Practice questions 2.3


1. Factorise fully each of the following expressions. (i) 6s + 30t (ii) 21u − 42v (iii) −ab +ac


(iv) 25ab − 35bx (v) 21 x2 (vi) 33 q2


− 24x − 22q


2. Factorise fully each of the following expressions. (i) 12mn + 8m (ii) 3uv + 4uw (iii) 18mp + 9mn


(iv) 27xyz + 45xz (v) 24xyz + 16yz (vi) 9 x2


c + 50 a2 b2 c2 + 3x + 15 x3


3. Factorise fully each of the following expressions. (i) − 25ab2 (ii) − 4 x5 (iii) ab2 (iv) l2


− 16 x4 c + a2 mn2 − m2 z − 8xy3


bc − abc2 n + ln2


4. Factorise fully each of the following expressions.


(i) 7xy − 49x + 5y − 35 (ii) 16xy − 56x + 2y − 7 (iii) 32uv − 20u + 24v − 15 (iv) 10xy + 30 + 25x + 12y


5. Factorise fully each of the following expressions. (i) 10ab + 15b + 4a + 6 (ii) 5xy − 8x − 10y + 16 (iii) 12ab − 14a − 6b + 7 (iv) 6 x2


+ 9xy − 14x − 21y


6. Factorise fully each of the following expressions. (i) 4ab + 4ac + 5xb + 5xc (ii) qx + qy + 4x + 4y (iii) 2bc − 2bd + 17c − 17d (iv) 5as − 10bs + 2aq − 4bq


7. Factorise fully each of the following expressions. (i) tp − 2t + 16p − 32 (ii) uv − 2cd − vc + 2ud (iii) ih − 4ij + 8gj − 2gh (iv) 16s + 2r − rs − 32


8. Factorise fully each of the following expressions. (i) 6 x3 (ii) 4 a2


− 15 x2 − 21 b3


+ 2x − 5 + 6ab − 14ab2


(iii) 7 + y − 3xy − 21x (iv) 8xy − 12y + 15 − 10x


2.4 Changing the subject of a formula


By the end of this section you should be able to: ● change the subject of a formula


A formula is a way of giving a mathematical relationship between diff erent things, expressed using algebra. For example, the relationship between the area of a rectangle and its length and width can be shown by the simple formula:


Length


Area of a rectangle = length × width A = lw


Area = length × width


The subject of a formula is the single variable to which everything else in the formula is equal. The subject of a formula is always on its own, on one side of the equation.


For example, in the formula for the area of a rectangle A = lw , the subject of the formula is A .


Rearranging formulae In order to change the subject of a formula, we need to rearrange the formula so that a diff erent variable is the subject. Knowledge of solving equations and inverse operations is very useful.


In the formula A=lw , the area ( A ) is the subject of the formula. This means it is the area that is being calculated. Section A Applying our skills 37


