2010 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. Simplify 0.000215 x 0.000028 and express your answer In standard form
   1. $6.03x10^{9}$
   2. $6.02x10^{9}$
   3. $6.03x10^{-9}$
   4. $6.02x10^{-9}$
2. Factorise $x-y-ax-ay$
   1. ${\Bigl (}x-y{\Bigr )}{\Bigl (}1-a{\Bigr )}$
   2. ${\Bigl (}x+y{\Bigr )}{\Bigl (}1+a{\Bigr )}$
   3. ${\Bigl (}x+y{\Bigr )}{\Bigl (}1-a{\Bigr )}$
   4. ${\Bigl (}x-y{\Bigr )}{\Bigl (}1+a{\Bigr )}$

3. 

   In the diagram, $\angle PSR=22^{\circ },\angle SPQ=58^{\circ },$ and $\angle PQR=41^{\circ }$.Calculate the obtuse angle QRS.
   1. $99^{\circ }$
   2. $100^{\circ }$
   3. $121^{\circ }$
   4. $165^{\circ }$
The bar chart shows the marks distribution in an English test. Use it to answer questions 4 and 5.
4. If 50% is the pass mark, how many students passed the test?
   1. 100
   2. 85
   3. 80
   4. 70
5. What percentage of the students had marks ranging from 35 to 50?
   1. $55{\frac {1}{3}}\%$
   2. $60\%$
   3. $65\%$
   4. $66{\frac {2}{3}}\%$
6. A car uses one litre of petrol for every 14 km. If one litre of petrol costs N63.00, how far can the car go with N900.00 worth of petrol?
   1. 420 km
   2. 405km
   3. 210 km
   4. 200 km
7. Correct 0.002473 to 3 significant figures.
   1. 0.002
   2. 0.0024
   3. 0.00247
   4. 0.0025
8. Simplify: $1{\frac {1}{2}}+2{\frac {1}{3}}x{\frac {3}{4}}-{\frac {1}{2}}$
   1. $-2{\frac {1}{3}}$
   2. $-2{\frac {1}{4}}$
   3. $2{\frac {1}{8}}$
   4. $2{\frac {3}{4}}$
9. The sum of 2 consecutive whole numbers is ${\frac {5}{6}}$ of their product. Find the numbers.
   1. 3, 4
   2. 1, 2
   3. 2, 3
   4. 0,1

10. 

    What Is the value of m in the diagram?
    1. $20^{\circ }$
    2. $30^{\circ }$
    3. $40^{\circ }$
    4. $50^{\circ }$

11. 

    In the diagram, QR// ST, /PQ/ = /PR/ and $\angle$PST = 75°. Find the value of y.
    1. $105^{\circ }$
    2. $110^{\circ }$
    3. $130^{\circ }$
    4. $150^{\circ }$
12. A casting is made up of Copper and Zinc If 65% of the casting is Zinc and there are 147g of Copper. what is the mass of the casting?
    1. 320 g
    2. 420 g
    3. 520 g
    4. 620 g
13. Given that $P=\{{x:1\leq x\leq 6}\}$ and $Q=\{{x:2<x<10}\}$, where x is an integer. Find $n{\Bigl (}P\cap Q{\Bigr )}$?
    1. 4
    2. 6
    3. 8
    4. 10
14. The sum of 6 and one-third of x is one more than twice x. Find x.
    1. x = 7
    2. x = 5
    3. x = 3
    4. x = 2
15. Given that $T=\{{x:-2<x\leq 9}\}$, where x is an integer. What is $n{\Bigl (}T{\Bigr )}$
    1. 9
    2. 10
    3. 11
    4. 12
16. Solve the inequality: $3{\Bigl (}x+1{\Bigr )}\leq 5{\Bigl (}x+2{\Bigr )}+15$
    1. $x\geq -14$
    2. $x\leq -14$
    3. $x\leq -11$
    4. $x\geq -11$
17. An empty rectangular tank is 250cm long. and 120cm wide. If 180 litres of water is poured into the tank, calculate the height of the water.
    1. 66.0 cm
    2. 5.5 cm
    3. 5.0 cm
    4. 4. cm
18. Given that ${\frac {5^{n+3}}{25^{2n-3}}}=5^{0}$, find n
    1. n=1
    2. n=2
    3. n=3
    4. n=4

19. Number of pets	0	1	2	3	4
    Number of students	8	4	5	10	3

    The table shows the number of pets kept by’ 30 | students in a class. If a student is picked at random from the class, what is the probability that. he/she kept more than one pet?

