. In a particular year, the exchange rate of Naira (N) varies directly with the Dollar ($). If N is equivalent to $8, find the Naira equivalent of $6. A. N8976 B. N049 C. N40. D. N.7. If log = x, log = y and log 7 = z, find, in 8 terms of x, y and z, the value of log A. x + y z B. x + z y C. x + y z D. x + z y OBJECTIVE TEST Answer all questions C. N,600.00 D. N,00.00. Simplify 4 6 6. Express the square root of 0.00044 in A. B. 8 C. D. 47 standard form 4 A.. x 0-4 B.. x 0 - C.. x 0 - D.. x 0-7. Two sets are disjoint if A. they are both empty B. their union is an empty set C. their intersection is an empty set D. one of them is a subset of the other 8. Solve the following simultaneous equations: x + y = 7 x + y = 0 A. x =, y = - B. x =, y = - 4. Arrange the following numbers in descending order of magnitude: three, 4 five, six A. six, three, 4 five B. six, 4 five, three C. three, 4 five, six D. 4 five, six, three. Find the value to which N000.00 will amount in years at 6% per annum simple interest A. N,900.00 B. N,70.00 C. x = -, y = D. x = -, y = 9. If 4, solve for x. x x 4 4 A. B. C. D. 4 4 MATHEMATICS (CORE) Page
The following is the graph of a quadratic function. Use it to answer questions 0 and 0. Find the co-ordinates of point P. A. (0, 4) B. (4, 0) C. (0, -4) D. (-4, 0). Find the value of x when y = 0 A., B., 4 C., D., 6. Find bottles of Fanta and two packets of biscuits cost Gh 6.00. Three bottles of Fanta and four packets of biscuits cost Gh.00. Find the cost of a bottle of Fanta. A. Gh 0.0 B. Gh.00 C. Gh.0 D. Gh.00 6. The diameter of a bicycle wheel is 4cm. If the wheel makes 6 complete revolutions, what will be the total distance covered by the wheel? (Take = ) 7 A. 67cm B. 06cm C. cm D. 44cm. If (x + ) =, find the value of x. A. B. C. D. 4 4. Factorise x x xy + 6y completely. A. (x )(x y) B. (x y)(x ) C. (x )(x + y) D. (x + y)(x ). Which of the following illustrates the (x 4) solution of x? PQRS is a trapezium. QR//PS, /PQ/ = cm, /QR/ = 6cm, /PS/ = 0cm and angle QPS = 4 o. Use the information to answer questions 7 and 8. 7. Calculate the perpendicular distance between the parallel sides. MATHEMATICS (CORE) Page
A..cm B..7cm C. 4.0cm D. 4.6cm. 8. Calculate, correct to the nearest cm, the area of the trapezium. A. 7cm B. 0cm C. 6cm D. 7cm 9. Find the value of x in the diagram A. 0 o B. 0 o C. o D. 7 o In the diagram, /TP/ = cm and it is 6cm from O, the centre of the circle. Calculate TOP. A. 0 o B. 90 o C. 60 o D. 4 o 4. In the diagram, /SQ/ = 4cm, /PT/ = 7cm, /TR/ = cm and ST//QR. If /SP/ = x cm, find the value of x. 0. The interior angles of a pentagon are (x + ) o, (x + 0) o, x o, (x ) o and (x + ) o. Find the value of x A. 80 o B. 70 o C. 6 o D. 40 o. A..6 B. 6. C. 6.6 D. 6.8 In the diagram, IG is parallel to JE, J ÊF = 0 o and F ĤG = 0 o. Find the angle marked t. A. 40 o B. 70 o C. 80 o D. 00 o. If M and N are two fixed points in a plane, find the locus L = {P : PM = PN} A. A line equal to MN B. A line parallel to MN C. Perpendicular bisector of MN D. A circle centre P, radius MN MATHEMATICS (CORE) Page. Given that sin 60 o = calculate A. C. sin60 cos 60 o o and cos 60 o =, B. D. Use the diagram below to answer questions 6 and 7
A. 7.cm B. 0.cm C. 7.0cm D. 6.cm E. 8.cm. Two towns are 8km apart. If the towns are on the same line of longitude, find the difference in their latitudes to the nearest degree (Take =.4, R = 6400km) A. o B. o C. 4 o D. o E. 6 o 6. Find the bearing of X from Y A. 00 o B. 40 o C. 0 o D. 60 o 7. If /XY/ = 0m, how far east of X is Y? A..m B. 40.6m C. 40.8m D. 4.m 8. In an examination, Kofi scored x% in Physics, 0% in Chemistry and 70% in Biology. If his mean score for the three subjects was %, find x. A. 40 B. 4 C. D. 60 9. What is the median of the following scores:, 4,, 6, 8, 74? A. 8 B. C. 49 D.. How many cubes of sugar are contained in a rectangular packet of size cm by 9cm by 6cm if each cube is of side.cm? A. 00 cubes B. 0 cubes C. 00 cubes D. 40 cubes E. 80 cubes 4. A cuboid is a prism whose uniform crosssection is a A. circle B. rectangle C. rhombus D. square E. triangle. The length and width of a rectangle are in the ratio :. If the perimeter is 80cm, calculate the length of its diagonal to decimal places. A. 9.cm B..cm C..cm D. 0.cm E. 9.cm 0. Express.7864 x 0 - to two significant figures. A. 0.8 B. 0.7 C. 0.008 D. 0.007. ABC is an equilateral triangle with sides 0cm and DEFG is a rectangle of sides cm by 6cm. Find, correct to decimal place, the area of the triangle not covered by the rectangle. 6. PQRS is parallelogram, find <PQS if <PSQ is 7 o. A. 9 o B. o C. 40 o D. 49 o E. 8 o MATHEMATICS (CORE) Page 4
