2012 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. Express 302.10495 correct to five significant figures.
   1. 302.10
   2. 302.11
   3. 302.105
   4. 302.1049
2. Simplify: ${\tfrac {3{\sqrt {5}}\times 4{\sqrt {6}}}{2{\sqrt {2}}\times 3{\sqrt {3}}}}$
   1. ${\sqrt {2}}$
   2. ${\sqrt {5}}$
   3. $2{\sqrt {2}}$
   4. $2{\sqrt {5}}$
3. In 1995, the enrolments of two schools X and Y were 1,050 and 1,190 respectively. Find the ratio of the enrolments of X to Y
   1. 50: 11
   2. 15 :17
   3. 13: 55
   4. 12: 11
4. Convert 35₁₉ to a number in base 2
   1. 1011
   2. 10011
   3. 100011
   4. 11001
5. The n^th term of a sequence is T_n = 5 + (n - 1)². Evaluate T₄ - T₆
   1. 30
   2. 16
   3. -16
   4. -30
6. Mr Manu travelled from Accrs to Pamfokrom a distance of 720 km in 8 hours. What will be his speed in m/s?
   1. 25 m/s
   2. 150 m/s
   3. 250 m/s
   4. 500 m/s
7. If ₦2,500.00 amounted to ₦3,500.00 in 4 years at simple interest, find the rate at which the interest was charged.
   1. 5%
   2. 7½%
   3. 8%
   4. 10%
8. Solve for x in the equation: ${\tfrac {1}{x}}+{\tfrac {2}{3x}}={\tfrac {1}{3}}$
   1. 5
   2. 4
   3. 3
   4. 1
9. Simplify: ${\tfrac {54k^{2}-6}{3k+1}}$.
   1. 6(1 − 3k²)
   2. 6(3k² − 1)
   3. 6(3k − 1)
   4. 6(1− 3k)
10. Represent the inequality −7 < 4x + 9 ≤ 13 on a number line

    1. 

    2. 

    3. 

    4. 

11. Make p the subject of the relation: q = ${\tfrac {3p}{r}}+{\tfrac {s}{2}}$
    1. p = ${\tfrac {2q-rs}{6}}$
    2. p = 2qr − sr − 3
    3. p = ${\tfrac {2qr-s}{6}}$
    4. p = ${\tfrac {2qr-rs}{6}}$
12. If x + y = 2y – x + 1 = 5, find the value of x
    1. 3
    2. 2
    3. 1
    4. -1
13. The sum of 12 and one third of n is 1 more than twice n. Express the statement in the form of an equation.
    1. 12n – 6 = 0
    2. 3n – 12 = 0
    3. 2n – 35 = 0
    4. 5n – 33 = 0
14. Solve the inequality: ${\tfrac {-m}{2}}-{\tfrac {5}{4}}\leq {\tfrac {5m}{12}}-{\tfrac {7}{6}}$
    1. $m\geq {\tfrac {5}{4}}$
    2. $m\leq {\tfrac {5}{4}}$
    3. $m\geq -{\tfrac {1}{11}}$
    4. $m\leq -{\tfrac {1}{11}}$
15. The curved surface area of a cylindrical tin is 704 cm². If the radius of its base is 8 cm, find the height. [Take π = ${\tfrac {22}{7}}$]
    1. 14 cm
    2. 9 cm
    3. 8 cm
    4. 7 cm
16. The lengths of the minor and major arcs of a circle are 54 cm and 126 cm respectively. Calculate the angle of the major sector
    1. 306°
    2. 252°
    3. 246°
    4. 234°
17. A sector of a circle which subtends 172° at the centre of the circle has a perimeter of 600 cm. Find, correct to the nearest cm, the radius of the circle. [Take π = ${\tfrac {22}{7}}$]
    1. 120 cm
    2. 116 cm
    3. 107 cm
    4. 100 cm

18. 

    In the diagram, |QR| = 10 m, |SR| = 8 m, $\angle$QPS = 30°, $\angle$QRP = 90° and |PS| = x. Find x.
    1. 1.32 m
    2. 6.32 m
    3. 9.32 m
    4. 17.32 m
19. In △XYZ, |XY| = 8cm, |YZ| = 10cm and |XZ| = 6cm. Which of these relations is true?
    1. |XY| + |YZ| = |XZ|
    2. |XY| - |YZ| = |XZ|
    3. |XZ|² = |YZ|² – |XY|²
    4. |YZ|² = |XZ|² – |XY|²

20. 

