Cambridge International AS and A Level Mathematics Pure Mathematics 1

Vectors P1^ 8 The next example shows you how to use it to find the angle between two vectors given numerically. ExamPlE 8.11 Fin ...

The (^) angle (^) between (^) two (^) vectors P1^ 8 Further points concerning the scalar product ●●You will notice that the scal ...

Vectors P1^ 8 ●^ Show^ that^ the^ angle^ between^ the^ three-dimensional^ vectors a = a 1 i + a 2 j + a 3 k and b = b 1 i + b 2 ...

Exercise (^) 8C 275 P1^ 8 Substituting gives cosθ= × 36 21 78 ⇒ θ = 27.2° ! You must be careful to find the correct angle. To ...

Vectors P1^ 8 3  Three points P, Q and R have position vectors, p, q and r respectively, where p = 7 i + 10 j, q = 3 i + ...

Exercise (^) 8C P1^ 8 7  Relative to an origin O, the position vectors of the points A and B are given by O → A = 2 i − 8 ...

Vectors P1^ 8 11  The diagram shows the roof of a house. The base of the roof, OABC, is rectangular and horiz ...

Key (^) points P1^ 8 KEY POINTS 1  A vector quantity has magnitude and direction. 2  A scalar quantity has magnitude only. 3  Ve ...

Answers Answers 280 P1^ 280 Answers Chapter  1 ●?^ (Page^ 1) Like terms have the same variable; unlike terms do not. Note that t ...

Chapter (^1) 281 P1^  2 (i) a + 6 a + 75 = 180 (ii) 15°, 75°, 90°  3 (i) 2(r − 2) + r = 32 (ii) 10, 10, 12  4 (i) 2 d + 2(d − 40 ...

Answers 282 P1^   8 (i) x = ±1 or x = ±2 (ii) x = ±1 or x = ±3 (iii) x = ±^23 or x = ±1 (iv) x = ±1.5 or x = ±2 (v) x = 0 or x = ...

Chapter (^1) (viii) (a) x–– (^191241) P1^ 2 () (b) x=^1121 ;,()^12 –9^14 (c) (ix) (a) x–^141516 2 ()+^ (b) x= 41 ;,()^141516 (c) ...

Answers P1^  6 (i) h + 4 r = 100, 2 πrh + 2 πr^2 = 1400 π (ii) 6000 π or^9800027 π cm^3  7 (i) (3x + 2 y)(2x + y) m^2 (iii) xy=^ ...

Chapter (^2) P1^   6 (i) 18 (ii) − 2 (iii) 0 or 8 (iv)  8   7 (i) (ii) AB = BC = 125 (iii) (^) ()–, (^31212) (iv) 17.5 square un ...

Answers 286 P1^ (xv) (xvi) (xvii) (xviii) (xix) (xx)   2 (i) Perpendicular (ii) Neither (iii) Perpendicular (iv) Neither (v) Nei ...

Chapter (^2) 287 P1^ (ii) AB:BC: CD: AD: 5 12 5 12 1 3 4 3 ,– ,, (iii) AB = 13; BC = 13; CD = 40 ; AD = 10 (iv) AB: 5x − 12 ...

Answers 288 P1^  6  7  8  9 y = (x + 1)^2 (x − 2)^2 ●?^ (Page^ 68) (x − a)^3 : crosses the x axis at (a, 0) but is flat at that ...

Chapter (^3) 289 P1^ 17 (i) 2 (ii) 40 (iii) n 2 (3n^ + 1) (iv) n 2 (9n^ + 1) 18 (i) a + 4 d = 205; a + 18 d = 373 (ii) 12 ticket ...

Answers 290 P1^   2 (i) 6 (ii) 15 (iii) 20 (iv) 15 (v) 1 (vi) 220   3 (i) 56 (ii) 210 (iii) 673 596 (iv) − 823 680 (v) 13 440    ...

Chapter (^4) P1^ f: x  1016 x (approx.) f−^1 : x  10 −^16 x (approx.) (iv) (a) Function but no inverse function since fares ar ...