7. In the diagram below, XY is the diameter of o the circle with centre O. If XŶA and o ABˆY, calculate X ÂY. 4. PQRS is a kite with PQ = QR, PS = SR, QS = 0cm. Find PS. A. o B. o C. 86 o D. 90 o E. 80 o 8. Calculate the value of n in the diagram below, if D is the centre of the circle. A. 0cm B. cm C. 0 6 cm 0 6 D. cm 0 E. cm 4. A. 8 o B. 86 o C. 88 o D. 9 o E. 84 o 9. The ratio of the sides of a triangle is ::4. If the perimeter of the triangle is 7cm, find the largest side of the triangle. A. 7cm B. 8cm C. cm D. 9cm E. 6cm 40. The exterior angles of a pentagon are (x + ) o, (x + 0) o, x o, (x + 0) o, and (x - ) o. Find the value of x. A. 0 o B. 0 o C. 00 o D. 90 o E. 60 o 4. When two parallel lines are cut by a transversal, which of the following is NOT applicable? A. Opposite angles at any point of cut are equal B. The alternate angles are equal C. The corresponding angles are equal D. The interior angles are complementary E. The interior angles are supplementary Calculate AC in the figure above. A. cm B. cm C. 4cm D. cm E. 6cm 44. How many sides has a polygon whose sum of interior and exterior angles are the same? A. B. 0 C. 8 D. 6 E. 4 4. If sin x = and 0 o < x < 90 o, find the value of 4 ( tan x). A. B. 4 D. 4 E. C. 4 MATHEMATICS (CORE) Page
44. A train takes y hours to cover a certain distance when its average speed is x km/h. How many hours would it take to cover the A. y D. distance at x B. E. y km/h? C. y 4. ABC is a triangle in which AB = cm, BC = cm and <ABC = 64 o. Find its area, correct to decimal place. A. 4.cm B. 46.7cm C. 70.cm D. 40.cm E. 6.0cm 46. The angles of elevation of the top of a pole from two points on the horizontal ground are 0 o and 4 o. If the two points are on opposite side of the pole, find the distance between them if the pole is 0m high. 0( A. C. ) m B. 40 m 400 m D. E. 0 m 0 m.99 49. If, find. o sin sin09 A. 7. o B. 9.76 o C. 0.4 o D. 09.00 o E. 9.76 o 0. The perimeter of an isosceles triangle is 7x. If the base is 7x, find, correct to the nearest degree the vertical angle of the triangle. A. 0 o B. 0 o. 40 o D. 4 o E. 70 o D. E. 8 7. All are distinctive features of histogram EXCEPT A. class boundaries are used B. it has straight bars C. the height of bars are proportional to its frequencies D. the width of each rectangle corresponds to its interval size E. there are spaces between the bars 4. The following are the test scores of ten students in a mathematics test:,,,, 7, 9, 8,,,. Find the value of twice the mode multiplied by the mean and divided by the median A..4 B. 4.60 C.. D. 6.90 E. 9.0. If balls are drawn without replacement from a bag containing 0 blue and red identical balls, find the probability that the two balls drawn are of different colours. 0 A. B. C. 7 D. 7 E. 6. The table below shows the number of students for each age group in a class Age (yrs) 6 7 8 Number 7 Find the sum of the median and the mode. A. 4 B. 9 C. D. E. 0. Given that the variance of a set of data is 9, calculate the standard deviation. A. B. 6 C. 7 D. 8 E. 8. A coin is tossed thrice, what is the probability of having at least two heads? A. B. C. 8 8 MATHEMATICS (CORE) Page 6
The table below shows the marks scored by candidates in a mathematics test. Use the information to answer questions 7 and 8. Marks % 0 40 0 60 80 Number of students 8 4 7. What is the probability that a candidate chosen at random will score above 0%? 7 A. B. C. 0 8 D. 8 E. 4 8. What is the probability that a student chosen at random will pass the test if the pass mark is 70%? A. B. C. 0 0 D. 0 7 E. The scores below are the outcomes of an Economics test conducted by a teacher for 0 students. Use the information to answer questions 9 and 60., 0,,, 4, 0,,, 0,, 6, 8,, 6, 8, 4, 0,, 7, 9 9. Find the inter-quartile range A. B. 9 C. 0 D. E. 7 60. Find the range of the data A. B. 9 C. 0 D. E. 7 MATHEMATICS (CORE) Page 7
