PA.6B, SEC 2, slving w/ fctzn & a coeff ↗️ (50)
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Question 1 of 50
1. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 18x − 10 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 2 of 50
2. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
8x² + 22x + 5 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 3 of 50
3. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² − 13x + 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 4 of 50
4. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² − 7x + 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 5 of 50
5. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
10x² + 29x + 12 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 6 of 50
6. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
5x² + 11x + 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 7 of 50
7. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
8x² + 10x – 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 8 of 50
8. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
5x² – 17x + 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 9 of 50
9. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
10x² + 27x + 5 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 10 of 50
10. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 3x − 10 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 11 of 50
11. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 13x + 10 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 12 of 50
12. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² – 3x – 35 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 13 of 50
13. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
5x² + 13x − 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 14 of 50
14. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 9x + 2 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 15 of 50
15. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² – 9x + 10 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 16 of 50
16. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² – 5x + 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 17 of 50
17. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
20x² + 13x + 2 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 18 of 50
18. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² + 7x + 5 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 19 of 50
19. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 7x − 15 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 20 of 50
20. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
20x² – 71x + 63 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 21 of 50
21. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
5x² − 26x + 5 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 22 of 50
22. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
8x² − 14x + 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 23 of 50
23. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
16x² + 44x + 10 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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-
Question 24 of 50
24. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² − 25x + 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 25 of 50
25. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
8x² + 14x + 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 26 of 50
26. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
6x² – 21x + 9 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
-
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Question 27 of 50
27. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 11x − 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
-
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Question 28 of 50
28. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² – 8x + 6 = 0
-
x₁ =x₂ =Turning point:
( , )⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 29 of 50
29. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
20x² – 9x – 20 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 30 of 50
30. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
20x² − 13x + 2 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 31 of 50
31. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² + 11x + 5 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 32 of 50
32. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² – 9x + 4 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 33 of 50
33. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
10x² + 7x – 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 34 of 50
34. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
6x² − 15x − 9 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 35 of 50
35. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² + 9x + 4 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 36 of 50
36. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² + 5x + 2 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 37 of 50
37. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
20x² + 19x – 6 = 0
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 38 of 50
38. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
20x² + 17x + 3 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 39 of 50
39. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² + 7x – 15 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 40 of 50
40. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² – 5x – 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 41 of 50
41. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
10x² − 7x − 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 42 of 50
42. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
2x² – 6x – 20 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 43 of 50
43. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 11x + 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 44 of 50
44. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
20x² + 3x − 2 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 45 of 50
45. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
5x² – 13x – 6 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 46 of 50
46. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
5x² + 13x + 6= 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 47 of 50
47. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
8x² + 2x − 15 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 48 of 50
48. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
5x² + 17x − 12 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 49 of 50
49. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
4x² + 7x − 2 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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Question 50 of 50
50. Question
Topic: Solving Quadratics with Factorisation.
Please have pen and paper handy to show workings out. 📝
Solve the quadratic equation by factorisation, finding both solutions, and determine the coordinates of the turning point:
8x² − 26x + 15 = 0
-
x₁ =x₂ =
⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 When factorising a quadratic equation with a coefficient in front of x², start by multiplying the coefficient of x² with the constant term.
Find two numbers that multiply to give this product and add to give the middle coefficient.
Rewrite the middle term using these numbers, then group the terms into two pairs and factorise each group.
After factorising, solve for x by setting each bracket to zero. This will give two solutions.
To find the turning point, calculate the midpoint of the two solutions for x and substitute it back into the original equation to find the corresponding y value. 📈✨
Work carefully, and don’t forget to double-check your factorisation and calculations! 🧠✨
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