2011 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. If ₦112.00 exchanges for D14.94. Calculate the value of D1.00 in naira
   1. 0.13
   2. 7.49
   3. 8.00
   4. 13.00
2. Solve for x in the equation ${\tfrac {3}{5}}{\bigl (}2x-1)$ = ${\tfrac {1}{4}}{\bigl (}5x-3{\bigr )}$
   1. 0
   2. 1
   3. 2
   4. 3
3. Given that cos x° = ${\tfrac {1}{r}}$_’ express tan x° in terms of r.

   

   1. ${\tfrac {1}{\sqrt {r}}}$
   2. ${\sqrt {r}}$
   3. ${\sqrt {r^{2}+1}}$
   4. ${\sqrt {r^{2}-1}}$
4. The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?

   

   1. △ PQK
   2. △PKS
   3. △SKR
   4. △PSR
5. In the diagram, OP and OR are radii, |PQ| =|QR| and reflex $\angle$POR is 240°. Calculate the value of x.

   

   1. 60°
   2. 55°
   3. 50°
   4. 45°
6. If a number is chosen at random from the set (x: 4≤x≤15), find the probability that it is a multiple of 3 or a multiple of 4.
   1. ${\tfrac {1}{12}}$
   2. ${\tfrac {5}{12}}$
   3. ${\tfrac {1}{2}}$
   4. ${\tfrac {11}{12}}$
7. Solve the equations: ${\begin{cases}3x-2y=7\\x+2y=-3\end{cases}}$
   1. x = 1, y = -2
   2. x = 1, y = 3
   3. x = 2, y = -1
   4. x = 4, y = -3
8. One of the factors of (mn − nq − n² + mq) is (m − n). The other factor is:
   1. (n − q)
   2. (q − n)
   3. (n + q)
   4. (q − m)
9. A cylindrical container has a base radius of 14cm and height 18cm. How many litres, correct to the nearest litre, of liquid can it hold? [Take π = ${\tfrac {22}{7}}$ ]

   

   1. 11
   2. 14
   3. 16
   4. 18
10. Find the size of the angle marked x in the diagram.

    

    1. 108°
    2. 112°
    3. 128°
    4. 142°
11. A regular polygon of a n sides has each exterior angle equal to 45°. Find the value of n.
    1. 6
    2. 8
    3. 12
    4. 15
12. Esther was facing S 20° W. She turned 90° in the clockwise direction. What direction is she facing?

    

    1. N 70° W
    2. S 70° W
    3. N 20° W
    4. S 20° E

       

       The histogram shows the age distribution of members of a club. Use the information to answer questions 13 and 14.
13. How many members are in the club?
    1. 52
    2. 50
    3. 48
    4. 40
14. What is their modal age?
    1. 44.5
    2. 42.5
    3. 41.5
    4. 40.5
15. The cross section of a uniform prism is a right-angled triangle with sides 3, 4 and 5 cm. If its length is 10 cm, calculate the total surface area.
    1. 142 cm²
    2. 132 cm²
    3. 122 cm²
    4. 112 cm²
16. Form the equation whose roots are x = ${\tfrac {1}{2}}$ and −${\tfrac {2}{3}}$.
    1. 6x² − x + 2 = 0
    2. 6x² − x − 2 = 0
    3. 6x² + x + 2 = 0
    4. 6x² + x − 2 = 0
17. Simplify: ${\tfrac {\log {\sqrt {27}}}{\log {\sqrt {81}}}}$.
    1. 3
    2. 2
    3. ${\tfrac {3}{2}}$
    4. ${\tfrac {3}{4}}$
18. Which of these angles can be constructed using ruler and a pair of compasses only?
    1. 115°
    2. 125°
    3. 135°
    4. 145°
19. The perimeter of a sector of a circle of radius 4 cm is ( π + 8) cm. Calculate the angle of the sector.
    1. 45°
    2. 60°
    3. 75°
    4. 90°
20. The length of a piece of stick is 1.75 m. A girl measured it as 1.80 m. Find the percentage error.
    1. ${\tfrac {284}{7}}$%
    2. ${\tfrac {29}{7}}$%
    3. 5%
    4. ${\tfrac {20}{7}}$%
21. What is the value of 3 in the number 42.7531?
    1. ${\tfrac {3}{10000}}$
    2. ${\tfrac {3}{1000}}$
    3. ${\tfrac {3}{100}}$
    4. ${\tfrac {3}{10}}$
22. The height of a cylinder is equal to its radius. If the volume is 0.216πm³, calculate the radius.
    1. 0.46m
    2. 0.60m
    3. 0.87m
    4. 1.80m
23. In the diagram MN//OP, $\angle$NMQ = 65° and $\angle$QOP = 125°. What is the size of $\angle$MQR?