    In the diagram, O is the centre of the circle PQRS and $\angle$PSR = 86°. If $\angle$PQR = x°, find x.
    1. 274
    2. 172
    3. 129
    4. 86

21. 

    The diagram is a circle centre O. If $\angle$SPR = 2m and $\angle$SQR = n, express m in terms of n.
    1. M = ${\tfrac {n}{2}}$
    2. m = 2n
    3. m = n – 2
    4. m = n + 2

22. 

    In the diagram, MQ||RS, $\angle$TUV = 70° and $\angle$RLV = 30°, Find the value of x
    1. 150°
    2. 110°
    3. 100°
    4. 95°

23. 

    In the diagram, MN,PQ, and RS are three intersecting straight lines. Which of the following statement(s) is/are true? I. t = y II. x + y + z + m = 180° III. x + m + n = 180° IV. x + n = m + z
    1. I and IV only
    2. II only
    3. III only
    4. IV only
24. If cos (x + 40)° = 0.0872, what is the value of x?
    1. 85°
    2. 75°
    3. 65°
    4. 45°
25. A kite flies on a taut string of length 50 m inclined at an angle of 54° to the horizontal ground. The height of the kite above the ground is
    1. 50 tan36°
    2. 50 sin 54°
    3. 50 tan 54°
    4. 50 sin 36°

26. 

    The positions of three ships P, Q and R at sea are illustrated in the diagram. The arrows indicate the North direction. The bearing of Q from P is 050° and $\angle$PQR = 72°. Calculate the bearing of R from Q.
    1. 130°
    2. 158°
    3. 222°
    4. 252°
27. Given that the mean of the scores 15, 21, 17, 26, 18 and 29 is 21, calculate the standard deviation of the scores
    1. ${\sqrt {10}}$
    2. 4
    3. 5
    4. ${\sqrt {30}}$
28. A bag contains 4 red and 6 black balls of the same size. If the balls are shuffled briskly and two balls are drawn one after the other without replacement, find the probability of picking balls of different colours.
    1. ${\tfrac {8}{15}}$
    2. ${\tfrac {13}{25}}$
    3. ${\tfrac {11}{15}}$
    4. ${\tfrac {13}{15}}$
**The bar chart shows the frequency distribution of marks scored by students in a class test. Use the bar to answer questions 29 to 31
29. How many students are in the class?
    1. 10
    2. 24
    3. 25
    4. 30
30. Calculate the mean of the distribution.
    1. 6.0
    2. 3.0
    3. 2.4
    4. 1.8
31. What is the median of the distribution?
    1. 2
    2. 4
    3. 6
    4. 8
32. Which of these statements about $y=8{\sqrt {m}}$ is correct?
    1. $\log y=\log 8\times \log {\sqrt {m}}$
    2. $\log y=3\log 2\times {\tfrac {1}{2}}\log m$
    3. $\log y=3\log 2-{\tfrac {1}{2}}\log m$
    4. $\log y=3\log 2+{\tfrac {1}{2}}\log m$
33. If x + 0.4y = 3 and y = ${\tfrac {1}{2}}$x, find the value of (x + y)
    1. $1{\tfrac {1}{4}}$
    2. $2{\tfrac {1}{2}}$
    3. $3{\tfrac {3}{4}}$
    4. 5
34. Express $3-({\tfrac {x-y}{y}})$ as a single fraction.
    1. ${\tfrac {3xy}{y}}$
    2. ${\tfrac {x-4y}{y}}$
    3. ${\tfrac {4y+x}{y}}$
    4. ${\tfrac {4y-x}{y}}$
35. Find the coefficient of m in the expansion of $({\tfrac {m}{2}}-1{\tfrac {1}{2}})(m+{\tfrac {2}{3}})$
    1. $-{\tfrac {1}{6}}$
    2. $-{\tfrac {1}{2}}$
    3. -1
    4. $-1{\tfrac {1}{6}}$

36. 

