Introduction: This lesson expands on your algebra skills. Solving simultaneous equations with fractions requires careful LCM calculations. For quadratics, you now have three methods: factoring, completing the square, and the formula. Learn to choose the fastest method for the exam.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Method): What is the first step to solve the simultaneous equations 3x​+4y​=2 and 6x​−y=−1?

• Prompt 2 (Solve): Solve the quadratic equation by factoring: x2−8x+15=0.

• Prompt 3 (Method): What term must be added to x2+10x to make it a perfect square?

• Prompt 4 (Formula): Write down the quadratic formula for solving ax2+bx+c=0.

• Prompt 5 (Solve): Solve by factoring: 3x2−12x=0.

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Solve): Solve the simultaneous equations: x+y=7, x2​+y3​=2.

• Prompt 2 (Solve): Solve by completing the square: x2−4x−3=0.

• Prompt 3 (Solve): Solve using the quadratic formula: 2x2+5x−4=0. Give your answer to two decimal places.

• Prompt 4 (Problem Solve): The sum of two numbers is 15 and their product is 54. Find the two numbers by forming a quadratic equation.

• Prompt 5 (Problem Solve): The length of a rectangle is 4 cm longer than its width. If its area is 96 cm², find its dimensions.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Word Problem): A man bought a certain number of articles for Rs. 1200. If the price of each article was Rs. 10 less, he could have bought 2 more articles for the same amount. Find the number of articles he bought.

• Prompt 2 (Solve): Solve the equation x−15​−x4​=1.

• Prompt 3 (Application): The hypotenuse of a right-angled triangle is 26 cm. The sum of the other two sides is 34 cm. Find the lengths of the other two sides.

• Prompt 4 (Solve): Solve by completing the square: 3x2−6x−1=0.

• Prompt 5 (Simultaneous): Two people buy fruits. The first buys 3 kg of mangoes and 2 kg of apples for Rs. 1300. The second buys 4 kg of mangoes and 1 kg of apples for Rs. 1100. Find the price per kg of each fruit.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Nature of Roots): For the quadratic equation ax2+bx+c=0, the expression b2−4ac is called the discriminant (). What can you say about the roots if (a) Δ>0, (b) Δ=0, (c) Δ<0?

• Prompt 2 (Challenge): Find the values of k for which the quadratic equation x2−(k−2)x+1=0 has equal roots.

• Prompt 3 (Problem Solve): A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

• Prompt 4 (Derive): If α and β are the roots of the quadratic equation ax2+bx+c=0, prove that α+β=−b/a and αβ=c/a.

• Prompt 5 (Synthesis): Form a quadratic equation whose roots are the reciprocals of the roots of the equation 5x2+2x−3=0.