Algebra
1. Solve: 2x+3=112x + 3 = 112x+3=11
o Solution:
2x=11−32x = 11 - 32x=11−3
2x=82x = 82x=8
x=82=4x = \frac{8}{2} = 4x=28=4
Answer: x=4x = 4x=4
2. Solve: 3(x−2)=93(x - 2) = 93(x−2)=9
o Solution:
3x−6=93x - 6 = 93x−6=9
3x=9+63x = 9 + 63x=9+6
3x=153x = 153x=15
x=153=5x = \frac{15}{3} = 5x=315=5
Answer: x=5x = 5x=5
3. Solve: x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0
o Solution (Factoring):
(x−2)(x−3)=0(x - 2)(x - 3) = 0(x−2)(x−3)=0
x=2 or x=3x = 2 \text{ or } x = 3x=2 or x=3
Answer: x=2,3x = 2, 3x=2,3
4. Solve: 4x+7=3x−54x + 7 = 3x - 54x+7=3x−5
o Solution:
4x−3x=−5−74x - 3x = -5 - 74x−3x=−5−7
x=−12x = -12x=−12
Answer: x=−12x = -12x=−12
5. Simplify: (x+2)(x−2)(x + 2)(x - 2)(x+2)(x−2)
o Solution:
x2−2x+2x−4=x2−4x^2 - 2x + 2x - 4 = x^2 - 4x2−2x+2x−4=x2−4
Answer: x2−4x^2 - 4x2−4
, Geometry
6. Find the area of a triangle with base 10 cm10 \, \text{cm}10cm and height 15
cm15 \, \text{cm}15cm:
o Solution:
Area = 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21
×base×height
Area = 12×10×15=75 cm2\frac{1}{2} \times 10 \times 15 = 75 \, \text{cm}^221
×10×15=75cm2
Answer: 75 cm275 \, \text{cm}^275cm2
7. Calculate the circumference of a circle with radius 7 cm7 \, \text{cm}7cm:
o Solution:
Circumference = 2πr=2π×7=14π2\pi r = 2 \pi \times 7 = 14\pi2πr=2π×7=14π
Answer: 14π cm14\pi \, \text{cm}14πcm
8. Solve for xxx: x+2y=10x + 2y = 10x+2y=10 and 2x−y=52x - y = 52x−y=5
o Solution (Substitution/Elimination):
From x+2y=10,x=10−2yx + 2y = 10, x = 10 - 2yx+2y=10,x=10−2y
Substituting into 2x−y=52x - y = 52x−y=5:
2(10−2y)−y=52(10 - 2y) - y = 52(10−2y)−y=5
20−4y−y=520 - 4y - y = 520−4y−y=5
20−5y=520 - 5y = 520−5y=5
−5y=−15-5y = -15−5y=−15
y=3y = 3y=3, x=10−2(3)=4x = 10 - 2(3) = 4x=10−2(3)=4
Answer: x=4,y=3x = 4, y = 3x=4,y=3
9. Find the volume of a cylinder with radius 5 cm5 \, \text{cm}5cm and height 10
cm10 \, \text{cm}10cm:
o Solution:
Volume = πr2h=π(52)(10)=250π\pi r^2 h = \pi (5^2)(10) = 250\piπr2h=π(52)
(10)=250π
Answer: 250π cm3250\pi \, \text{cm}^3250πcm3
1. Solve: 2x+3=112x + 3 = 112x+3=11
o Solution:
2x=11−32x = 11 - 32x=11−3
2x=82x = 82x=8
x=82=4x = \frac{8}{2} = 4x=28=4
Answer: x=4x = 4x=4
2. Solve: 3(x−2)=93(x - 2) = 93(x−2)=9
o Solution:
3x−6=93x - 6 = 93x−6=9
3x=9+63x = 9 + 63x=9+6
3x=153x = 153x=15
x=153=5x = \frac{15}{3} = 5x=315=5
Answer: x=5x = 5x=5
3. Solve: x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0
o Solution (Factoring):
(x−2)(x−3)=0(x - 2)(x - 3) = 0(x−2)(x−3)=0
x=2 or x=3x = 2 \text{ or } x = 3x=2 or x=3
Answer: x=2,3x = 2, 3x=2,3
4. Solve: 4x+7=3x−54x + 7 = 3x - 54x+7=3x−5
o Solution:
4x−3x=−5−74x - 3x = -5 - 74x−3x=−5−7
x=−12x = -12x=−12
Answer: x=−12x = -12x=−12
5. Simplify: (x+2)(x−2)(x + 2)(x - 2)(x+2)(x−2)
o Solution:
x2−2x+2x−4=x2−4x^2 - 2x + 2x - 4 = x^2 - 4x2−2x+2x−4=x2−4
Answer: x2−4x^2 - 4x2−4
, Geometry
6. Find the area of a triangle with base 10 cm10 \, \text{cm}10cm and height 15
cm15 \, \text{cm}15cm:
o Solution:
Area = 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21
×base×height
Area = 12×10×15=75 cm2\frac{1}{2} \times 10 \times 15 = 75 \, \text{cm}^221
×10×15=75cm2
Answer: 75 cm275 \, \text{cm}^275cm2
7. Calculate the circumference of a circle with radius 7 cm7 \, \text{cm}7cm:
o Solution:
Circumference = 2πr=2π×7=14π2\pi r = 2 \pi \times 7 = 14\pi2πr=2π×7=14π
Answer: 14π cm14\pi \, \text{cm}14πcm
8. Solve for xxx: x+2y=10x + 2y = 10x+2y=10 and 2x−y=52x - y = 52x−y=5
o Solution (Substitution/Elimination):
From x+2y=10,x=10−2yx + 2y = 10, x = 10 - 2yx+2y=10,x=10−2y
Substituting into 2x−y=52x - y = 52x−y=5:
2(10−2y)−y=52(10 - 2y) - y = 52(10−2y)−y=5
20−4y−y=520 - 4y - y = 520−4y−y=5
20−5y=520 - 5y = 520−5y=5
−5y=−15-5y = -15−5y=−15
y=3y = 3y=3, x=10−2(3)=4x = 10 - 2(3) = 4x=10−2(3)=4
Answer: x=4,y=3x = 4, y = 3x=4,y=3
9. Find the volume of a cylinder with radius 5 cm5 \, \text{cm}5cm and height 10
cm10 \, \text{cm}10cm:
o Solution:
Volume = πr2h=π(52)(10)=250π\pi r^2 h = \pi (5^2)(10) = 250\piπr2h=π(52)
(10)=250π
Answer: 250π cm3250\pi \, \text{cm}^3250πcm3