    In the diagram, MN//PO, $\angle$PMN = 112°, $\angle$PNO = 129°, $\angle$NOP = 37° and $\angle$MPN = y. Find the value of y.
    1. 51°
    2. 54°
    3. 56°
    4. 68°
37. If P = {prime factors of 210} and Q = {prime numbers less than 10}, find P$\cap$Q.
    1. {1,2,3}
    2. {2,3,5}
    3. {1,3,5,7}
    4. {2,3,5,7}
38. Alfred spent ${\tfrac {1}{4}}$ of his money on food, ${\tfrac {1}{3}}$ on clothing and saved the rest. If he saved ₦72,000.00, how much did he spend on food?
    1. ₦43,200.00
    2. ₦43,000.00
    3. ₦42,200.00
    4. ₦40,000.00
39. Solve: $({\tfrac {27}{125}})^{-{\tfrac {1}{3}}}\times ({\tfrac {4}{9}})^{\tfrac {1}{2}}$
    1. ${\tfrac {10}{9}}$
    2. ${\tfrac {9}{10}}$
    3. ${\tfrac {2}{5}}$
    4. ${\tfrac {12}{125}}$
40. The sum of the interior angles of a regular polygon is 1800°. How many sides has the polygon?
    1. 16
    2. 12
    3. 10
    4. 8

41. 

    The diagram is a circle with centre C. PRST are points on the circle. Find the value of $\angle$PRS.
    1. 144°
    2. 72°
    3. 40°
    4. 36°

42. 

    The diagram is a circle of radius |OQ| = 4cm. ${\overline {TR}}$ is a tangent to the circle at R. If $T{\widehat {P}}O$ = 120°, find |PQ|
    1. 2.32cm
    2. 1.84cm
    3. 0.62cm
    4. 0.26cm
43. If x and y are variables and k is a constant, which of the following describes an inverse relationship between x and y?
    1. y = kx
    2. $y={\tfrac {k}{x}}$
    3. $y=k{\sqrt {x}}$
    4. y = x + k

44. 

    In the diagram, |SR| = |QR|, $\angle$SRP = 65° and $\angle$RPQ = 48°, find $\angle$PRQ.
    1. 65°
    2. 45°
    3. 25°
    4. 19°
**The graph is that of y = 2x² – 5x – 3. Use it to answer questions 45 and 46.
45. For what values of x will y be negative?
    1. $-{\tfrac {1}{2}}\leq x<3$
    2. $-{\tfrac {1}{2}}<x\leq 3$
    3. $-{\tfrac {1}{2}}<x<3$
    4. $-{\tfrac {1}{2}}\leq x\leq 3$
46. What is the gradient of y = 2x² – 5x – 3 at the point x = 4?
    1. 11.1
    2. 10.5
    3. 10.3
    4. 9.9

47. 

    The diagram is a polygon. Find the largest of its interior angles.
    1. 30°
    2. 100°
    3. 120°
    4. 150°
48. The volume of a cuboid is 54 cm³. If the length, width and height of the cuboid are in the ratio 2:1:1 respectively, find its total surface area.
    1. 108 cm²
    2. 90 cm²
    3. 80 cm²
    4. 75 cm²
49. A side and a diagonal of a rhombus are 10cm and 12cm respectively. Find its area
    1. 20 cm²
    2. 24 cm²
    3. 48 cm²
    4. 96 cm²
50. Factorize completely: 32x²y – 48x³y³
    1. 16x²y (2 – 3xy²)
    2. 8xy (4x – 6x²y²)
    3. 8x²y (4 – 6xy²)
    4. 16xy (2x – 3x²y²)

Theory

Section A

1. 1. Simplify: ${\tfrac {1{\tfrac {1}{4}}+{\tfrac {7}{9}}}{1{\tfrac {4}{9}}-2{\tfrac {2}{3}}\times {\tfrac {9}{64}}}}$
   2. Given that $\sin x={\tfrac {2}{3}}$, evaluate, leaving your answer in surd form and without using tables or calculator, $\tan x-\cos x$.
2. Sonny is twice as old as Wale. Four years ago, he was four times as old as Wale. When will the sum of their ages be 66?

3. 1. 

      In the diagram, ${\overline {TU}}$ is a tangent to the circle. $R{\widehat {V}}U$ = 100° and $\angle$URS = 36°. Calculate the value of angle STU.
   2. In triangle XYZ, |XY| = 5cm, |YZ| = 8cm and |XZ| = 6cm. P is a point on the side XY such that |XP| = 2cm and the line through P, parallel to YZ at Q. Calculate |QZ|.
4. 1. A box contains 40 identical discs which are either red or white. If the probability of picking a red disc is ${\tfrac {1}{4}}$, calculate the number of:
      1. white discs;
      2. red discs that should be added such that the probability of picking a red disc will be ${\tfrac {1}{3}}$.
   2. A salesman bought some plates at ₦50.00 each. If he sold all of them for ₦600.00 and made a profit of 20% on the transaction, how many plates did he buy?