2 Exploring patterns, expressions, equations and functions Width


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71  |  Page 72  |  Page 73  |  Page 74  |  Page 75  |  Page 76  |  Page 77  |  Page 78  |  Page 79  |  Page 80  |  Page 81  |  Page 82  |  Page 83  |  Page 84  |  Page 85  |  Page 86  |  Page 87  |  Page 88  |  Page 89  |  Page 90  |  Page 91  |  Page 92  |  Page 93  |  Page 94  |  Page 95  |  Page 96  |  Page 97  |  Page 98  |  Page 99  |  Page 100  |  Page 101  |  Page 102  |  Page 103  |  Page 104  |  Page 105  |  Page 106  |  Page 107  |  Page 108  |  Page 109  |  Page 110  |  Page 111  |  Page 112  |  Page 113  |  Page 114  |  Page 115  |  Page 116  |  Page 117  |  Page 118  |  Page 119  |  Page 120  |  Page 121  |  Page 122  |  Page 123  |  Page 124  |  Page 125  |  Page 126  |  Page 127  |  Page 128  |  Page 129  |  Page 130  |  Page 131  |  Page 132  |  Page 133  |  Page 134  |  Page 135  |  Page 136  |  Page 137  |  Page 138  |  Page 139  |  Page 140  |  Page 141  |  Page 142  |  Page 143  |  Page 144  |  Page 145  |  Page 146  |  Page 147  |  Page 148  |  Page 149  |  Page 150  |  Page 151  |  Page 152  |  Page 153  |  Page 154  |  Page 155  |  Page 156  |  Page 157  |  Page 158  |  Page 159  |  Page 160  |  Page 161  |  Page 162  |  Page 163  |  Page 164  |  Page 165  |  Page 166  |  Page 167  |  Page 168  |  Page 169  |  Page 170  |  Page 171  |  Page 172  |  Page 173  |  Page 174  |  Page 175  |  Page 176  |  Page 177  |  Page 178  |  Page 179  |  Page 180  |  Page 181  |  Page 182  |  Page 183  |  Page 184  |  Page 185  |  Page 186  |  Page 187  |  Page 188  |  Page 189  |  Page 190  |  Page 191  |  Page 192  |  Page 193  |  Page 194  |  Page 195  |  Page 196  |  Page 197  |  Page 198  |  Page 199  |  Page 200  |  Page 201  |  Page 202  |  Page 203  |  Page 204  |  Page 205  |  Page 206  |  Page 207  |  Page 208  |  Page 209  |  Page 210  |  Page 211  |  Page 212  |  Page 213  |  Page 214  |  Page 215  |  Page 216  |  Page 217  |  Page 218  |  Page 219  |  Page 220  |  Page 221  |  Page 222  |  Page 223  |  Page 224  |  Page 225  |  Page 226  |  Page 227  |  Page 228  |  Page 229  |  Page 230  |  Page 231  |  Page 232  |  Page 233  |  Page 234  |  Page 235  |  Page 236  |  Page 237  |  Page 238  |  Page 239  |  Page 240  |  Page 241  |  Page 242  |  Page 243  |  Page 244  |  Page 245  |  Page 246  |  Page 247  |  Page 248  |  Page 249  |  Page 250  |  Page 251  |  Page 252  |  Page 253  |  Page 254  |  Page 255  |  Page 256  |  Page 257  |  Page 258  |  Page 259  |  Page 260  |  Page 261  |  Page 262  |  Page 263  |  Page 264  |  Page 265  |  Page 266  |  Page 267  |  Page 268  |  Page 269  |  Page 270  |  Page 271  |  Page 272  |  Page 273  |  Page 274  |  Page 275  |  Page 276  |  Page 277  |  Page 278  |  Page 279  |  Page 280  |  Page 281  |  Page 282  |  Page 283  |  Page 284  |  Page 285  |  Page 286  |  Page 287  |  Page 288  |  Page 289  |  Page 290  |  Page 291  |  Page 292  |  Page 293  |  Page 294  |  Page 295  |  Page 296  |  Page 297  |  Page 298  |  Page 299  |  Page 300  |  Page 301  |  Page 302  |  Page 303  |  Page 304  |  Page 305  |  Page 306  |  Page 307  |  Page 308  |  Page 309  |  Page 310  |  Page 311  |  Page 312  |  Page 313  |  Page 314  |  Page 315  |  Page 316  |  Page 317  |  Page 318  |  Page 319  |  Page 320  |  Page 321  |  Page 322  |  Page 323  |  Page 324  |  Page 325  |  Page 326  |  Page 327  |  Page 328  |  Page 329  |  Page 330  |  Page 331  |  Page 332  |  Page 333  |  Page 334  |  Page 335  |  Page 336  |  Page 337  |  Page 338  |  Page 339  |  Page 340  |  Page 341  |  Page 342  |  Page 343  |  Page 344  |  Page 345  |  Page 346  |  Page 347  |  Page 348  |  Page 349  |  Page 350  |  Page 351  |  Page 352  |  Page 353  |  Page 354  |  Page 355  |  Page 356  |  Page 357  |  Page 358  |  Page 359  |  Page 360  |  Page 361  |  Page 362  |  Page 363  |  Page 364  |  Page 365  |  Page 366  |  Page 367  |  Page 368  |  Page 369  |  Page 370  |  Page 371  |  Page 372  |  Page 373  |  Page 374  |  Page 375  |  Page 376  |  Page 377  |  Page 378  |  Page 379  |  Page 380  |  Page 381  |  Page 382  |  Page 383  |  Page 384  |  Page 385  |  Page 386  |  Page 387  |  Page 388  |  Page 389  |  Page 390  |  Page 391  |  Page 392  |  Page 393  |  Page 394  |  Page 395  |  Page 396  |  Page 397  |  Page 398  |  Page 399  |  Page 400  |  Page 401  |  Page 402  |  Page 403  |  Page 404  |  Page 405  |  Page 406