2017 General Mathematics WAEC SSCE (School Candidates) May/June

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Objective Test Questions

1. Express 0.0000407 correct to 2 significant figures
   1. 0.0
   2. 0.00004
   3. 0.000041
   4. 0.0000407
2. If x varies inversely as y and y varies directly as z. What is the relationship between x and z?
   1. x α z
   2. x α 1/z
   3. x α z
   4. x α 1/z²
3. Evaluate: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3\frac{1}{4}\text{x}1\frac{3}{5}}{11\frac{1}{3}-5\frac{1}{3}}}
   1. 14/15
   2. 13/15
   3. 4/5
   4. 11/15

4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bigoplus}	0	1	2	3	4
   0	0	1	2	3	4
   1	1	2	3	4	0
   2	2	3	4	0	1
   3	3	4	0	1	2
   4	4	0	1	2	3

   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bigotimes}	0	1	2	3	4
   0	0	0	0	0	0
   1	0	1	2	3	4
   2	0	2	4	1	3
   3	0	3	1	4	2
   4	0	4	3	2	1

   Fig. 1 and Fig. 2 are the addition and multiplication tables respectively in modulo 5. Use these tables to solve the equationFailed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (n \bigotimes4) \bigoplus 3 = 0} (mod5).
   1. 1
   2. 2
   3. 3
   4. 4
5. The ages of Tunde and Ola are in the ratio 1:2. If the, ratio of Ola’s age to Musa’s age is 4:5, what is the ratio of Tunde’s age to Musa’s age?
   1. 1:4
   2. 1:5
   3. 2:5
   4. 5:2
6. If M= {x:3 ≤ x < 8} and N= {x:8 < x ≤ 12} , Which of the following is true? 1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 8\in M \cap N} 2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 8\in M \cup N} 3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M \cap N = \varnothing}
   1. 3 only
   2. 1 and 2 only
   3. 2 and 3 only
   4. 1,2 and 3
7. Given that a = log 7 and b = log 2, express log 35 in terms of a and b.
   1. a + b + 1
   2. ab - 1
   3. a - b + 1
   4. b - a + 1
8. If x= 2/3 and y = -6, evaluate xy-y/x.
   1. 0
   2. 5
   3. 8
   4. 9
9. Solve the equation: 1/5x + 1/x = 3
   1. 1/5
   2. 2/5
   3. 3/5
   4. 4/5
10. A sum of N18,100.00 was shared among 5 boys and 4 girls with each boy taking N20.00 more than each girl. Find a boy's share.
    1. N 1,820.00
    2. N 2,000.00
    3. N 2,020.00
    4. N 2040.00
11. One factor of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7x^2+33x-10} is
    1. 7x + 5
    2. x - 2
    3. 7x - 2
    4. x - 5
12. Solve: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1/4 < 3/4(3x-2) < 1/2}
    1. 5/9 < x < 8/9
    2. -8/9 < x <7/9
    3. -8/9 < x < 5/9
    4. -7/9 < x < 8/9
13. Simplify: 3x — (p - x) — (r—p)
    1. 2x - r
    2. 2x + r
    3. 4x - r
    4. 2x- 2p - r
14. An arc of a circle of radius 7.5 cm is 7.5 cm long. Find, correct to the nearest degree, the angle which the is arc subtends at the center of the circle.
    1. 29°
    2. 57°
    3. 65°
    4. 115°
15. Water flows out of a pipe at a rate of 40 pi cm3 per second into an empty cylindrical container of base radius 4cm. Find the height of water in the container after 4 seconds.
    1. 10cm
    2. 14cm
    3. 16cm
    4. 20cm
16. The dimensions of a water tank are 13cm, 10cm and 70 cm. If it is half-filled with water, calculate the volume of water in litres.
    1. 4.55 litres
    2. 7.50 litres
    3. 8.10 litres
    4. 9.55 litres
17. If the total surface area of a solid hemisphere is equal to its volume. find the radius.
    1. 3.0 cm
    2. 4.5cm
    3. 5.0cm
    4. /.0cm
18. Which of the following is true about parallelograms?
    1. Opposite angles are supplementary.
    2. Opposite angles are complementary
    3. Opposite angles are equal
    4. Opposite angles are reflex angles

