find $P\cap Q$.
    1. {3,4}
    2. {3,7}
    3. {3,4,5,6,7}
    4. {4,5,6}
32. Find the values of k in the equation 6k² = 5k + 6.
    1. ${\tfrac {-2}{3}},{\tfrac {-3}{2}}$
    2. ${\tfrac {-2}{3}},{\tfrac {3}{2}}$
    3. ${\tfrac {2}{3}},{\tfrac {-3}{2}}$
    4. ${\tfrac {2}{3}},{\tfrac {3}{2}}$
33. If y varies directly as the square root of (x + 1) and y = 6 when x = 3. find x when y = 9.
    1. 8
    2. 7
    3. 6
    4. 5
34. The graph of the relation y = x² + 2x + k passes through the point (2,0). Find the value of k.
    1. 0
    2. −2
    3. −4
    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.
35. How many textbooks are for the Technical class?
    1. 100
    2. 150
    3. 200
    4. 250
36. What percentage of the total number of textbooks belongs to science?
    1. $12{\tfrac {1}{2}}\%$
    2. $20{\tfrac {5}{6}}\%$
    3. 25%
    4. $41{\tfrac {2}{3}}\%$

37. 

    In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of $\angle$RVS.
    1. 36
    2. 54
    3. 60
    4. 72
38. What is the locus of the point X which moves relative to two fixed points P and M on a plane such that $\angle$PXM = 30°?
    1. The bisector of the straight line joining P and M
    2. An arc of a circle with ${\overrightarrow {PM}}$ as a chord
    3. The bisector of angle PXM
    4. A circle centre X and radius PM.

39. 

    In the diagram, PQ is a straight line. Calculate the value of the angle labelled 2y.
    1. 130°
    2. 120°
    3. 110°
    4. 100°
40. When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number
    1. 11
    2. ${\tfrac {15}{2}}$
    3. 5
    4. ${\tfrac {5}{2}}$
41. Express ${\tfrac {2}{x+3}}-{\tfrac {1}{x-2}}$ as a simple fraction.
    1. ${\tfrac {x-7}{x^{2}+x-6}}$
    2. ${\tfrac {x-1}{x^{2}+x-6}}$
    3. ${\tfrac {x-2}{x^{2}+x-6}}$
    4. ${\tfrac {x+7}{x^{2}+x-6}}$
42. An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
    1. 15
    2. 12
    3. 9
    4. 6

43. 

    In the diagram, ${\overline {ST}}//{\overline {PQ}}$ reflex angle SRQ = 198° and $\angle$RQP = 72°. Find the value of y.
    1. 18°
    2. 54°
    3. 92°
    4. 108°

44. 

    Using the Venn diagram, find n(X$\cap$Y').
    1. 2
    2. 3
    3. 4
    4. 6
45. Given that P = x² + 4x − 2. Q = 2x and Q − P = 2, find x.
    1. −2
    2. −1
    3. 1
    4. 2
46. A pyramid has a rectangular base with dimensions 12 m by 8 m. If its height is 14 m, calculate the volume.
    1. 344 m²
    2. 448 m²
    3. 632 m²
    4. 840 m²
47. 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 = ${\tfrac {22}{7}}$]
    1. 48 cm³
    2. 47 cm³
    3. 38 cm³
    4. 13 cm³
48. The distance between two towns is 50 km. It is represented on a map by 5 cm. find the scale used.
    1. 1 : 1,000,000
    2. 1 : 500,000
    3. 1 : 100,000
    4. 1 : 10,000
49. Given that (x + 2)(x² – 3x + 2) + 2(x + 2)(x – 1) = (x + 2)M, find M.
    1. (x + 2)²
    2. x(x + 2)
    3. x² + 2
    4. x² + x
50. 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 = ${\tfrac {22}{7}}$].
    1. 8800 cm²
    2. 8448 cm²
    3. 4400 cm²
    4. 4224 cm²