    1. ${\frac {1}{5}}$
    2. ${\frac {2}{5}}$
    3. ${\frac {3}{5}}$
    4. ${\frac {4}{5}}$
20. Simplify $2{\sqrt {3}}-{\frac {6}{\sqrt {3}}}+{\frac {3}{\sqrt {27}}}$
    1. $1$
    2. ${\frac {1}{3}}{\sqrt {3}}$
    3. $2{\sqrt {3}}-5{\frac {2}{3}}$
    4. $6{\sqrt {3}}-17$

21. 

    In the diagram, triangles HKL and HIJ are similar Which of the following ratios is equal to ${\frac {LH}{JH}}$
    1. ${\frac {KL}{JI}}$
    2. ${\frac {HK}{JK}}$
    3. ${\frac {JI}{KL}}$
    4. ${\frac {HK}{LK}}$

22. 

    In the diagram, the tangent MN makes an angle of 55° with chord PS. If O is the centre of the circle, find $\angle$RPS.
    1. 55°
    2. 45°
    3. 35°
    4. 25°
23. Simplify: ${\frac {2}{2+x}}+{\frac {2}{2-x}}$
    1. ${\frac {4}{4-x^{2}}}$
    2. ${\frac {8}{4-x^{2}}}$
    3. ${\frac {4x}{4-x^{2}}}$
    4. ${\frac {8-4x}{4-x^{2}}}$
24. A rectangle has length x cm and width (x-1) cm. If the perimeter is 16 cm, find the value of x.
    1. $3{\frac {1}{2}}cm$
    2. $4cm$
    3. $4{\frac {1}{2}}cm$
    4. $5cm$
25. Given that tan x = 1, where 0° < x < 90°, evaluate ${\frac {1-\sin ^{2}x}{\cos x}}$
    1. $2{\sqrt {2}}$
    2. ${\sqrt {2}}$
    3. ${\frac {\sqrt {2}}{2}}$
    4. ${\frac {1}{2}}$
26. If sin 3y=cos 2y and 0°<y< 90°, find the value of y.
    1. 18°
    2. 36°
    3. 54°
    4. 90°
27. The sum of the exterior angles of an n-sided convex polygon is half the sum of its interior angles. Find n.
    1. 6
    2. 8
    3. 9
    4. 12
28. What is the length of a rectangular garden whose perimeter is 32 cm and area 39 $cm^{2}$?
    1. 25 cm
    2. 18 cm
    3. 13 cm
    4. 9 cm
29. If y= ${\frac {2{\Bigl (}{\sqrt {x^{2}+m}}{\Bigr )}}{3N}}$, make x the subject of the formula.
    1. ${\frac {\sqrt {9y^{2}N^{2}-2m}}{2}}$
    2. ${\frac {\sqrt {9y^{2}N^{2}+2m}}{2}}$
    3. ${\frac {\sqrt {9y^{2}NT^{2}-4m}}{2}}$
    4. ${\frac {\sqrt {9y^{2}N^{2}+4m}}{2}}$
30. The nth term of tHe sequence: —2, 4, — 8, 16 is given by
    1. $T_{n}=2^{n}$
    2. $T_{n}={\Bigl (}-2{\Bigr )}^{n}$
    3. $T_{n}={\Bigl (}-2n{\Bigr )}$
    4. $T_{n}=n^{2}$
31. In the diagram, 0 is the centre of the circle $\angle$SQR = 60°, $\angle$SPR =y and $\angle$SOR = 3x. Find the value of (x + y).
    1. 110°
    2. 100°
    3. 80°
    4. 70°
32. How many times correct to XX number, will a man run round a track of diameter 100m to cover a distance of 1000 m7?
    1. 3
    2. 4
    3. 5
    4. 6

33. 

    The shaded portion in the diagram is the solution
    1. $x+y\leq 3$
    2. $x+y<3$
    3. $x+y>3$
    4. $x+y\geq 3$

34. 

