Latihan Aljabar Kelas 8 A

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Text of Latihan Aljabar Kelas 8 A

  • EXERCISE A

    1 Complete these expansions:

    a 2(x+ 5) = 2x+ :::::: b 5(y + 3) = ::::+ 15 c 6(3 + a) = ::::+ 6a

    d 7(4 + b) = 28 + :::: e 3(z + 4) = 3z + :::: f 8(a+ 3) = ::::+ 24

    2 Expand these expressions:

    a 3(a+ 2) b 2(x+ 5) c d 7(2x+ 3)

    e

    3(2y + 1)

    f g3(10 + y) h5(2 + x) 4(2a+ b) 3(2x+ 3y)

    3 Expand:

    a a(a 4) b 2a(a 3) c a(a 6) d y(4y 10)e f g h k(k 1)y(1 y) 5x(3x 2) 7p(2p 4)

    4 Expand:

    a (x+ 2)3 b (x+ y)4 c (2 + y)3 d (a+ b)c

    e (m+ n)d f (k + 7)7 g (k + 7)k h (p+ 4)p

    5 Expand:

    a k(l + 3) b k(l 1) c k(l + 5) d x(y 2)e (a 2)b f g h2a(a+ c) 4k(k 2l) 2x(3x 4y)

    6 Use the distributive law to expand:

    a 3(z + 2) b c10(2z 3y)d

    7(x+ 3z + 1)

    e6(2 3a 5b) f4(5z 2x+ 3y)g

    2a(3x 4y + 7)h i10x(x+ 5) + 16a(a+ 5b+ 2c) 3x(x2 + 3x+ 9)

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    THE DISTRIBUTIVE LAW

    ALGEBRAIC EXERCISES

    EXERCISE B

    1 Expand and then simplify by collecting like terms:

    a 2 + 3(x+ 2) b 2 + 5(a+ 7) c 3(n+ 1) + 2(n+ 3)

    d 3n+ 2(n+ 3) e 2(x 6) + 5(x 1) fg

    3(x+ 4) + 6(5 + x)

    h6(2 + y) + 8(y + 1) i12(y + 3) + 3(3 + y) 2(x 4) + (x 4)x

    SIMPLIFYING ALGEBRAIC EXPRESSIONS

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    Y:\HAESE\IB_MYP2\IB_MYP2_10\203IB_MYP2_10.CDR Monday, 18 August 2008 11:00:34 AM PETER

    EXERCISE C

    1 Complete the following expansions:

    a 2(x+ 5) = 2x :::: b 2(x 5) = 2x+ ::::c 3(y + 2) = 3y :::: d 3(y 2) = 3y + ::::e (b+ 3) = b :::: f (b 3) = b+ ::::g 4(2m+ 3) = :::: 12 h 4(2m 3) = ::::+ 12

    2 Expand:

    a 2(x+ 5) b 3(2x+ 1) c 3(4 x) d 6(a+ b)e (x+ 6) f (x 3) g (5 + x) h (8 x)i 5(x+ 1) j 4(3 + x) k (3b 2) l 2(5 c)

    3 Expand and simplify:

    a 3(x+ 2) 2(x+ 1) b 4(x 7) 2(3 x) c 3(x 2) 2(x+ 2)d 3(y 4) 2(y + 3) e 5(y + 2) 2(y 3) f 6(b 3) 3(b 1)

    4 Expand and simplify:

    a x(x+ 4) x(x+ 2) b x(2x 1) x(7 x) c (x+ 6) 2(x+ 1)d 2(x 1) 3(5 x) e a(a+ 2) 2a(1 a) f (11 a) 2(a+ 6)

    BRACKETS WITH NEGATIVE COEFFICIENTS

    2 Expand and then simplify by collecting like terms:

    a m(m+ 2) +m(2m+ 1) b x(x+ 2) x2c 3a(a+ 2) 2a2 d 5x(x+ 2) 2e 3a(a+ 2) + 5a(a+ 1) f 4(p+ 3q) + 2(p+ 2q)

    g x(x+ 3y) + 2x(x+ y) h 4(3 + 2x) + 4x(x+ 1)

    1 Expand and simplify:

    a (a+ b)(m+ n) b c(x+ y)(a+ b)

    d (a b)(c+ d) e f(x y)(a+ 2)

    (a+ b)(m n) (r s)(p 4)

    THE PRODUCT (a + b )( c + d )EXERCISE D

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    2 Expand and simplify:

    a (x+ 2)(x+ 3) b (x+ 5)(x+ 3) c

    d

    (2x+ 1)(x+ 2)

    e(3x+ 2)(x+ 6) f

    g

    (x 1)(x+ 5)h

    (x 4)(x+ 7)i

    j

    (x y)(x+ 3)k

    (x+ 2)(x 3)l

    m

    (x 4)(x 3)

    n

    (x 5)(x 8)o

    (a+ 2)2 (b+ 5)2

    (c+ 7)2 (x 1)2 (x 4)2

    1 Find, in simplest form, an expression for the perimeter P of:

    a b c

    2 Find, in simplest form, an expression for the perimeter P of:

    a b c

    d e f

    ( )x cm

    x cm

    ( )x cm

    ( )x cm

    ( )x cm

    ( )x cm

    ( )x cm

    ( )x cm

    x cm ( )x cm

    ( )x cm ( )x cm(2 )x cm

    ( )x cm

    GEOMETRIC APPLICATIONS

    EXERCISE E

    3 Find in simplest form, an expression for the area A of:

    a b c

    ( )x cm

    x cm

    ( )x m

    ( )x m

    ( )x cm

    x cm

    d e f

    ( ) x cm

    x cm

    x m ( )x m( )x m

    x m

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    4 Find, in simplest form, expressions for the perimeter P and area A in the OpeningProblem.