    

    1. 110°
    2. 120°
    3. 130°
    4. 160°
24. A circle is divide into two sectors in the ratio 3:7. If the radius of the circle is 7 cm, calculate the length of the minor arc of the circle.
    1. 18.85 cm
    2. 13.20 cm
    3. 12.30 cm
    4. 11.30 cm

       

       Use the cumulative frequency curve to answer questions 25 and 26.
25. Estimate the median of the data represented on the graph.
    1. 35.5
    2. 36.5
    3. 37.5
    4. 38.5
26. What is the 80th percentile?
    1. 45.5
    2. 46.5
    3. 47.5
    4. 48.5
27. From the diagram which of the following statements are true? I. m = q II. n = q III. n + p = 180° IV. p + m =180°

    

    1. I and III
    2. I and IV
    3. II and III
    4. II and IV
28. Factorize the expression am + bn − an − bm.
    1. (a − b)(m + n)
    2. (a − b)(m − n)
    3. (a + b)(m − n)
    4. (a + b)(m + n)

       

       The graph represents the relation y = x² − 3x − 3. Use it to answer questions 29 and 30.
29. Find the values of x for which x² − 3x = 7
    1. −1.55, 4.55
    2. 1.55, −4.55
    3. −1.55, −4.55
    4. 1.55, 4.55
30. What is the equation of the line of symmetry of the graph?
    1. x = 0.5
    2. x = 1.0
    3. x = 1.5
    4. x = 4.5
31. Simplify ${\tfrac {m}{n}}+{\tfrac {{\bigl (}m-1{\bigr )}}{5n}}-{\tfrac {{\bigl (}m-2{\bigr )}}{10n}}$ where n ≠ 0
    1. ${\tfrac {m-3}{10n}}$
    2. ${\tfrac {11m}{10n}}$
    3. ${\tfrac {m+1}{10n}}$
    4. ${\tfrac {11m+4}{10n}}$
32. If ${\sqrt {72}}+{\sqrt {32}}-3{\sqrt {18}}=x{\sqrt {8}}$ , find the value of x.
    1. 1
    2. ${\tfrac {3}{4}}$
    3. ${\tfrac {1}{2}}$
    4. ${\tfrac {1}{4}}$
33. G varies directly as the square of H. If G is 4 when H is 3, find H when G = 100.
    1. 15
    2. 25
    3. 75
    4. 225
34. Given that n(P) = 19, n(P$\cup$Q) =38 and n(P$\cap$Q) = 7, find n(Q).
    1. 26
    2. 31
    3. 36
    4. 50
35. What must be added to (2x − 3y) to get (x − 2y)?
    1. 5y − x
    2. y − x
    3. x − 5x
    4. x − y
36. Simplify $1{\tfrac {3}{4}}-{\bigl (}2{\tfrac {1}{3}}+4{\bigr )}$
    1. $3{\tfrac {5}{12}}$
    2. $2{\tfrac {7}{12}}$
    3. $-4{\tfrac {7}{12}}$
    4. $-5{\tfrac {5}{12}}$
37. In the diagram, STUV is a straight line. $\angle$TSY = $\angle$UXY = 40° and $\angle$VUW = 110°. Calculate $\angle$TYW.