    In the diagram, /EF/ = 8 cm, /FG/=x cm, /GH/ = (x+2) cm, $\angle$EFC= 90°. If the area of the shaded portion is 40 $cm^{2}$, find the area of $\bigtriangleup$JEFG.
    1. 128 $cm^{2}$
    2. 72 $cm^{2}$
    3. 64 $cm^{2}$
    4. 32 $cm^{2}$
35. In the diagram, GI is a tangent to the circle at H. EFI/GI, calculate the size of $\angle$EHF
    1. 126°
    2. 72°
    3. 54°
    4. 28°
36. Bala sold an article for #6,900.00 and made a profit of 15%. If he sold it for #6,600.00 he would make a:
    1. profit of 13%.
    2. loss of 12%.
    3. profit of 10%.
    4. loss of 5%.

37. 

    In the diagram above, $\angle$ROS = 66° and $\angle$POQ = 3 x. Some construction lines are shown. Calculate the value of x.
    1. 10°
    2. 11°
    3. 22°
    4. 30°
38. The mean age of R men in a club is 50 years. Two men, aged 55 and 63, left the club and the mean age reduced by 1 year. Find the value of R.
    1. 18
    2. 20
    3. 22
    4. 28

x	0	2	4	6
y	1	2	3	4

The table is for the relation y = mx + c where m and c are constants. Use it to answer questions 39 and 40.

39. What is the equation of the line described in the table?
    1. y = 2x
    2. y = x+1
    3. y = x
    4. y=${\tfrac {1}{2}}$x+1
40. What is the value of x when y = 5?
    1. 8
    2. 9
    3. 10
    4. 11

41. 

    The diagram is a net of a right rectangular pyramid. Calculate the total surface area.
    1. 208 $cm^{2}$
    2. 112 $cm^{2}$
    3. 92 $cm^{2}$
    4. 76 $cm^{2}$

42. 

    The diagram shows a rectangular cardboard from which a semi-circle is cut off. Calculate the area of the remaining part.
    1. 44 $cm^{2}$
    2. 99 $cm^{2}$
    3. 154 $cm^{2}$
    4. 165 $cm^{2}$
43. The subtraction below is in base seven. Find the missing number
    1. 2
    2. 3
    3. 4
    4. 5
44. In the diagram O is the centre of the circle Find the value of x
    1. 34
    2. 29
    3. 17
    4. 14
45. If the sum of the roots of the equation (x — p) (2x +1) =0 is1, find the value of p.
    1. $1{\frac {1}{2}}$
    2. ${\frac {1}{2}}$
    3. $-{\frac {1}{2}}$
    4. $-1{\frac {1}{2}}$

46. 

    In the diagram, $\angle$WOX = 60°,$\angle$YOE = 50° and $\angle$OXY =.30°. What is the bearing of x from Y?
    1. 300°
    2. 240°
    3. 190°
    4. 150°
47. .|n an athletics competition, the probability that an athlete wins a 100 m race is ${\frac {1}{8}}$and the probability that he wins in high jump is ${\frac {1}{4}}$. What is the probability that he wins only one of the events?
    1. ${\frac {3}{32}}$
    2. ${\frac {3}{32}}$
    3. ${\frac {7}{32}}$
    4. ${\frac {5}{16}}$
48. If $x^{2}+kx+{\frac {16}{9}}$ is a perfect square, find the value of x
    1. ${\frac {8}{3}}$
    2. ${\frac {7}{3}}$
    3. ${\frac {5}{3}}$
    4. ${\frac {2}{3}}$
49. If $xkmh^{-}1=yms^{-}1$, the y =
    1. ${\frac {7}{18}}x$
    2. ${\frac {11}{20}}x$
    3. ${\frac {4}{15}}x$
50. The mean of the numbers 2, 5, 2x and 7 is less than or equal to 5. Find the range of values. of x.
    1. $x\leq 3$
    2. $x\geq 3$
    3. $x<3$
    4. $x>3$

Theory

Section A

1. $A=\{2,4,6,8\}$, $B=\{2,3,7,9\}$ and $B=\{x:3<x<9\}$ are subsets of the universal set $U=\{2,3,4,5,6,7,8,9\}$. Find
   1. $A\cap {\Bigl (}B\cap C{\Bigr )}$
   2. ${\Bigl (}A\cup B{\Bigr )}\cap {\Bigl (}B\cup C{\Bigr )}$
2. 1. The angle of depression of a boat from the mid-point of a vertical cliff is 35° If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.
   2. )Towns P and Q are x km apart. Two motorist set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the Value of x.