5. 

   In the diagram, O is the centre of the circle and XY is a chord. If the radius is 5cm and |XY| = 6cm, calculate, correct to 2 decimal places, the:
   1. angle which XY subtends at the centre O,
   2. area of the shaded portion.

Section B

6. 1. A boy had M Dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister's share was equal to ${\tfrac {1}{3}}$ of M, find the value of M.
   2. A number of tourists were interviewed on their choice of means of travel, Two-thirds said that they travelled by road, ${\tfrac {13}{30}}$ by air and ${\tfrac {4}{15}}$ by both air and road. If 20 tourists did not travel by either air and road,
      1. represent the information on a Venn diagram;
      2. how many tourists (A) were interviewed; (B) travelled by air only?
7. 1. 1. Using a scale of 2cm to 1 unit on both axes, on the same graph sheet, draw the graphs of $y-{\tfrac {3x}{4}}=3$ and y + 2x = 6
      2. From your graph, find the coordinates of the point of intersection of the two graphs.
      3. Show, on the graph sheet, the region satisfied by the inequality $y-{\tfrac {3x}{4}}\geq 3$
   2. Given that x² + bx + 18 is factorized as (x + 2)(x + c). Find the values of c and b
8. A point // is 20m away from the foot of a tower on the same horizontal ground. From the point //, the angle of elevation of the point (P) on the tower and the top (T) of the tower are 30° and 50° respectively. Calculate, correct to 3 significant figures:
   1. PT;
   2. the distance between // and the top of the tower;
   3. the position of // if the angle of depression of // from the top of the tower is to be 40°
9. Three towns X,Y and Z are such that Y is 20km from X and 22km from Z. Town X is 18km from Z, A Health Centre is to be built by the government to serve the three towns. The centre is to be located such that patients from X and Y will always travel equal distance to access the Health Centre while patients from Z will travel exactly 10km to reach the Health Centre.
   1. Using a scale of 1cm to 2km, find by construction, using a pair of compasses and ruler only, the possible positions the Health Centre can be located.
   2. In how many possible locations can the Health Centre be built?
   3. Measure and record the distances of the locations from town X.
   4. Which of these locations would be convenient for all the three towns?

10. Class Interval	Frequency
    60 - 64	2
    65 - 69	3
    70 - 74	6
    75 - 79	11
    80 - 84	8
    85 - 89	7
    90 - 94	2
    95 - 99	1

    The table shows the distribution of marks scored by students in an examination. Calculate, correct to 2 decimal places, the
    1. mean;
    2. standard deviation of the distribution.

11. 1. 

       In the diagram, ABCD is a rectangular garden (3n – 1)m long and (2n + 1)m wide. A wire-mesh 135m long is used to mark its boundary and to divide it into 8 equal long plots. Find the value of n.
    2. A cylinder with base radius 14cm has the same volume as a cube of side 22cm. Calculate the ratio of the total surface area of the cylinder to the cube. [Take π = ${\tfrac {22}{7}}$].
12. 1. Copy and complete the table of values for y = 1 – 4 cos x.

       x	0°	30°	60°	90°	120°	150°	180°	210°	240°	270°	300°
       y	-3.0			1.0				4.5			-1.0

    2. Using a scale of 2cm to 30° on the x-axis and 2cm to 1 unit on the y-axis, draw the graph of y = 1 − 4 cos x for 0°≤ x ≤ 300°
    3. Use the graph to:
       1. solve the equation 1 − 4 cos x = 0;
       2. find the value of y when x = 105°;
       3. find x when y = 1.5.

13. 1. 

       In the diagram, |PQ| = 6cm; |QR| = 13cm, |RS| = 5cm and $\angle$RSQ is a right angle. Calculate, correct to one decimal place, |PS|.

    2. 

       The diagram shows a wooden structure in the form of a cone mounted on a hemispherical base. The vertical height of the cone is 24cm and the base radius 7cm. Calculate, correct to 3 significant figures, the surface area of the structure. [Take π = ${\tfrac {22}{7}}$].