19. Error creating thumbnail: Unable to save thumbnail to destination

    The diagram shows a circle centre O. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} STR = 29° and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} RST = 46°. Calculate the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} STO.
    1. 12°
    2. 15°
    3. 29°
    4. 34°

20. Error creating thumbnail: Unable to save thumbnail to destination

    In the diagram, XY is a straight line, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} POX = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} POQ and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} ROY = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} QOR. Find the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} POQ + Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} ROY.
    1. 60°
    2. 90°
    3. 100°
    4. 120°

21. Error creating thumbnail: Unable to save thumbnail to destination

    The diagram shows a circle centre O. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} ZYW = 33°, find Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} ZWX
    1. 33°
    2. 57°
    3. 90°
    4. 100°

22. Error creating thumbnail: Unable to save thumbnail to destination

    In the diagram, PQ and PS are tangents to the circle centre O. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} PSQ = m, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} SPQ = n and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} SQR = 33°. find the value of (m +n)
    1. 103°
    2. 123°
    3. 133°
    4. 143°
23. Calculate the gradient (slope) of the line joining points (— 1, 1) and (2, -2).
    1. -1
    2. -1/2
    3. 1/2
    4. 1
24. 4. If P(2, 3) and Q(2, 5) are points on a graph, calculate the length PQ.
    1. 6 units
    2. 5 units
    3. 4 units
    4. 2 units
25. A bearing of 320° expressed as a compass bearing is
    1. N 50° W
    2. N 40° W
    3. N 50° E
    4. N 40° E
26. Given that cos 30° = sin 60° = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left ( \frac{\sqrt{3}}{2} \right )} and sin 30° = cos60° =Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left ( \frac{1}{2} \right )} , evaluate Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left ( \frac{\tan 60-(-1)}{1-\tan 30} \right )}
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\sqrt{3-2}}}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {2-\sqrt{3}}}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{3}}
    4. -2
27. A stationary boat is observed from a height of 100m, If the horizontal distance between the observer and the boat is 80m. calculate correct to two decimal places. the angle of depression of the beat from the point of observation
    1. 36.87°
    2. 39.70°
    3. 51.34°
    4. 53.13°
28. The average age of a group 25 girls is 10 years: If one girl aged 12 years and 4 months joins the group. find correct to one decimal place the new average age of the group.
    1. 10.1 years
    2. .3 years
    3. 8.7 years
    4. 8.3 years

29. 

    The bar chart shows the statistics of the number of passes and failures in an examination in a school from 2001 to 2004. What is the ratio of the total number of passes to the total number of failures?
    1. 60:13
    2. 10:3
    3. 5:1
    4. 40:13

Marks	0	1	2	3	4	5
Frequency	7	4	18	12	8	11

The table gives the distribution of marks obtained by a number of pupils in a class test. Use this information to answer questions 30 and 31.
30. Find the median of the distribution
    1. 4
    2. 3
    3. 2
    4. 1
31. Find the first quartile.
    1. 1.0
    2. 1.5
    3. 2.0
    4. 2.5
32. In a class of 45 students 28 offer chemistry and 25 offer Biology. If each student offers at least one of the two subjects. calculate the probability that a student selected at random from the class offers Chemistry only.
    1. 2/9
    2. 4/9
    3. 5/9
    4. 7/9
33. In what number base was the addition, 1 + nn = 100, where n > 0. done?
    1. n-1
    2. n
    3. n+1
    4. n+2
34. Simplify: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}(\sqrt{6}-2\sqrt{2})-2\sqrt{3}}
    1. 4
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{3}+4}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4\sqrt{2}}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4\sqrt{3} + 4}
35. Three exterior angles of a polygon are 30°, 40° and 60°. if the remaining exterior angles are, 46° each, name the polygon.
    1. Decagon
    2. Nonagon
    3. Octagon
    4. Hexagon

36. 

