# Monthly Assesment – 1

ASSESMENT

Q1- Fully Factorise by removing a common factor:

• 2x^3 + 11x^2 + 4x

• ax^2 + 2ax

• 3(x+5) + x(x+5)

• 2(x+1)^2 + x + 1

Q2- Fully Factorise:

• x^2 – 4

• 3x^2 – 27

• x^3 – 49x

Q3- Factorise into Linear Factors:

• (x+1)^2 – 6

Q4- Factorise using the difference of two squares:

• 16x^2 – (2x+3)^2

• (2x+1)^2 – (x-2)^2

Q5- Perfect Square Factorisation::

• x^2 + 2x + 1

• t^2 + 12t + 36

• m^2 – 20m + 100

• 25x^2 – 20x + 4

Q6- Find two numbers which have:

• product 12 and sum 7

• product -12 and sum -4

Q7- Factorise :

• x^2 + 9x + 20

• x^2 – x – 2

• x^2 – 14x + 33

• x^2 – 7x – 60

• -2x^2 – 14x – 36

Q8- Solve for x:

• 3x^2 = -12

• (5x + 1)^2 = 4

• 3x^2 = 21x

• x^2 + 6x + 8 = 0

• 5x^2 – 5x – 100 = 0

• 2x^2 – 7x = 15

• 2x(x-1) -3(x+2) = -3

Q9- Solve for x using the null factor law:

• wxyz = 0

• x(x+3) = 0

• -6(x-5)(3x+2) = 0

Q10- What must be added to create a perfect square and write each equation in the form (x+p)^2

= k:

• x^2 – 2x = 4

• x^2 + 3x = -1

Q11- Solve for x by completing the square. Leave your answer in the simplest radical form:

• x^2 -4x -2 = 0

• x^2 + 8x +5 = 0

Q12- When 15 is added to the square of a number, the result is eight times the original number.

Find the number.

Q13- Use Pythagoras theorem to find x:

Q14- A 52m long fence is constructed on three sides of a property with area 240m^2. The fourth

side facing the road is left open. Find the dimensions of the property.

Q15- State whether each function is quadratic. If it is, give values for a, b and c. If not explain

why?

• y = 2x^2 + x+ 4

• y = x^2

• 2y + 4x^2 + 5 = 0

Q16- Suppose y = x^2 + 2x – 5. Find y when:

a. x = 3 b. x = 0 c. x = -2

Q17- Suppose y = -2x^ – 4x + 7. Find y when:

a. x = 1 b. x = -3 c. x= ½

Q18-

a. The point C(2, k) lies on y = x^2 + 3x – 7. Find k.

b. The point E(5, m) lies on y = -x^2 + 6x – 12. Find m.

Q19- Consider the quadratic function y = -2x^2 + 4x + 1.

a. Determine whether (2, 1) and (-2, -13) lie on its graph.

b. The points (0, k) and (3, m) lie on the graph of the quadratic function. Find the

values of k and m.

c. Sketch the graph of the quadratic, including the information from a and b.

Q20- Sketch each of the following functions on the same set of axes as y = x^2. Use a separate

set of axes of each part.

• Y = x^2 + 1

• Y = (x-1)^2

• Y = (x+4)^2 – 2

Q21- State the y – intercept of eac of the following functions:

• Y = x^2 + x + 1

• Y =(x+1)(x-2)

Q22- For each of the following functions, find the x-intercepts:

• Y = (x-1)(x+3)

• Y = (x+5)^2

• Y = x^2 – 9

• Y = 3x – x^2

• Y = x^2 – 6x + 9

Q23- For each of the following functions:

a. Find x-intercept b. Find y-intercept c. Sketch the function

• Y = (x-1)(x-3)

• Y = 3(x+2)(x-3