Assessment · The Quadratic Formula

20 marks

Answer all questions. Show all your working; you get marks for method. Work on your own.Name: __________ Class: ______ Date: ______

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 9x + 6 = 0$.

Answer: (2 marks)

Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 + 9x - 2 = 0$.

Answer: (2 marks)

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 6x + 1 = 0$.

Answer: (2 marks)

Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 - 3x + 3 = 0$.

Answer: (2 marks)

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 6x + 5 = 0$.

Answer: (2 marks)

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 3x + 3 = 0$.

Answer: (2 marks)

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 4x + 5 = 0$.

Answer: (2 marks)

Mark scheme · The Quadratic Formula

Total: 20 marks

Award the marks shown for each correct step, then add up the total out of 20. A method mark counts even if the final answer is wrong.

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 9x + 6 = 0$.[2 marks]

Method

$a = 2,\ b = 9,\ c = 6$

$b^2 - 4ac = 81 - 4(2)(6) = 81 - 48 = 33$

The discriminant is positive, so the equation has two distinct real roots.

Answer: $33$

Marks

✔1 markSubstitute a, b, c (mind the signs)

✔1 markb² − 4ac = 33

Work out the value of the discriminant $b^2 - 4ac$ for $3x^2 + 9x - 2 = 0$.[2 marks]

Method

$a = 3,\ b = 9,\ c = -2$

$b^2 - 4ac = 81 - 4(3)(-2) = 81 + 24 = 105$

The discriminant is positive, so the equation has two distinct real roots.

Answer: $105$

Marks

✔1 markSubstitute a, b, c (mind the signs)

✔1 markb² − 4ac = 105

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 6x + 1 = 0$.[2 marks]

Method

$a = 2,\ b = -6,\ c = 1$

$b^2 - 4ac = 36 - 4(2)(1) = 36 - 8 = 28$

The discriminant is positive, so the equation has two distinct real roots.

Answer: $28$

Marks

✔1 markSubstitute a, b, c (mind the signs)

✔1 markb² − 4ac = 28

Work out the value of the discriminant $b^2 - 4ac$ for $4x^2 - 3x + 3 = 0$.[2 marks]

Method

$a = 4,\ b = -3,\ c = 3$

$b^2 - 4ac = 9 - 4(4)(3) = 9 - 48 = -39$

The discriminant is negative, so the equation has no real roots.

Answer: $-39$

Marks

✔1 markSubstitute a, b, c (mind the signs)

✔1 markb² − 4ac = -39

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 6x + 5 = 0$.[2 marks]

Method

$a = 2,\ b = 6,\ c = 5$

$b^2 - 4ac = 36 - 4(2)(5) = 36 - 40 = -4$

The discriminant is negative, so the equation has no real roots.

Answer: $-4$

Marks

✔1 markSubstitute a, b, c (mind the signs)

✔1 markb² − 4ac = -4

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 - 3x + 3 = 0$.[2 marks]

Method

$a = 2,\ b = -3,\ c = 3$

$b^2 - 4ac = 9 - 4(2)(3) = 9 - 24 = -15$

The discriminant is negative, so the equation has no real roots.

Answer: $-15$

Marks

✔1 markSubstitute a, b, c (mind the signs)

✔1 markb² − 4ac = -15

Work out the value of the discriminant $b^2 - 4ac$ for $2x^2 + 4x + 5 = 0$.[2 marks]

Method

$a = 2,\ b = 4,\ c = 5$

$b^2 - 4ac = 16 - 4(2)(5) = 16 - 40 = -24$

The discriminant is negative, so the equation has no real roots.

Answer: $-24$

Marks

✔1 markSubstitute a, b, c (mind the signs)

✔1 markb² − 4ac = -24