Name: ___________ Teacher: WL Cheng Class : 4A Lesson No.:2 Sekolah Menengah Seri Omega Date : 7/1/09 Time :8.10-9.20Subject: MathematicsChapter:2Topic: Quadratic Expressions and Equations (1)Sub-topic: 2.1 Quadratic Expressions

2.1 Quadratic ExpressionsNotes:-

1. Quadratic expressions are expressions which fulfill the following characteristics: (a) have only one variable (b) have 2 as the highest power of the variable

2 Quadratic with three terms are of the form ax2 + bx + c, where a ≠ 0, b ≠ 0 and c ≠ 0, e.g. 2x2 + 3x + 5.

3 The following are also quadratic expressions: (a) with two terms, e.g. 2x2 + 4x, c = 0 (b) with one term, e.g. 5p2, b = c = 0

2.1a Identify quadratic expressions

Exercise 2.1a

1. State whether each of the following is a quadratic expression in one variable. (a) (b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

2. Find the product of the following pairs of Linear expressions.

(a) (i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(ix)

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(x)

(b) (i)

(ii)

(iii)

(iv)

(v)

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(vi)

(vii)

(viii)

(ix)

(x)

Answer1 (a) Yes (b) No (c) No (d) Yes (e) Yes (f) Yes (g) No (h) Yes (i) Yes (i) Yes

2 (a) (i) m2

(ii) p2 + p (iii) –q2 + 2q (iv) 3x2 + 15x (v) d2 + 4d (vi) 6m2 - 54 (vii) 3h2+6h (viii) 4f-0.5f2

(ix) -4n2

(x) 2x2+2x

(b) (i) x2+4x-21 (ii) –x2-3x-2 (iii) x2-2x-15 (iv) p2-5p+4 (v) -m2 - m + 6 (vi) 2m2+ 11m+5 (vii) 12p2-5p - 2

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(viii) p2+11p+24 (ix) 15+14x+3x2

(x) -25x2+5x+2

Exercise 2.1b

1. Expand the following algebraic expressions.

a)

b)

c)

d)

e)

f)

g)

h)

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i)

j)

4. Write a quadratic expression to represent the

area, in cm2, of each of the following figures.

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5. ABCD is a rectangle in which AB = (4x - 7) cm and BC = (2x - 1) cm. Find, in term of x, an expression for the area of ABCD

6. John is x years old and Mary is (5x -12) yearsold. Form an expression for the product of their ages.

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7. A car travels at a speed of (2x - 3) km per hour for (x + 1) hours. Write a quadratic

expression for the distance traveled by the car. [Ans. ]

8 A cylindrical container is to be packed into a cubical box. The length of the box is (2p - 4) cm. The container fits into the box as shown in the diagram. Write a quadratic expression for the area of the base of the box

occupied by the container. (Let π= )

[ ]

Notes:-

1. Quadratic equations are equations which fulfill the following characteristics: (a) have an equal ‘=’ sign (b) have only one unknown (c) have 2 as the highest power of the unknown.2. The general form of a quadratic equation is written as: (a) ax2 + bx + c = 0, where a≠ 0, b ≠ 0 and c ≠ 0, e.g. 3x2 + 2x + 7 = 0 (b) ax2 + bx = 0, where a≠ 0, b ≠ 0 but c = 0, e.g. 2x2 + 5x = 0

(c) ax2 + c = 0, where a≠ 0, c ≠ 0 but b = 0, e.g. 3x2 + 7 = 0

Notes:-1 Roots of a quadratic equation are values of the unknown which satisfy the quadratic equation.

2 To determine whether a given value of the unknown is a root of a specific quadratic equation, substitute the given value for the unknown into the equation. If it satisfies the equation, then the value of the unknown is a

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root of the equation and vice versa.

3 Roots of an equation are also called the solution of an equation. Therefore, in the above example, x = - 1 and x = 1 are solutions of the equation 3x2 + 4x + 1 = 0.

Exercise

1 Using the substitution method, determine whether the given values of the unknowns are roots of the respective quadratic equations.

(a) (b)

2. Determine the roots of the following quadratic equations.

(a)

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(b)

(c)

(d) =0

(e)

(f)

(g)

(h)

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3. Solve the following quadratic equations.

(a)

(b)

(c)

(d)

(e)

(f)

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(g)

(h)

(i)

(j)

(k)

(l)

(m)

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(n)

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