Year 10Name: ______

Department of Mathematics 2013

Parade CollegeTutor Group:

TEST:Ch 7Quadratic Expressions

Section / No. of questions / Marks / Your mark is
A: Vocabulary knowledge
B: Multiple Choice
C: Short Answer
D: Analysis Problem / 5
10
5
2 / 5
10
34
11 / %

Instructions

  • Read questions carefully
  • CAS calculators may be used.
  • No sharing of equipment, including calculators.
  • Use a pencil when completing questions.

Section A:Vocabulary Knowledge (5 x 1 = 5 marks)

Complete the sentence by choosing the appropriate word from the word list below.

1 / When expanding an algebraic expression with two brackets and two terms in each bracket, we use ______.
2 / The expression a2–b2 can be factorized by using ______.
3 / Before factorizing we must always look for any ______.
4 / To factorise an expression of the form x2 + bx + c, we look for factors of c that ______to give us b.
5 / To change an expression into turning point form, we need to ______.

WORD LIST

Multiply / FOIL / Common factors
Add / Expanding / DOPS
Perfect square / Cross Product Rule / Complete the square

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Section B Multiple Choice(10 marks)

1- When expanded, (x – 4)(x + 9) becomes:

Ax2 + 13x + 36

Bx2 + 13x – 36

Cx2 + 5x + 36

Dx2 + 5x – 36

Ex2 – 5x + 36

2- When expanded, (3x + 7)2 becomes:

A

B

C

D

E

3- The factorised form of 4x2 – 8x + 4 is:

A4(x + 1)(x – 1)

B4(x + 1)2

C4(x – 1)2

D(2x + 1)2

E(2x – 1)2

4- The solutions to the equation x2+9x10 = 0 are:

Ax = 1 and x = 10

Bx = 1 and x = 10

Cx = 1 and x = 10

Dx = 1 and x = 10

Ex = 1 and x = 9

5- What is y = x2 – 6x + 2 when written in turning point form?

Ay = (x + 6)2 – 34

By = (x 6)2 – 34

Cy = (x + 3)2 – 7

Dy = (x 3)2 – 7

Ey = (x + 6)2 + 2

6- When fully expanded, 4(x + 3)2 becomes:

A

B

C

D

E

7- The factorised form of 3x2 + 10x + 3 is:

A

B

C

D

E

8- The solutions to the equation x2 – 9 = 0 are:

Ax = 0 and x = 3

Bx = 0 and x = 3

Cx = 3 and x = 3

Dx = 0 and x = 9

Ex = 9 and x = 9

9- The factorised form of b2 – 11b – 26 is:

A

B

C

D

E

10- The solutions to the equation x2–16x=0 are:

Ax = 0 and x = 4

Bx = 0 and x = 4

Cx = 4 and x = 4

Dx = 0 and x = 16

Ex = 16 and x = 16

Section C- Short/Extended answer (34marks)

Working out must be shown to gain full marks.

1Expand and simplify the following expressions;

(a) (3x + 1)(3 – 2x) (2 marks)

(b) 2(x – 3)2 (3 marks)

(c) (3 – x)(x + 2)(2 – x)(3 marks)

2 Factorise the following expressions;

(a)c2 + 13c – 48(2 marks)

(b)2x2 + 8x - 10(3 marks)

(c)4x – 4y + x2 – y2(3 marks)

3Factorise the following expressions;

(a)(x − 7)2 − 7(x − 7) – 8(3 marks)

(b)25p2 − 36q2(3 marks)

(c)12x2 − 7x + 1(3 marks)

4Factorize by completing the square;

(a)x2 − 10x(2 marks)

(b) x2 + 8x + 9(3 marks)

5Simplify the following by first factorizing(4 marks)

Section D: Analysis Question: (11 marks)

1A box has a square base length of x + 3 cm and its height is 2 cm greater than the base.

(a)Write an expression for the surface area in expanded form.(2 marks)

(b)Write an expression for the volume in factorised form.(2 marks)

(c)What is the volume when x = 2 cm?(1 mark)

2A piece of cardboard 25cm x 17cm has four squares of side length x cm cut from each corner.

(a)Find the area of the cardboard after the cuts are made.(2 mark)

The cardboard is then folded so that the flaps form the side of an open topped box of height x cm.

(b)Find the length and width of the base of the box that is formed.(2 marks)

(c)Find the volume of the box(give in expanded form )(2 marks)

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