3. 1. 

      In the diagram, $\angle$PQR =125°, $\angle$QRS=r, $\angle$RST 80° and $\angle$STU = 44°. Calculate the value of r.

   2. 

      In the diagram, TS is a tangent to the circle at A. AB//CE, $\angle$AEC =5x°, $\angle$ADB = 60° and $\angle$TAE = x. Find the value of x.

4. 

   The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 $cm^{2}$, calculate, correct to 3 significant figures, the:
   1. base radius, r;
   2. height, h;
   3. volume of the cone [ Take $\pi ={\frac {22}{7}}$]
5. Two fair dice are thrown. M is the event described by " the sum of the scores is 10" and N is the event described by "the difference between the scores is 3".
   1. Write out the elements of M and N.
   2. Find the probability of M or N.
   3. Are M and N mutually exclusive? Give reasons.

Section B

6. 1. The area of a map is 1:20,000. Calculate the area, in square centimetres, on the map of a forest reserve which covers 85 km².
   2. A rectangular playing field is 18 m wide. It is surrounded by a path 6 m wide such that its area is equal to the area of the path. Calculate the length of the field.

   3. 

      The diagram shows a circle centre O. If POQ = x°, the diameter of the circle is 7 cm and the area of the shaded portion is 27.5 cm². Find, correct to the nearest degree, the value of x. [Take $\pi ={\frac {22}{7}}$]
7. 1. Madam Kwakyewaa imported a quantity of frozen fish costing GH¢400.00 The goods attracted an import duty of 15% of its cost. She also paid a sales tax of 10% of the total cost of the goods including the import duty and then sold the goods for GH¢660.00. Calculate her percentage profit.
   2. In a school, there are 1000 boys and a number of girls. The 48% of the total number of students that were successful in an examination was made up of 50% of the boys and 40% of the girls. Find the number of girls in the school.
8. Using ruler and a pair of compasses only,
   1. Construct
      1. a quadrilateral PQRS with /PS/= 6cm, $\angle$RSP=90°, /RS/ = 9cm, /QRI/ = 8.4cm and /PQ/ =5.4cm;
      2. the bisectors of $\angle$RSP and $\angle$SPQ to meet at X;
      3. the perpendicular XT to meet PS at T.
   2. Measure /XT/.

9. 

   In the diagram, /AB/ = 8km, /BC/ = 13km,the bearing of A from B is 310° and the bearing of B from C is 230°. Calculate, correct to 3 significant figures,
   1. the distance AC;
   2. the bearing of C from A;
   3. how far east of B, C is.
10. 1. Copy and complete the table of values for the relation $y=-x^{2}+x+2$ for $-3\leq x\leq 3$.

    x	-3	-2	-1	0	1	2	3
    y		-4		2			-4

    
    

    2. Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw a graph for the relation $y=-x^{2}+x+2$
    3. From the graph, find the
       1. minimum value of y.
       2. roots of the equation $x^{2}-x-2=0$
       3. gradient of the curve at x = -0.5

    4. 

       In the diagram, $\angle$PTQ = $\angle$PSR= 90°, /PQ/ = 10cm, /PS/ = 14.4cm and /TQ/ =6cm. Calculate the area of quadrilateral QRST.
       1. Two opposite sides of a square are each decreased by 10% while the other two are each increased by 15% to form a rectangle. Find the ratio of the area of the rectangle to that of the square.
    5. The frequency distribution of the weight of 100 participants in a high jump competition is as shown below:
       1. Construct the cumulative frequency table.
       2. Draw the cumulative frequency curve.
       3. From the curve, estimate the:
          1. median;
          2. semi-interquartile range;
          3. probability that a participant chosen at random weighs at least 60kg.
    6. 1. The third term of a Geometric Progression (G.P) is 24 and its seventh term is . Find its first term.
       2. Given that y varies directly as x and inversely as the square of z. If y =4, when x = 3.and z= 1, find y when x = 3 and z = 2.