**Waec 2024 general mathematics questions and answers**

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Subject: General mathematics ESSAY & OBJ.

Date: 2nd — 2024

Time: 9:30am-12:00pm(ESSAY)

Time: 3:00pm-4:30pm(OBJ)

Password: **3990**

**OBJECTIVES:**

**1-10: ABBDBBBCAC
11-20: ABDDCCCBDD
21-30: ADCDBBCBCC
31-40: DCBCABBCCD
41-50: DBABAAACBB**

*COMPLETED*

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**OBJECTIVE QUESTIONS**

**ESSAY:**

**MATHS TYPE FORMAT**

**(2a)**

**y= (Pr/m – P²r) -³/²**

**Multiply both index by -⅔**

**y-⅔= (Pr/m – P²r)-³/²*-⅔**

**y-⅔/1 = Pr/m – P²r/1**

**my-⅔ = Pr – mP²r**

**my-⅔/P-mP² = r (P-mP²)/P-mP²**

**m/(P-mP²)y⅔ = r**

**(2b)**

**y= -8, m=1, P=3**

**r = m/(P-mP²)y⅔**

**r = 1/(3-1*3²)* -8⅔**

**r = 1/(3-9)*(³√-8)²**

**r = 1/-6*(-2)² = 1/-6*4 = 1/-24**

**:. r = -1/24**

**(3)**

**Perimeter of minor segment= AB + AB**

**AB = 2AM = 2rSin36°**

**= 2*24.5*Sin36°**

**= 28.8m**

**AB = 72°/360° * 2*22/7* 24.5**

**= 72/360* 154 = 30.8m**

**:. Perimeter= 30.8+28.8**

**= 57.6m**

**(4a)**

**2(2y+10) = 5x-35 (angle at centre = twice at circle)**

**4y+20= 5x-35**

**5x = 4y+55**

**x = 4/5y +11……….(1)**

**(2y+10)+(2x+40) = 180 (supplementary angle)**

**2x+2y+50 = 180**

**x+y = 65……..(2)**

**Put (1) into (2)**

**4/5y +11+y =65**

**9/5y = 54**

**y = 5/9*54 = 30**

**From (2) x=65-y = 65-30= 35**

**(4b)**

**<ABC = 360 – (5x-35+40+2x+40)**

**= 360 – (175-35+40+70+40)**

**= 360-290**

**= 70°**

**(5a)**

**Given m= tan30° = 1/√3**

**n = tan45° = 1**

**m -n/mn= 1/√3 -1/(1/√3)(1)**

**= √3(1/√3 -1)**

**= 1 – √3**

**(5b)**

**15-x+x+10-x =20**

**25-x = 20**

**x= 25-20 = 5**

**PnB(both) = 5/20 = 1/4**

**(6a)**

**On x-axis: 2cm to 2units**

**On y-axis: 2cm to 10units**

**(6b)**

**(x+2)(x-4) = 0**

**x²-4x+2x-8 = 0**

**x²-2x-8= 0**

**mx² + nx + r = y**

**:. m=1, n= -2, r = -8**

**(6c)**

**Gradient= y2 -y1/x2 -x1**

**= -27 -5/-5 -3**

**= -32/-8 = 4**

**(6d)**

**(x+2)(x-4) > 0**

**x+2<0 or x-4<0**

**x< -2 or x<4**

**And x-4>0**

**x+2>0 or x-4>0**

**x> -2 or x>4**

**:. x> -2**

**(10a)**

**[TABULATE]**

**Age X; 3 4 5 6 7 8 9 10**

**Number of children F; 2 6 5 x=4 6 9 8 5**

**Fx; 6 24 25 6x=24 42 72 72 50**

**x – x̄; -4 – 3 – 2 – 1 0 1 2 3**

**(x – x̄)²; 16 9 4 1 0 1 4 9**

**f(x – x̄)²; 32 54 20 4 0 9 32 45**

**Σf = x + 41**

**Σfx = 6x + 291**

**Σf(x – x̄)² = 196**

**Mean x̄ = Σf/Σf**

**x̄ = 7 = (6x + 291)/(x +41)**

**7x + 287 = 6x + 291**

**7x – 6x = 291 – 287**

**x = 4**

**(10b)**

**S.D = √[(Σf(x – x̄)²]/Σf**

**S.D = √(196/x+41)**

**S.D = √(196/45)**

**S.D = 2.1**

**IMAGE ANSWERS**

No1.

No2

No3

**5a) m=tan30°= 1/√3 and n=tan45°=1**

**=> (m-n)/mn= (1/√3 -1)/(1/√3 ×1)**

**=> √3(1/√3 -1)=> 1-√3.**

**5b) let the probability that the a woman wear glasses be Pr(g) and that of wearing wristwatch be Pr(w)**

**=> Pr(g)=15/20 and Pr(w)=10/20**

**=> Pr(gnw)=Pr(g)×Pr(w) => 15/20 ×10/20=150/400=15/40=3/8**

**5a) m=tan30°= 1/√3 and n=tan45°=1**

**=> (m-n)/mn= (1/√3 -1)/(1/√3 ×1)**

**=> √3(1/√3 -1)=> 1-√3.**

**5b) let the probability that the a woman wear glasses be Pr(g) and that of wearing wristwatch be Pr(w)**

**=> Pr(g)=15/20 and Pr(w)=10/20**

**=> Pr(gnw)=Pr(g)×Pr(w) => 15/20 ×10/20=150/400=15/40=3/8**

No6:

13a) Area=2πr²+2πrh

=> Area=2πr(r+h)

=> r+h=Area/(2πr)

=> h=(Area/(2πr))-r

given that area=209cm² and r=7cm and π=22/7

=> h=(209)/(2×22/7×7) -7

=> h=(209/44) -7

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