Theory

Section A

1. 1. Simplify without using tables or calculator, ${\tfrac {{\tfrac {3}{4}}(3{\tfrac {3}{8}}+1{\tfrac {5}{6}})}{2{\tfrac {1}{8}}-1{\tfrac {1}{2}}}}$
   2. Given that log₁₀2 = 0.3010 and log₁₀3 = 0.4771, evaluate correct to 2 significant figures and without using tables or calculator, log₁₀1.125.
2. 1. Solve: 7x + 4 < ${\tfrac {1}{2}}$ (4x + 3)
   2. 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 ₦2.00. Find Shaka's share.
3. 1. 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 2:1?
   2. 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.
4. 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 = ${\tfrac {22}{7}}$]
5. 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.
   1. represent this information in a diagram.
   2. calculate the:
      1. length of the shadow of the boy cast by the lamp
      2. angle of deviation of the lamp from the boy, correct to the nearest degree.

Section B

6. 1. 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.
      1. Express P in terms of q.
      2. Hence, evaluate ${\tfrac {p^{2}+q^{2}}{Pq}}$
   2. 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.
7. 1. Copy and complete the table of values for the relation y = 3x² – 5x – 7.

   x	-3	-2	-1	0	1	2	3	4
   y	35			-7	-9		5

   2. 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.
   3. From your graph:
      1. find the roots of the equation 3x² – 5x – 7 = 0;
      2. estimate the minimum value of y;
      3. calculate the gradient of the curve at the point x = 2.
8. 1. If (3 – x), 6, (7 – 5x) are consecutive terms of a geometric progression (G.P) with constant ratio r > 0, find the:
      1. values of x:
      2. constant ratio

   2. 

      In the diagram, /AB/ = 3cm, /BC/ = 4cm, /CD/ = 6cm and /DA/ = 7cm. Calculate $\angle$ADC, correct to the nearest degree.
9. 1. Using ruler and a pair of compasses only, construct:
      1. a trapezium WXYZ, such that /WX/ = 10.2cm, /XY/ = 5.6cm, /YZ/ = 5.8cm, $\angle$WXY = 60° and ${\overline {WX}}$ is parallel to ${\overline {YZ}}$
      2. a perpendicular from Z to meet ${\overline {WX}}$ at N
   2. Measure:
      1. /WZ/;
      2. /ZN/

10. 1. 

       A segment of a circle is cut off from a rectangular board as shown in the diagram. If the radius of the circle is $1{\tfrac {1}{2}}$ times the length of the chord, calculate, correct to 2 decimal places, the perimeter of the remaining portion. [Take π = ${\tfrac {22}{7}}$]
    2. Evaluate without using calculators or tables, ${\tfrac {3}{\sqrt {3}}}[{\tfrac {2}{\sqrt {3}}}-{\tfrac {\sqrt {12}}{6}}]$
11. The frequency distribution table shows the marks obtained by 100 students in a Mathematics test.

    Marks(%)	1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100
    Frequency	2	3	5	13	19	31	13	9	4	1

    1. Draw a cumulative frequency curve for the distribution.
    2. Use the graph to find the:
       1. 60^th percentile;
       2. probability that a student passed the test if the pass mark was fixed at 35%.
12. An aeroplane flies due north from a town T on the equator at a speed of 950km per hour for 4 hours to another town P. It then flies eastwards to town Q on longitude 65°E. If the longitude of Tis 15°E
    1. represent this information in a diagram,
    2. calculate the:
       1. latitude of P and Q, correct to 4 significant figures [Take π = ${\tfrac {22}{7}}$, (Radius of the earth) = 6400km]
13. When one end of a ladder, LM is placed against a vertical wall at a point 5 metres above the ground, the ladder makes an angle of 37° with the horizontal ground.
    1. Represent this information in a diagram
    2. Calculate, correct to 3 significant figures, the length of the ladder.
    3. If the foot of the ladder is pushed towards the wall by 2 metres, calculate, correct to the nearest degree, the angle which the ladder now makes with the ground.