ESSAY ANSWER TEN QUESTIONS IN ALL PART I Answer all questions in this section. (a) if 9 cos x o 7 = and 0 o x 90 o, find x (b) Given that x is an integer, find the three greatest values of x which satisfy the inequality 7x < x. (a) Out of 0 candidates applying for a post, 7 have degrees, diplomas and 4 neither degree or diploma. How many of them have both? (b) In triangle PQR, M and N are points on the sides PQ and PR respectively such that MN is parallel to QR. If PRQ = 7 o, PN = QN and PNQ = o, determine (i) NQR (ii) NPM. Given that = {,,, 4,, 6, 7, 8} P = {x: x is a prime number} Q = {x: x is a multiple of 4} R = {x: (x - )(x - )(x - 8) = 0} (i) List the elements of P, Q and R (ii) Find P Q R' (iii) What is P Q R? 4. A survey of professionals and artisans taken in a certain community reveals that there are 8 Teachers, Masons, 4 Accountants, Engineers, 0 Doctors and Traders. (a) Draw a pie chart to illustrate this information (b) If a person is chosen at random for the community chairmanship, what is the probability that the person is a teacher?. (a) The sum of the first terms of an A. P. is 9 and the sum of the next terms is 6. List the first 6 terms of the A. P. (b) Give that log 0 (x ) + log 0 =, find x. PART II Answer only five questions from this section 6. The feet of two vertical poles of height m and 7m are in line with a point P on the level ground, the shorter pole being between the longer pole and P, and at a distance of 0m from P. The angle of elevation of the top T of the longer pole from the top R of the shorter pole is 0 o. Calculate the (a) distance RT (b) distance of the foot of the longer pole from P, correct to three significant figures; (c) angle of elevation of T from P, correct to one decimal place 7. A train covered a distance of 00km for three days from a point P on a bearing of 060 o to another point Q. It then continues the journey directly east of Q to another point R, a distance of 00km. Calculate, correct to decimal place, the (a) distance between P and R (b) bearing of P from R (c) shortest distance between Q and PR 8. (a) 6cm 4cm 4cm The above figure is a composite solid made up of cone, cylinder and hemisphere. Find its (i) volume (ii) total surface area correct to the nearest whole number 7 (b) If twice a given number is the same as the square of the number, what are the possible values of the number? 9. x - - 0 4 y -8 6-6 (a) Copy and complete the above table for the relation y = + 6x x MATHEMATICS (CORE) Page 8
(b) Using a scale of cm for unit on x-axis and cm to units on y-axis, draw a graph of the relation y = + 6x x for - x. (c) Using the same scale and axes, draw the graph of y = x - (d) On your graph, find correct to one decimal place, the (i) maximum value of y and the corresponding value of x (ii) solution to the equation + 6x x = x - 0. (a) A woman looking out from the window of a building at a height of 0m, observed that the angle of depression of the top of a flag pole was 44 o. If the foot of the pole is m from the foot of the building and on the same horizontal ground, find, correct to the nearest whole number, the (i) angle of depression of the foot of the pole from the woman (ii) height of the flag pole. (iii) coordinates of the other point where the graph cuts the x-axis. (a) A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 00cm, calculate the radius of the circle. Take 7 (b) A rope 60 cm long is made to form a rectangle. If the length is 4 times its breadth, calculate, correct to one decimal place, the (i) length; (ii) diagonal of the rectangle (b) P T o O S Q o R In the diagram, O is the centre of the circle, OQR = o and TPQ = o. Calculate (i) QPR (ii) TQO x x. (a) Simplify x x (b) The graph of the equation y = Ax +Bx + C passes through the points (0, 0), (, 4) and (, 0). Find (i) value of C (ii) values of A and B MATHEMATICS (CORE) Page 9
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