    

    1. 150°
    2. 140°
    3. 130°
    4. 120°
38. Given that 124_x = 7(14_x), find the value of x.
    1. 12
    2. 11
    3. 9
    4. 8
39. Find the smaller value of x that satisfies the equation: x² + 7x + 10 = 0
    1. −5
    2. −2
    3. 2
    4. 5
40. The perpendicular bisectors of the sides of an acute-angled triangle are drawn. Which of these statements is correct? They intersect:
    1. on one of the vertices
    2. at a midpoint of a side
    3. inside the triangle
    4. outside the triangle
41. A rectangular garden measures 18.6 m by 12.5 m. Calculate correct to three significant figures, the area of the garden.
    1. 230 m²
    2. 321 m²
    3. 232 m²
    4. 233 m²
42. John pours 96 litres of red oil into a rectangular container with length 220 cm and breadth 40 cm. Calculate, correct to the nearest cm, the height of the oil in the container.
    1. 11 cm
    2. 18 cm
    3. 21 cm
    4. 34 cm
43. In a quiz competition, a student answers n questions correctly and was given D(n + 50) for each questions correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?
    1. 18
    2. 15
    3. 12
    4. 10
44. The Venn diagram shows the number of students in a class who like reading (R), dancing (D) and swimming (S). How many students like dancing and swimming?

    

    1. 7
    2. 9
    3. 11
    4. 13
45. A shopkeeper allows a discount of 15% on the marked price of a mobile phone. If a customer paid GH¢170.00 for a mobile phone, what was the marked price of the phone?
    1. GH¢144.50
    2. GH¢195.40
    3. GH¢200.00
    4. GH¢225.00
46. If 27^x = 9^y, find the value of ${\tfrac {x}{y}}$
    1. ${\tfrac {1}{3}}$
    2. ${\tfrac {2}{3}}$
    3. $1{\tfrac {1}{2}}$
    4. 3
47. In the diagram, PQ//TS, PR//TU, reflex angle QPS = 245°, angle PŜT = 115°, $\angle$STU = 65° and $\angle$RPS = x. Find the value of x.

    

    1. 80°
    2. 70°
    3. 60°
    4. 50°
48. Illustrate the inequality -1< 3x + 5 < 14 on a number line.

    

49. A boy looks through a window of a building and sees a mango fruit on the ground 50 m away from the foot of the building. If the window is 9 m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window.
    1. 9°
    2. 10°
    3. 11°
    4. 12°
50. If $E={\tfrac {MN}{S+N}}$ and E = 75, M = 120, N = 5000, find S.
    1. 1000
    2. 2000
    3. 3000
    4. 4000

Theory

Section A

1. 1. Simplify: ${\tfrac {{\tfrac {1}{2}}of{\tfrac {1}{4}}\div {\tfrac {1}{3}}}{{\tfrac {1}{6}}-{\tfrac {3}{4}}+{\tfrac {1}{2}}}}$
   2. Given that ${\sqrt {x}}$ = 10^1.6741, without using calculators, find the value of x.
2. 1. Make q the subject of the relation $t={\sqrt {{\tfrac {pq}{r}}-r^{2}q}}$
   2. If $9^{1-x}=27^{y}$ and $x-y=-1{\tfrac {1}{2}}$, find the value of x + y
3. A sector of a circle with radius 21 cm has an area of 280 cm².
   1. Calculate, correct to 1 decimal place, the perimeter of the sector.
   2. If the sector is bent such that its straight edges coincide to form a cone, calculate, correct to the nearest degree, the vertical angle of the cone. [Take π = ${\tfrac {22}{7}}$]

4. 

   1. In the diagram, PQRST is a quadrilateral. PT//QS, $\angle$PTQ = 42°, $\angle$TSQ = 38° and $\angle$QSR = 30°. If $\angle$QTS = x and $\angle$PQT = y, find:
      1. x;
      2. y

         

   2. In the diagram, PQRS is a circle centre O. If PÔQ = 150°, $\angle$QSR = 40° and $\angle$SQP = 45°. Calculate $\angle$RQS.
5. A library received a $1,300 grant. It spends 10% of the grant on magazine subscriptions, 35% on new books, 15% to repair damaged books, 30% to buy new furniture and 10% to train library staff.
   1. Represent this information on a pie chart
   2. Calculate, correct to the nearest whole number, the percentage increase of the amount for buying new books over that of new furniture.

Section B

6. In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 Mathematics and Accounts only, 6 Mathematics only, 9 Accounts only, 2 Accounts and Economics only. If each student offered at least one of the subjects;
   1. How many students failed in all the subjects?
   2. Find the percentage number who failed in at least one of Economics and Mathematics;
   3. Calculate the probability that a student at random failed in Accounts.
7. 1. Divide ${\tfrac {x^{2}-4}{x^{2}+4}}$ by ${\tfrac {x^{2}-4x+4}{x+1}}$

   2. 