    OPENING PROBLEM

    A rectangle has length (2x+ 3) cm and

    width (x+4) cm. We let its perimeter beP and its area be A.

    Things to think about:

    1 How can we quickly write down formulae for Pand A in terms of x?

    2 How can we simplify the formulae so they do not contain brackets?

    ( ) x cm

    ( )x cm

  • EXERCISE F

    1 Find the missing factor:

    a 3 = 3x b 3 = 12b c 5 = 10xyd 4x = 4x2 e 5y = 10y2 f 3a = 3a2g x = 2xy h 2x = 6x2 i 6y = 12y2

    2 Find the HCF of:

    a 4x and 12 b 3x and 6 c 4y and 14

    d 3ab and 6b e 4y and 4xy f 5ad and 10a

    g 6x2 and 2x h 3y and 9y2 i 12a and 3a2

    j 2(x 1) and 3(x 1) k 4(x+ 2) and x+ 2 l 2(x+ 3) and 2x+ 63 Factorise:

    a 5a+ 10 b 6a+ 8 c 6a+ 12b d 4 + 8x

    e 11a+ 22b f 16x+ 8 g 4a+ 8 h 10 + 15y

    i 25x+ 20 j x+ ax k 3x+mx l ac+ an

    4 Factorise:

    a 2a 10 b 4y 20 c 3b 12 d 6x 24e 6x 14 f 14y 7 g 5a 15 h 10 15bi 20b 25 j 16b 24 k x xy l ab ac

    5 Factorise:

    a x2 + 3x b 2x2 + 8x c 3x2 12x d 6x x2e 8x 4x2 f 15x 6x2 g 2x3 + 4x2 h 2x3 + 5x2

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    Y:\HAESE\IB_MYP2\IB_MYP2_10\208IB_MYP2_10.CDR Thursday, 21 August 2008 2:35:46 PM PETER

    6 Factorise:

    a 2x3 + 2x2 + 4x b x4 + 2x3 + 3x2 c 6x3 3x2 + 5xd ax2 + 2ax+ a2x e 3my2 + 3my + 6m2y f 4x2a+ 6x2a2 + x4a3

    7 Factorise:

    a 2(x+ a) + p(x+ a) b n(x 2) + p(x 2) c r(y + 5) + 4(y + 5)d 3(x+ 4) x(x+ 4) e a(7 x) b(7 x) f 4(x+ 11) + y(x+ 11)g x(x+ 2) + x+ 2 h x(x+ 2) x 2 i x(x+ 3) + 2x+ 6j x(x 1) + 2x 2 k x(x+ 5) + 3x+ 15 l x(x 4) 2x+ 8

    FACTORISATION OF ALGEBRAIC EXPRESSIONS

  • REVIEW SET A

    1 Copy and complete:

    Using the area of rectangles, the

    diagram alongside shows that

    a(::::+ ::::+ ::::) =

    2 Expand:

    a x(y + z) b 3(2x 5) c x(3 x) d (x+ 5)d3 Expand:

    a 3(x2 6x+ 4) b 2(x2 x+ 1)4 Expand and simplify by collecting like terms:

    a 2(x+ 5) + 3(2x+ 1) b 3(x 2) + 4(3 x)c 3(x 4) 2(x+ 3) d x(x+ 3) + 5(x+ 6)e x(2 x) (x 1) f y(2 + y) 3y(2 y)

    5 Find, in simplest form, an expression for the perimeter P of:

    a b c

    6 Find, in simplest form, an expression for the area A of:

    a b c

    a

    b c d

    ( )x m

    xm ( ) x cm

    ( )x cm( )x cm (2 )x cm

    ( )x cm

    x cm

    3 m

    ( )x m

    ( )x mm

    x mm

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    Y:\HAESE\IB_MYP2\IB_MYP2_10\209IB_MYP2_10.CDR Monday, 11 August 2008 9:15:59 AM PETER

    7 Expand and simplify:

    a (x+ 3)(x+ 4) b (x 3)(2x+ 1) c (2x 1)(x 7)8 Factorise:

    a 3x+ 12 b x2 3x c ab+ bc 2bd a(x 2) + 3(x 2) e x(x+ 3) + 2x+ 6

  • REVIEW SET B

    1 Expand and simplify:

    a 3(2 y) b 4(3t+ 2) c a(a+ 2) d (x+ 6)n2 Expand and simplify:

    a x+ 2(x+ 1) b x 2(x 4)3 Expand:

    a 2x(x+ y 3) b 2x(3 x)4 Expand and simplify:

    a 3(x+ 5) + 2(x 3) b 4(y + 5) + 3(2 + x)c 5(x 2) 2(x 1) d 2x(x+ 2) + x(x 3)e 3x(x+ 5) (x 5) f n(n+ 2) 2n(1 n)

    5 Find, in simplest form, an expression for the perimeter P of:

    a b c

    6 Find, in simplest form, an expression for the area A of:

    a b c

    7 Expand and simplify:

    a (x+ 2)(x+ 9) b (x+ 3)(x 2) c (x 7)(x 4)8 Factorise:

    a 4x+ 24y b 2x2 8x c 3a+ 6ab+ 9a2d 3(x 6) + d(x 6) e 2x(x+ 4) + 3x+ 12

    ( )x m

    ( )x cm

    ( ) x cm

    ( )x cm

    ( )x mm ( )x m

    ( )x mx cm

    ( )x cm

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    Y:\HAESE\IB_MYP2\IB_MYP2_10\210IB_MYP2_10.CDR Thursday, 21 August 2008 2:42:12 PM PETER