%100 VERIFIED 2016 WAEC GCE MATHS OBJ AND ESSAY ANSWERS

MATHEMATICS OBJ 1abcdbcbadb 11dccccacdba 21bdbaabdaca 31ccacbdcdbd 41dacbdabbbc Dear Candidate Here Are The Symbol To Be Use For Physic And Mathematics Exam PHYSICS AND MATHEMATICS SYMBOLS TO BE USED FOR EXAM / means DIVISION * means Multiplication tita You Should Know that. rais means Raise to power Or ^ means Raise to power sqr rut/square rut means Square root ----(1) means Equation 1 yr means Year f(x-xbar) means x MINUS x BAR as in statistics which means that MINUS will be on Top of x. , (Comma) means NEXT LINE, This means that The Following Number is Under The Number its Following ie. UNDER. It is usually used during STATISTICS when drawing a table. EXAMPLE 1. X: 1,2,3,4,5,6 FX: 4,6,8,10,12 FX-Xbar: 10,8,6,4,2,1 DRAW A TABLE WITH X|FX|(FX-Xbar) The above statement means that: ~For X, it has 1 2 3 4 5 6 under it. which means 1 is under 2, 2 is under 1, 3 is under 2, 4 is under 3 and so on... ~Under FX you have 4, then 6 under 4, then 8 under 6, then 10 under 8, then 12 under 10..... ~Under FX-Xbar you have 10, then 8 under 10, then 6 under 8, then 4 under 6, then 2 under 4, then 1 under 2.... ANOTHER EXAMPLE: Class interval: 60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99. X: 62,67,72,77,82,87,92,97. F: 2,3,6,11,8,7,2,1. FX: 124,201,432,847,656,609,184,97. F(x-x bar)2: 561.12,414.18,273.36,33.66,84.48,476.42,351.12,333.06 MEANING OF THE ABOVE EXPRESSION Bar means Minus on top of d number or Variable and comma means next line which means each of them are unda. Eg 60-64 is unda Class interval, then 65-69 is unda 60-64,etc .So comma means unda. NOTE : When You See Something Like the above to Examples, You are requered to Draw a Table. ======================== WARNING : Please Study the above Symbols, If you Dnt want to write Rubbish in you MATHEMATICS Exam Or Calculation Exam NOTE THAT ANSWERS ARE ARRANGED ACCORDINGLY, SO ALWAYS SCROLL DOWN TO SEE NEW/MORE ADDED ANSWERS MATHEMATICS ANSWERS INFINITYGURU] Use this 1a ) 6whole 1 / 2 - 3 whole 2/ 5 / 2whole 1 / 2 - 1 whole 3/ 5 25 / 4- 17 / 5 , / 5/ 2- 8/ 5 125 - 68 / , 20 , / 25 - 16, / 10 ==> 57 / 20 / 9/ 10 =57 / 20 /9 / 10 =57 / 20 x 10 / 9 =57 / 20 x 10 / 9 =57 / 18 = 3whole 1 / 6 ======= 3a) c= -1, y= -3, z= -4 and w= -7 x^2 - y^2 / 2w - z (-1)^3 - (-3)^2 / 2(-7) -(-4) = -1-9/+4+4 = -10/-10 = 1 3b) < MQN + < NQO = 90 degree < MNQ + 46 = 90 degree < MNQ = 90 - 46 degree < MNQ = 44 degree Considering < MNQ y + n + MQN = 180 degree y + 44 + 44 = 180 y = 180 - 88 Y =92 degree 4a) 2/3(1-4x) -1/2(5-3x) less/equal to 1/4(7+9x)-1/3 multiply through by 12 8(1-4x) -6(5-3x) less/equal to 3(7+9x)-4 8-32x-30+18x less/equal to 21+27x-4 -32x+18x - 27x less/equal to 21-4+30-8 -41x less/equal to 39 x less/equal to -39/41 4b) DRAW THE ANGLE from DTMR/ Tan65degree = TR/3 TR = 3Tan65 = 3 x 22.1445 From DRMB Tan20 = RB/3 RB = 3Tan20 = 3 x 0.3640 = 1.092m H = TR+RB = 6.4335 + 1.092 = 7.5255 = 7.53m 5) Area of shed segment = Area of Sector - Area of Triangle =Φ/360*πr^2 - (½abSinc) =$90/360*22/7*7^2) - ½*7*7*sin90` =154/4 - 42/2 =(754-98)/4 =56/4 =14cm^2 Cost of painting it =14*750 =N10500 ======== 6a) Taxable income = x 25/100 x x/1 = 14,000 25x=1400000 X=1400000/25 X= 560000 Total income = 56,000/4 x 5 =70,000 6b) Education = 2/5 Clothes = 1/6 Food = 3/8 Expenditure = 2/5 + 1/6 + 3/8 48+20+45/120 = 113/120 * 36,000/1 Le 39,000 Savings annually = Le 21,000 To save Le 63,000.00 To save Le 63,000/2100 yrs = 30 years (7a ) diagram (7b ) Angula difference in long (tita)=42 - 12 tita=30 degree (7bi ) lenght of chord Xy=2 Rsin tita /2 XY= 2*6400*Sin 30 /2 =2 6400sin 15 degree =12800 *0. 2588 =3 . 312 . 64 km =3312. 64 km =3310km (to the nearest 10 km ) (7bii ) let the angle that the chord xy substends at the centre of the earth be alpha degree diagram sin alpha/ 2= opp / hyp =/ NY/ / 6400 /NY/ = 1/ 2 /XY /= 1/ 2 * 3312. 64 =1656. 32 km sin alpha/ 2= 1656. 32 / 6400 sin alpha/ 2= 0 . 25888 alpha/ 2= sin ^ - 1(0. 2588) alpha/ 2=14 . 999 alpha=14 . 999 *2 alpha= 29 . 998 alpha= 30 . 0 degree (to 1 dp ) (7biii) XY