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IRS OBJECTIVE

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***SECTION A***

***_(Answer ALL QUESTIONS From This Section)_***

**(1a)**

**6^n+1*9^n*4^2n/18^n*2^n*12^2n**

**=(2*3)^n+1*(3*3)^n*(2*2)^2n/(2*3*3)^n*2^n*(2*2*3)^2n**

**=2^n+1*2^n+1*3^n*3^n*2^2n*2^2n/2^n*3^n*3^n*2^n*2^n*2^n*3^2n**

**= 2^n*2^1*2^n*2^1*3^n*3^n*2^n*2^n*2^n*2^n/2^n*3^n*3^n*2^n*2^n*2^n*2^n*2^n*3^n*3^n**

**= 2^6n*3^2n*2*2/2^6n*3^4n**

**= (2^6n / 2^6n) *(3^2n / 3^4n)*2*2**

**=2^6n - 6n * 3^2n - 4n * 4**

**= 2^0 * 3^-2n * 4**

**= 4*3^-2n**

**= 4 * 1/3^2n**

**= 4/3^2n**

**(1b)**

**Log 243/log 27**

**= log 3^5/log 3^3**

**= 5log3/3log3 = 5/3 = 1 whole no 2/3**

**============================================**

**(2a) **

**3t - 2p = 8Ã—2 ...(I) **

**2t - 3p = 14Ã—2...(II) **

**6t - 4p = 16 ...(III) **

**6t - 9p = 42 ...(IV) **

** 9P - 4P = -42 + 16**

** 5p = -26**

**P = -26/5 = -5 1/5**

**Put p = -26/5 into eqn (I) **

**3t - 2(-26/5) = 8**

**3t + 52/5 = 8**

**3t = 8 - 52/5**

**3t = 40 - 52/5 = -12/5**

**Divide both sides by 3**

**36/3 = -12/5 / 3**

**t = -12/5 Ã— 1/3**

**= -12/15 = -4/5**

**(2b)**

**3/âˆš3(2/âˆš3 - âˆš12/6)**

**2/âˆš3 Ã— 3/âˆš3 - 3/âˆš3 Ã— âˆš12/6**

**6/âˆš9 - 3âˆš12/6/âˆš3**

**6/3 - 3âˆš12/6âˆš3**

**2 - âˆš12/2âˆš3**

**2 Ã— 2âˆš3 - âˆš12/2âˆš3**

**4âˆš3 - (âˆš4 Ã— 3)/2âˆš3**

**= 4âˆš3 - 2âˆš3/2âˆš3**

**= 2âˆš3/2âˆš3 = 1**

**============================================**

**(3)**

**P(k) = 2/3**

**P(Y) = 5/8**

**P(I) = 3/4**

**P(k fail) = 1- 2/3 = 1/3**

**P(Y fail) 1 - 5/8 = 3/8**

**P(I fail) = 1 - 3/4 = 1/4**

**(a) 2/3*5/8*3/4 = 5/16**

**(b) 1/3*3/8*1/4 = 1/32**

**(c) 2/3*5/8*1*4 = 5/48**

**==============================================**

**(4)**

**Draw the triangle **

**<GFN = 180 - ( 68+90)**

**Sum of angles in a Î”**

**= 180 - 158 = 22°**

**Sin 22/|GN| = Sin 68/8**

**|GN|= 8sin22/sin68**

**= 8Ã—0.3746/0.9272**

**= 2.9969/0.9272**

**= 3.2322cm**

**|GT| = |TN| = 3.2322**

**= 1.616â‰ˆ 1.62cm**

**Let tita = <FTG**

**(i) tan tita = 8/1.6161 = 4.9502**

**tita = tan^-¹(4.9502)**

**tita = 78.6°**

**FTN = 180 - tita**

**= 180 - 78.6**

**(sum of angles on a straight line) = 101.4**

**(ii) >TFN **

**= 180 - (68+101.4)**

**Sum of angles in a Î”**

**180 - 169.4**

**=10.6°**

**==============================================**

**(5a)**

**4 1/2 - 3(y - 2) = 2y + 1/3**

**= 9/2 - 3y + 6 = 2y + 1/3**

**= -3y + 6 + 9/2 = 2y + 1/3**

**6 + 9/2 = 2y + 1/3 + 3y**

**12 + 9/2 = 2y + 1/3 + 3y**

**21/2 = 2y + 1 + 9y/3**

**21 Ã— 3 = 2(2y + 1 + 9y)**

**63 = 4y + 2 + 18y**

**63 = 22y + 2**

**22y = 63 - 2**

**22y = 61**

**y = 61/22 = 2 17/22**

**(5b) **

**Let the number be y **

**7 - 2y >_ 16**

**-2y >_16 - 7**

**-2y >_ 9**

**y _< _9/2 = 4 1/2**

**The greatest possible values of y are; -4, -3, -2, -1, 0**

**===============================================**

***SECTION B***

**_(All Candidates should Answer FOUR while SECRETARIAL & BUSINESS CANDIDATES Should Answers Only TWO from this Section)_**