    In the diagram, NQ//TS, RTS = 50° and PRT = 100°. Find the value of NPR.
    1. 110°
    2. 130°
    3. 140°
    4. 150°
37. Simplify the expression Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{a^2b^4-b^2a^4}{a\, b(a+b)}}
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {a^2-b^2}}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {b^2-a^2}}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {a^2b-ab^2}}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {ab^2-a^2b}}
38. Find the 6th term of the sequence. 2/3, 7/15, 4/15...
    1. -1/3
    2. -1/5
    3. 1/15
    4. 1/5
39. The diagonal of a square Is 60 cm. Calculate its perimeter.
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {20\sqrt{2}}}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {40\sqrt{2}}}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 90\sqrt{2}}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 120\sqrt{2}}
40. The roots of a quadratic equation are: 1/2 and 2/3. Find the equation.
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6x^2-x+ 2 =0}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6x^2-x- 2 =0}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6x^2+x- 2 =0}
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6x^2+x+ 2 =0}
41. Make x the subject of the relation Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d= \sqrt {\frac{6}{x} -\frac{y}{2}}}
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x= \frac{6}{d^2} + \frac{12}{y}}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x= \frac{12}{2d^2- y}}
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x= \frac{12}{y}- 2d^2}
    4. $x={\frac {12}{2d^{2}+y}}$
42. Consider the statements: p: it is hot. q: it is raining, Which of the following symbols correctly represents the statement “It is raining if and only if it is cold”?
    1. $p\Longleftrightarrow \backsim q$
    2. $q\Longleftrightarrow p$
    3. $\backsim q\Longleftrightarrow \backsim q$
    4. $q\Longleftrightarrow \backsim p$
43. Given that $t=2^{-x}$, find $t=2^{x-1}$ in terms of t.
    1. ${\frac {2}{t}}$
    2. ${\frac {t}{2}}$
    3. ${\frac {1}{2t}}$
    4. $2t$

44. 

    Find the value of m in the diagram.
    1. 72°
    2. 68°
    3. 44°
    4. 34°
45. Two bottles are drawn with replacement from a crate containing 8 coke,12 Fanta and 4 sprite bottles. What is the probability that the first is coke and the second is not coke?
    1. 10/12
    2. 1/6
    3. 2/9
    4. 3/8
46. If the simple interest on a certain amount of money saved in a bank for 5 years at 21% per annum is N500.00, calculate the total amount due after 6 years at the same rate.
    1. N2500.00
    2. N2600.00
    3. N4500.00
    4. N4600.00
47. Calculate, the variance of,2, 3, 3, 4, 5, 5,5 7, 7 and 9
    1. 2.2
    2. 3.4
    3. 4.0
    4. 4.2
48. A circular pond of radius 4m has a path of width 2.5 m round it. Find, correct to two decimal places, the area of the path. Take π=22/7
    1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7.83m^2}
    2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 32.29m^2 }
    3. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 50.29 m^2 }
    4. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 82.50m^2 }

49. 

    The graph of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=ax^2+bx+c } is shown in the diagram. Find the minimum value of y.
    1. -2.0
    2. -2.1
    3. -2.3
    4. -2.5

50. 

    In the diagram, RP is a diameter of circle RSP. RP Is produced to T and TS is a tangent to the circle as S. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} PRS = 24°, calculate the value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} STR.
    1. 24°
    2. 42°
    3. 48°
    4. 66°

Theory

Section A

1. 1. If (UNCLEAR), without using mathematical tables or calculator, find the value of y.
   2. When I walk from my house at 4 Km/h, I will get to the office 30 minutes later than when I walk at 5 Km/h. Calculate the distance between my house and office.
2. 1. Solve the equation: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2/3 \bigl(3x-5\bigr)-3/5\bigl(2x-3\bigr)=3} .

   2. Error creating thumbnail: Unable to save thumbnail to destination

      In the diagram, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} STQ =m, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} TUO =80°.Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} UPO =r, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} PQU =n and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} ROT =88°. Find the value of (m+n).
3. 1. The angle of depression of a point P on the ground from the top T of a building is 23.6°. If the distance from P to the foot of the building is 50 m. calculate, - correct to the nearest meter, the Height of the building .

   2. 

