In Years 7-8, we work with integers, fractions, decimals, and percentages. We solve problems involving percentages and money, including calculating percentage discounts and profits.
Integers include all positive and negative whole numbers, including zero. We learn to perform operations with integers and understand their real-world applications.
Calculate 15% of $240.
0.15 × 240 = $36
A shirt originally costs $60 and is on sale for 25% off. What is the sale price?
Discount = 0.25 × 60 = $15, Sale price = $60 - $15 = $45
Calculate: -15 + 23 - (-7)
-15 + 23 = 8, 8 - (-7) = 8 + 7 = 15
We extend and apply the distributive law to the expansion of algebraic expressions. We factorise algebraic expressions by identifying numerical factors.
Expand: 3(2x + 5)
2x + 3x - x
Expand 4(3x - 2)
12x - 8
Factorise 15x + 10
5(3x + 2)
Solve for x: 3x + 7 = 22
3x = 15, x = 5
We plot linear relationships on the Cartesian plane with and without the use of digital technologies. We solve linear equations using algebraic techniques.
Plot the points (1, 2), (2, 4), and (3, 6) on a Cartesian plane. What do you notice?
These points form a straight line with the equation y = 2x
Find the gradient of the line that passes through points (1, 3) and (4, 9)
Gradient = (9-3)/(4-1) = 6/3 = 2
We identify corresponding, alternate, and co-interior angles when two straight lines are crossed by a transversal. We investigate conditions for two lines to be parallel.
Calculate the area of a circle with radius 5cm.
Area = πr² = 3.14 × 25 = 78.5 cm²
Find the volume of a rectangular prism with dimensions 5cm × 6cm × 10cm.
Volume = 5 × 6 × 10 = 300 cm³
In a pair of parallel lines cut by a transversal, if one angle is 75°, what is its corresponding angle?
Corresponding angles are equal, so it would also be 75°
We identify and investigate data issues through numerical summaries and visual displays. We describe probabilities using fractions, decimals, and percentages, and conduct chance experiments.
Click the button to simulate rolling a die:
In a class of 28 students, 16 are girls. What fraction of the class are boys?
12/28 = 3/7
If the probability of rain tomorrow is 0.3, what is the probability it won't rain?
1 - 0.3 = 0.7 or 70%
Quadratic equations are polynomial equations of the form:
Where a, b, and c are constants, and a ≠ 0. The graph of a quadratic equation is always a parabola.
The quadratic formula is used to find the roots (solutions) of any quadratic equation:
The expression under the square root (b² - 4ac) is called the discriminant. It tells us about the nature of the roots:
Solve: x² + 5x + 6 = 0
x = [-5 ± √(25 - 24)] / 2 = [-5 ± 1]/2 → x = -2 or x = -3
Solve: 2x² - 4x - 6 = 0
x = [4 ± √(16 + 48)] / 4 = [4 ± √64]/4 = [4 ± 8]/4 → x = 3 or x = -1
Many quadratic equations can be solved by factoring. The general approach is to find two numbers that multiply to ac and add to b.
Factor: x² + 7x + 12
(x + 3)(x + 4)
Factor: x² - 9
(x + 3)(x - 3)