3.1.3 2x


____ x + 5 × x 2 − 25


3.1.4 2a + 3c


_______ 4 x 2 − 6x


= 2x


_______ 2a + 10b ÷ 4 a 2 − 9 c 2


____ x + 5 × ( x − 5 ) ( x + 5 ) __________


2x ( 2x − 3 ) = x − 5


_____ 2x − 3


________ a 2 − 25 b 2 = 2a + 3c


3.2.1 6 ( 13 − x ) + 2x ( x − 13 ) = 0 78 − 6x + 2 x 2 − 26x = 0 2 x 2 − 32x + 78 = 0 2 ( x − 13 ) ( x − 3 ) = 0 x = 13 or x = 3


3.2.2 8 x 2 − 1 = 24 − x 2


9 x 2 − 25 = 0 ( 3x − 5 ) ( 3x + 5 ) = 0 x = 5


__ 3 or x = − 5


__ 3


3.2.3 12 ( 2 − x ) = 2x − x 2 24 − 12x = 2x − x 2


x 2 − 14x + 24 = 0 ( x − 12 ) ( x − 2 ) = 0 x = 12 or x = 2


Question 4 4.1


(3) [17]


4.2 Accurate construction of triangle KLM with KL = 6,4 cm, ^ and LM = 5,29 cm.


Accurate construction of an angle of 30°. L = 90°, (3)


4.3 Given rhombus ABCD with diagonals AC and BD: In △ABC and △ADC: AB = DC BC = AD


(sides of a rhombus) (sides of a rhombus)


4.4


Similarly, ∴ △ADB≡△CDB (SSS) and ∴ A ^ B ^


AC is common ∴ △ABC≡△ADC ∴ B ^


A C = D ^ E G = 29°


A ^ A ^ F ^


E F = 29°


E G = 151° E B = 151°


D ^ C ^


E ^ G H = 29°


G H = 151° G D = 151°


A C and A ^ C D = A ^ (SSS) C B


(alternate angles, AB ∙∙ CD)


(vertical opp angles) (straight line angles)


(vertical opposite angles OR straight line angles)


(vertical opposite angles)


(straight line angles) (vertical opposite angles OR straight line angles) (4) D B = C ^ D B and A ^ B D = C ^ B D (3) (2) (2)


_______ 2 ( a + 5b ) × ( a − 5b ) ( a + 5b ) _____________


( 2a − 3c ) ( 2a + 3c ) = a − 5b


________ 2(2a − 3c)


(3) (3)


(2)


Chapter 17: Programme of Assessment


351


CHAPTER 17


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