AssessPrep Mock Assessment - Quadratics & Linear Equations

Q1 Section 1: Factorization

2 marks

Factorize the expression completely:

x² + 13x + 40

Select your answer:

A (x + 5)(x + 8) B (x + 4)(x + 10) C (x + 2)(x + 20) D (x + 13)(x + 40)

Q2

3 marks

Factorize the expression $4 x ² + 12 x + 5$ completely.

Hint

First, factor out any common factors, then use the quadratic formula or complete the square method.

Q3

2 marks

Factorize completely:

50x² − 72

Select your answer:

A 2(5x − 6)(5x + 6) B 2(5x − 6) C 2(5x − 6)(5x + 6) D (10x − 12)(5x + 6)

Q4

3 marks

Given the trinomial $4 y ² - 19 y - 5$ , select and apply an appropriate algebraic method to fully factorize this expression into the form (ay + b)(cy + d), where a, b, c, and d are integers. Show all necessary steps in your logical reasoning, ensuring you handle the negative signs correctly throughout the process.

Q5

2 marks

Which of the following represents the complete factorization of $x ² - 16$ ?

Select your answer:

A (x − 4)(x + 4) B (x − 16)(x + 1) C (x − 8)(x + 2) D (x − 4)²

Q6 Section 2: Solving Quadratic Equations

2 marks

Solve the equation:

9x² − 4 = 0

Select your answer:

A x = ±2/3 B x = ±3/2 C x = ±4/9 D x = 2/3 only

Q7

3 marks

Solve the equation $x ² + 13 x + 40 = 0$ and write your answers as x = value.

Hint

You can use the quadratic formula or factorization method. Remember to find both roots!

Q8

2 marks

What are the solutions to the equation $x ² - 25 = 0$ ?

Select your answer:

A x = 5 and x = −5 B x = 25 and x = −25 C x = 5 only D x = ±12.5

Q9

3 marks

Use the quadratic formula to solve $2 x ² + 7 x - 15 = 0$ . Give your answers as exact values.

Remember

The quadratic formula is: x = (−b ± √(b² − 4ac)) / (2a)

Q10

2 marks

How many real solutions does the equation $x ² + 4 x + 4 = 0$ have?

Select your answer:

A One real solution (repeated root) B Two distinct real solutions C No real solutions D Infinite solutions

Q11 Section 3: Vertex Form & Parabolas

3 marks

Given the quadratic function $y = 2 x ² + 8 x - 1$ , what is the x-coordinate of the vertex?

Hint

Use the formula x = −b/(2a) or complete the square.

Q12

3 marks

Find the coordinates of the turning point (vertex) of the curve:

y = 5 − 4x − x²

Enter your answer as coordinates (x, y). Use format: x,y

Q13

2 marks

For the quadratic function written in vertex form $y = (x + 3)² - 5$ , what is the equation of the axis of symmetry?

Select your answer:

A x = −3 B x = 3 C y = −5 D x = −5

Q14

3 marks

Consider the function $y = 0.5(x + 2)(x - 6)$ . What are the coordinates of the vertex?

Q15 Section 4: Linear Equations & Gradients

2 marks

Given points A(−4, 1) and B(6, 6), find the gradient of line AB.

Formula

Gradient m = (y₂ − y₁) / (x₂ − x₁)

Q16

3 marks

A line L is defined by the equation:

2x − 5y + 10 = 0

Find the gradient of any line perpendicular to L.

Q17

2 marks

The gradient of a line that is perpendicular to the horizontal line $y = 10$ is:

Select your answer:

A 0 B 1 C undefined D −10

Q18

3 marks

For the line $y = kx - 1$ to be parallel to $3 x + y = 2$ , the value of k is:

Select your answer:

A −1/3 B 1/3 C 3 D −3

Q19

3 marks

A line is parallel to $y = 2 x + 7$ and passes through the point (1, 10). What is its equation?

Select your answer:

A y = 2x + 8 B y = 2x + 7 C y = −2x + 12 D y = 2x + 10

Q20

2 marks

Which of the following is the equation of the line passing through points (5, −1) and (5, 10)?

Select your answer:

A x + y = 4 B x = 5 C y = 5 D y = x + 5

Quadratics & Linear Equations

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