1. **Mean, Median, Mode, Range** - Problem: Find the mean, median, mode, and range of the data set: 3, 7, 7, 2, 9, 10, 3. - Formulae: - Mean: $$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$ - Median: Middle value when data is ordered. - Mode: Most frequent value. - Range: $$\text{Range} = \text{Maximum value} - \text{Minimum value}$$ - Steps: 1. Order data: 2, 3, 3, 7, 7, 9, 10. 2. Mean: $$\frac{2 + 3 + 3 + 7 + 7 + 9 + 10}{7} = \frac{41}{7} = 5.857$$ 3. Median: Middle value is 7. 4. Mode: Values 3 and 7 both appear twice, so modes are 3 and 7. 5. Range: $$10 - 2 = 8$$ 6. Therefore, the mean is approximately 5.86, the median is 7, the modes are 3 and 7, and the range is 8. 2. **Graphing** - Problem: Plot the points (1,2), (3,4), (5,1) and find the slope between (1,2) and (3,4). - Formula: $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ - Steps: 1. Calculate slope: $$\frac{4 - 2}{3 - 1} = \frac{2}{2} = 1$$ 2. Therefore, the slope between the points is 1. 3. **Algebra Word Problem** - Problem: If 3 times a number plus 5 equals 20, find the number. - Equation: $$3x + 5 = 20$$ - Steps: 1. Subtract 5: $$3x + 5 - 5 = 20 - 5 \Rightarrow 3x = 15$$ 2. Divide by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{15}{3} \Rightarrow x = 5$$ 3. Therefore, the number is 5. 4. **Shapes - Area and Perimeter** - Problem: Find the area and perimeter of a rectangle with length 8 and width 3. - Formulae: - Area: $$A = l \times w$$ - Perimeter: $$P = 2(l + w)$$ - Steps: 1. Area: $$8 \times 3 = 24$$ 2. Perimeter: $$2(8 + 3) = 2 \times 11 = 22$$ 3. Therefore, area is 24 and perimeter is 22. 5. **Circles - Circumference** - Problem: Find the circumference of a circle with radius 7. - Formula: $$C = 2\pi r$$ - Steps: 1. Substitute: $$2 \times \pi \times 7 = 14\pi$$ 2. Therefore, circumference is $$14\pi$$ units. 6. **3D Geometry - Volume and Surface Area** - Problem: Find the volume and surface area of a cube with side length 4. - Formulae: - Volume: $$V = s^3$$ - Surface Area: $$SA = 6s^2$$ - Steps: 1. Volume: $$4^3 = 64$$ 2. Surface Area: $$6 \times 4^2 = 6 \times 16 = 96$$ 3. Therefore, volume is 64 and surface area is 96. Therefore, this review covers key concepts with examples and solutions for your daughter's 8th grade math exam based on the Ontario curriculum.