**(6a)**

**Let the water melon be x**

**Let the mango be y**

**12x + 24y = 432 ...(i) Ã— 24**

**24x + 12y = 360...(ii) Ã— 12**

**288x + 576y = 10368 ...(iii) **

**288x + 144y = 4320 ... (iv) **

**-144y + 576y = -4320+10368**

**432y = 6048**

**y = 6018/432 = 14**

**Put y = 14 into eqn (i) **

**12x + 24(14) = 432**

**12x + 336 = 432**

**12x = 432 - 336**

**12x = 96**

**X = 96/12 = 8**

**(i) Water melon per kg = 8**

**(ii) Mango per kg = 14**

**(iii) (3 Ã— 8) + (2 Ã— 14)**

**= 24 + 28**

**= 52**

**(6b) **

**123x = 83ten**

**1*X² + 2*X¹ + 3*X^0**

**= 83**

**X² + 2x + 3 = 83**

**X² + 2x + 3 - 83 = 0**

**X² + 2x - 80 = 0**

**X² + 10x -8x - 80 = 0**

**X(x+10) - 8(x+10) = 0**

**Then either **

**X - 8 = 0 or X + 10 = 0**

**X = 8 or X = -10**

**================================================**

**(8a) **

**Distance /xy/ = tita/360 Ã— 2Ï€r**

**tita = 45° - 15° = 30°**

**r = RcosÎ±**

**r = 6400 Ã— cos40°**

**r = 6400 Ã— 0.7600**

**r = 4902.4km**

**Distance /xy/ = 30/360 Ã— 2 Ã— 22/7 Ã— 4902.4**

**= 30 Ã— 2 Ã— 22 Ã— 4902.4/2520**

**=6471168/2520 = 2567.9238**

**= 2600km**

**(8bi) **

**Time taken to fly from X to y**

**Speed = Total distance/Total time taken **

**850 = 2600/t**

**t = 2600/850 = 3.0588hrs**

**t = 3hours**

**Time taken to fly to Y from X**

**Time = Distance/Speed**

**= 6700/850 = 7.8824hrs = 8hrs**

**Total time = 3hrs + 8hrs = 11hrs**

**(8bii) **

**Latitude of Z**

**Distance /yz/ = tita/360 Ã— 2Ï€r**

**6700 = Z-40/360Ã—2Ã—22/7Ã—6400**

**6700Ã—360Ã—7 =(Z - 40)281600**

**16884000 = 281600Z - 11264000**

**281600Z = 16884000 + 11264000**

**281600Z = 28148000**

**Z = 28148000/281600**

**Z = 99.9574 = 100°**

**=================================================**

**(9a)**

**DRAW THE TRIANGLE DAIGRAM**

**|YX| = x + 620**

**From âˆ† YFP**

**Tan56 = R/620**

**R = 620 x tan56**

**= 620 x 1.4826**

**h = 919.19m**

**To find x**

**Tan 20 = h/x**

**X = h/tan20 = 919.19/0.3639**

**X = | XF | = 2525.45m**

**|YX| = |XF| + |FY|**

**|YX| = 2525.45 + 620**

**= 3145.5.45m**

**Hence the value of |YX| correct to the four significant figure is 3145m**

**|XY| = 3145m**

**(9b)**

**DRAW THE DAIGRAM**

**|YX|² = |OY|² + |OX|² - 2|OY| |OX| cosÃ˜**

**(6)² = (5)² + (5)² - 2 (5) (5) cosÃ˜**

**36 = 25 +25 â€“ 50cosÃ˜**

**36 = 50 â€“ 50cos Ã˜**

**50cosÃ˜ = 50 â€“ 36**

**50cos = 14**

**cosÃ˜ = 14/50 = 0.28**

**Ã˜ = cos-¹ (0.028) = 73.34º**

**Therefore <XZY = ½ (73.74) (Angle at the center twice the angle at the circumference)**

**<XZY = ½ (73.74) = 36.87º**

**<XZY = 37º (nearest degree)**

**(9bii)**

**Let |XZ| = |YZ| = y**

**|XY|² = |YZ|² + |XZ|² - 2 |YZ| |XZ| Cosã€†**

**(6)² = y² + y² - 2y² cos 36.87**

**36 = 0.4y²**

**y² = 36/0.4 = 60**

**y = âˆš60 = 7.75m**

**hence, |XZ| = 7.8m (1dp)**

**=================================================**

**(11a)**

**In a tabular form **

**Under scores(x)**

**2, 3, 4, 5, 6, 7**

**Under frequency(f) **

**2, 4, 5, 3, 4, 2 Ef, = 20**

**Under fx **

**4, 12, 20, 15, 24, 14 Efx = 89**

**(i) Modal score = 4**

**(ii) Median = n1+n2 = 4+4/2 = 8/2 = 4**

**(iii) Mean X = Efx/Ef = 89/20 = 4.45**

**(11b) **

**A = P(1+r/100)n **

**A = amount in compound interest.**

**P = principal, r = rates, n = no of years the compound interest is charged. **

**A = 53000(1+7/100)^5**

**= 53000(1+0.07)^5 = 53000(1.07)^5**

**In a tabular form **

** No | Log**

**53000| 4.7243 = 4.7243**

** | 0.0294Ã—5 = 0.1469**

** 4.8712**

**Antilog of 4.8712 = â‚¦74436.14**

**Compound interest = 74436.14 - 53000 = â‚¦21336.14**

**=================================================**

***SECTION C***

**_(Only For SECRETARIAL & BUSINESS Candidates. They shoud answers only TWO from this section)_**

**(12a) **

**If passengers paid â‚¦8,400.00 per trip **

**Commission on each trip = 5/100 Ã— 8400 = â‚¦420.00**

**For 52 trips, his commission would be 52 Ã— â‚¦420 = â‚¦21,840.00**

**His take home for the month = â‚¦6000.00 + â‚¦21,840.00 = â‚¦27,840.00**

**(12bi) **

**Gross pay = â‚¦125018.35 per month. **

**5% income tax = 5/100 Ã— 125018.35 = 6250.9175**

**2% Union dues = 2/100 Ã— 125018.35 = 2500.3670**

**1% housing fund = 1/100 Ã— 125018.35 = 1250.1835**

**7.5% pension scheme = 7.5/100 Ã— 125018.35 = 9376.3763**

**2.5% health insurance scheme = 2.5/100 Ã— 125018.35 = 3125.4588**

**10% cooperative contribution = 10/100 Ã— 125018.35 = 12501.8350**

**Total deductions = 6250.9175+2500.3670+1250 1835+9376.3763+3125.4588+12501.8350 = 35005.14**

**(12bii)**

**His net pay = â‚¦125018.35 - 35005.14 = â‚¦90013.21**

**=====================================================**

**(13a)**

**4 - point moving average. **

**16, 18, 20, 27, 28, 31, 32**

**16+11+20+27/4 = 81/4 = 20.25**

**18+20+27+28/4 = 93/4 = 23.25**

**20+27+28+31/4 = 106/4 = 23.25**

**20+27+28+31/4 = 106/4 = 26.5**

**27+28+31+32/4 = 118/4 =**

** 29.5**

**(13b)**

**First 20weeks, she earns â‚¦400Ã—20 = â‚¦8000**

**The next 20weeks she earns â‚¦720Ã—20 = â‚¦14400**

**Total earns for 40weeks = â‚¦8000 + â‚¦14400 = â‚¦22400**