      The diagram shows the graphs of y = ax² + bx + c and y = mx + k where a, b, c, m and k are constants. Use the graph(s) to:
      1. Find the roots of the equation ax² + bx + c = mx + k;
      2. Determine the values of a, b and c using the coordinates of points L, M and N, hence write down the equation of the curve;
      3. Determine the line of symmetry of the curve y = ax² + bx + c.
8. 1. Given that sin x = 0.6 and 0°≤x≤90°, evaluate 2 cos x + 3 sin x, leaving your answer in the form ${\tfrac {m}{n}}$ where m and n are integers.

   2. 

      In the diagram, a semi circle WXYZ with centre O is inscribed in an isosceles triangle ABC. If /AC/ = /BC/, /OC/ = 30 cm and AĈB = 130°. Calculate, correct to one decimal place,
      1. radius of the circle;
      2. area of the shaded portion. [Take π = ${\tfrac {22}{7}}$]
9. Using ruler and a pair of compasses only,
   1. construct a rhombus PQRS of side 7 cm and $\angle$PQR = 60°;
   2. locate point X lies on the locus of points equidistant from PQ and QR and also equidistant from Q and R;
   3. Measure /XR/.
10. 1. The total surface area of two spheres are in the ratio 9:49. If the radius of the smaller sphere is 12 cm, find, correct to the nearest cm³, the volume of the bigger sphere.
    2. A cyclist starts from a point X and rides 3 km due West to a point Y. At Y, he changes direction and rides 5 km North-West to a point Z
       1. How far is he from the starting point. Correct to the nearest km?
       2. Find the bearing of Z from X, to the nearest degree.
11. The table shows the scores obtained when a fair die was thrown a number of times. If the probability of obtaining a 3 is 0.26, find the;

    Score	1	2	3	4	5	6
    Frequency	2	5	x	11	9	10

    1. median;
    2. standard deviation of the distribution.
12. 1. The area of trapezium PQRS is 60 cm². PQ//RS, /PQ/ = 15 cm, /RS/ = 25 cm and $\angle$PSR = 30°. Calculate the:
       1. perpendicular height of PQRS;
       2. /PS/
    2. Ade received ${\tfrac {3}{5}}$ of a sum of money, Nelly ${\tfrac {1}{3}}$ of the remainder while Austin took the rest. If Austin's share is greater than Nelly's share by ₦3,000, how much did Ade receive?
13. 1. P varies directly as Q and inversely as the square of R. If P = 1 when Q = 8 and R = 2, find the value of Q when P = 3 and R = 5
    2. An aeroplane flies from town A(20°N, 60°E) to town B(20°N, 20°E).
       1. If the journey takes 6 hours, calculate, correct to 3 significant figures, the average speed of the aeroplane.
       2. If it then flies due North from town B to town C, 420 km away. Calculate, correct to the nearest degree, the latitude of town C. [Take radius of the earth = 6400 km and π = 3.142].

    QUESTIONS 14 AND 15 ARE FOR CANDIDATES IN GHANA, SIERRA LEONE AND THE GAMBIA ONLY.

14. 1. Using a scale of 2 cm to 2 units on both axes, draw on a graph sheet, two perpendicular axes OX and OY for the interval -8≤x≤8 and -8≤y≤8.
    2. Draw clearly and label the vertices as appropriate:
       1. rectangular PQR with P(1,2), Q(5,3) and ${\overrightarrow {RQ}}={\binom {2}{-3}}$;
       2. the image △P'Q'R' of △PQR under a rotation of 180° about the origin where P → P', Q → Q' and R → R'.
       3. the image of △P"Q"R" of △P'Q'R' under a reflection in the line x = 0 where P' → P", Q' → Q" and R' → R"
    3. Describe fully a single transformation that maps
15. 1. Find the image of (-2, 4) under the mapping ${\binom {x}{y}}\rightarrow {\binom {2x}{y-3x}}$.
    2. Two functions f and g are defined as: $f:x\rightarrow {\tfrac {x^{2}}{4}}-9$ $g:x\rightarrow {\tfrac {1}{2x}}(x\neq 0)$
       1. Evaluate: $f(4)+g{\bigl (}-{\tfrac {1}{3}}{\bigr )}$
       2. If f x g = 2, solve for x.