ANSWERS
(d) (x – 1) (x + 1) (x - 3) (x + 2) (e) (x – 2) (x + 2) (x + 3) (f) (x – 3) (x + 3) (x + 1)
9. –2, –0.3, 2.3, (x + 2) (x + 0.3) (x –2.3) 10. x2
+ y2 = 16; x2 (b) x2
+ y2 + y2
+ y2
11. (0, 0), 6; (0, 0), ; (0, 0), 12. (a) x2
= 36; x2 30
–2x –2y + 1 = 0 –30x + 200 = 0
+ y2 = 2
1 3
13. (0, –1), 2; (–1, –2), 2; (–1, –1), ; 2
4. Formulas 1. 9 x 1016
5. 6.
a vu = t
−
x v= u x =
sw ,
w + wy
x bc d ea fa a
,
x de c
= +100 2
2 , x = 10 y
= ++ ––23 4 5 5
a
x ba= – 2
7. 31/304, 24/297, 38/311, 16/289, –17/256. Northern hemisphere summer.
8. €689·47, €689·47 9. 2356cm3 10. 3.26cm3
, 633cm3 , 6.51cm3
11. 53.05cm, 65.77cm 12.
r 13.
= s 4π
h sr r
= –2 4
π π
5. Co-ordinate geometry 1. Star 2. Star 3. Star 4. L I N E 8.
2
8. Algebra 1. 6, –3, 9, 0, 8, 21, 42, 61, 162, 1
2. 3.
a c
2 2
1, 2, 2a, 4. 7a + 3a2 2a , a 1 , 6 + 5c, 2a + b + c
5. 3c 6. x + y = 25; 5x + 8y = 167; 3x –2y = 5; 28x = 22y; 11 cent; 14 cent
(i) Reversed (ii) Reversed and inverted
7. Pears 8. 4, 1 9. 96 @ €1 54 @ €2 10. 2, –3, 5 11. No, because the first two equations are effectively the same, one is twice the other.
12. 2, 3, 4 163 6. Pythagoras’ Theorem
1. 20 – divisors 10, 5, 4, 2, 1; sum is 22 ⇒excessive 21 – divisors 7, 3, 1; sum is 11 ⇒defective 22 – etc.
3. (d) (h) (m) (r) 5.
,, , , 20 2 6 8 180 3·1 ,, , ,
6. 15, 54, 7·2, 5·4, 9·6 7.
2 18181818
2. 6,428,571,429 days ~ 17 million years 3. 9 × 1013 4. 9 × 1025
J J
J
1. €167 €333 €500 2. 3.
7. Ratio and Fibonacci 4 : 5 : 11
1 : 12
4. (a) 24 : 35 (b) 24 : 315 (c) 4 : 21 (d) 18 : 5 (e) 21 : 4 (f) 21 : 2
6. 256 7. 360° – 137.5° = 222.5°
360 222 5 1 618
· = ·
Causes irregular patterns which is less likely to split and is therefore stronger.
,,,, 1 18 16 17 24 7 12 ,
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