      In the diagram PT//SU.QS//TR, /SR/ =6cm and /RU/ =10cm. If the area of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bigtriangleup} TRU = 45Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cm^2} , calculate the Area of trapezium QTUS.
4. If the sixth term of an Arithmetic Progression (A. P.) is 37. and the sum of the first six terms is 147, find the:
   1. first term;
   2. sum of the first fifteen terms.
5. Out of 120 customers in a shop, 45 bought both bags and shoes. If all the customers bought either bags or shoes and 11 more customers bought shoes than bags;
   1. illustrate this information in a diagram;
   2. find the number of customers who bought shoes;
   3. calculate the probability that a customer selected at random bought bags.

Section B

6. 1. A manufacturing company: requires 3 hours of direct labour to process every 87.00 worth of raw materials. If the company uses $30,450.00 worth of raw materials, what amount should it budget for direct labour at $18.25 per hour?
   2. An investor invested ₦x in bank M at the rate of 6% simple interest per annum and ₦y in bank N at the rate of 8% simple interest per annum. If a total of ₦8,000,000.00 was invested in two banks and the investors received ₦2,320,000.00 as interest from two banks after 4 years. Calculate the
      1. values of x and y
      2. interest paid by the second bank
7. 1. Copy and complete the table of values for the equation y = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2x^2-7x-9} for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3\leq x \leq 6}

   x	-3	-2	-1	0	1	2	3	4	5	6
   y		13		-9	-14		-12		6

   2. using scales of 2cm to1 unit on the x-axis and 2cm to 4 units on the y-axis, draw the graph of y = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2x^2-7x-9} for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3\leq x \leq 6}
   3. Use the graph to estimate the:
      1. roots of equation
      2. coordinates of the minimum point of v
      3. range of Values for which Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2x^2-7x-9}

8. Marks	1	2	3	4	5
   No. of Students	m-2	m-1	2m-3	m-5	3m-4

      The table shows the distribution of marks scored by some students in a test.
   

   1. If the mean mark is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3 \frac{6}{23} } . find the value of m.
   2. Find the:
      1. interquartile range
      2. probability of selecting a student who scored at least 4 marks in the test
9. 1. PQ is a tangent to a circle RST at the point S. PRT is a straight line, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} TPS =34° and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} TSQ = 65°.
      1. illustrate the information in a diagram
      2. Find the value of: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} RTS: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} SRP
   2. In the diagram, /VZ/ = /YZ/, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} YXZ= 20° and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} ZVY = 52°. Calculate the size of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \angle} WYZ.
10. 1. Given that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin x =\frac{5}{13}, 0^\circ<x<90^\circ} find Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\cos x-2 \sin x}{2\tan x}}
    2. A ladder. LA, leans against a vertical pole at a point L which is 9.6 metres above the ground. Another ladder, LB, 12 metres long, leans on the opposite side of the pole and at the same point L. If A and B are 10 metres apart and on the same straight line as the foot of the pole. calculate, correct to 2 significant figures the,
       1. length of ladder LA:
       2. angle which LA makes with the ground.
11. 1. It takes 8 students two-thirds of an hour to fill 12 tanks with water. How many tanks of water will 4 students fill in one-third of an hour at the same rate?
    2. A chord, 20 cm long, is 12cm from the centre of circle. Calculate, correct to one decimal place, the:
       1. angle subtended by the chord at the centre of the circle;
       2. perimeter of minor segment cut off by the chord. [Take 7=3.142]
12. 1. Using completing the square method, solve, correct to 2 decimal places, the equation Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3y^2-5y+2=0} .
    2. Given that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M= \begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}, N=\begin{bmatrix} m & x \\ n & y \end{bmatrix}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MN=\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}} . Find the MATRIX N.
13. 1. The operation (*) is defined on the set of real numbers, R, by Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x\bigl(*\bigr)y=\left ( \frac{x+y}{2} \right ),x,y\in R}
       1. Evaluate Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3\bigl(*\bigr)2/5 }
       2. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 8\bigl(*\bigr)y=8\frac{1}{4} } , find the value of y.
    2. In ABC, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overrightarrow{A B} =\binom{-4}{6}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overrightarrow{A C} =\binom{3}{-8}} . If P is the midpoint of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overrightarrow{A B}} , express ${\overrightarrow {CP}}$ as a column