**Total earns for the whole**

** year = â‚¦52Ã—600 = â‚¦31200**

**Amount earns for the remaining 12months = â‚¦31200 - â‚¦22400 = â‚¦8800**

**Average weekly earns for the last 12 months = 8800/12 = â‚¦733.33**

**======================================================**

**(15a)**

**Rent = 15/100 * â‚¦365,500 = â‚¦54,825**

**Personal allowance = 12/100 Ã—â‚¦365,500 = â‚¦43,860**

**Annual tax free allowance **

**= â‚¦54825 + â‚¦43860 = â‚¦98685**

**(15b) **

**Taxable income = â‚¦(365500 - 98685) = â‚¦266,815**

**Tax calculation **

**The first â‚¦65,000 = 0% = â‚¦0**

**Next â‚¦100,000 = 10/100 Ã— 100,000 = â‚¦10,000**

**Next 100,000 = 15/100 Ã— 100,000 = â‚¦15,000**

**The remaining â‚¦1815 = 20/100 Ã— 1815 = â‚¦363**

**Annual income tax = â‚¦(0 + 10,000 + 15,000 + 363)**

**=â‚¦25,363**

**(15c) **

**Percentage of his salary paid as tax = 25,363/365,500 Ã— 100 = 6.94%**

**=======================================================**

**Answers loading... **

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A1: 1 x 4 = 4 B2: 3 x 3.6 = 10.8 C4: 1 x 2.8 = 2.8 Total points: 4 + 10.8 + 2.8 = 17.6 Now, we divide the UTME by 8 i.e 280 ? 8 = 35 So, the aggregate score will be 17.6 + 35 + Post-UTME score.

A1: 1 x 4 = 4 B2: 3 x 3.6 = 10.8 C4: 1 x 2.8 = 2.8 Total points: 4 + 10.8 + 2.8 = 17.6 Now, we divide the UTME by 8 i.e 280 ? 8 = 35 So, the aggregate score will be 17.6 + 35 + Post-UTME score.

A1: 1 x 4 = 4 B2: 3 x 3.6 = 10.8 C4: 1 x 2.8 = 2.8 Total points: 4 + 10.8 + 2.8 = 17.6 Now, we divide the UTME by 8 i.e 280 ? 8 = 35 So, the aggregate score will be 17.6 + 35 + Post-UTME score.

waec expo runs is real. WAEC Answers, NECO ANSWERS and GCE answers comes a night before exam or Hours before exam

You are required to get at least a credit pass (50%) in your core subjects. Under the new WAEC grading system, A1 is Excellent, B2 Very Good, B3 Good, C4, C5 and C6 are interpreted as Credit, D7 and D8 are interpreted as Pass, while F9 is Fail.

waec expo runs is real. WAEC Answers, NECO ANSWERS and GCE answers comes a night before exam or Hours before exam

Under the new WAEC grading system, A1 is Excellent, B2 Very Good, B3 Good, C4, C5 and C6 are interpreted as Credit, D7 and D8 are interpreted as Pass, while F9 is Fail. A1 and B2 in the WASSCE means Excellent, B3 is B (Very Good), C4 is C (Good), C5 and C6 are D (Credit), D7 and E8 are E (Pass) and F9 is F (Fail).

waec expo runs is real. WAEC Answers, NECO ANSWERS and GCE answers comes a night before exam or Hours before exam