Mary Jane Sterling - Algebra I - 1001 Practice Problems For Dummies (+ Free Online Practice)

307 314

308 315

309 316

310 317

311 318

312 319

313 320

314 321

315 322

316 323

317 324

318 325

319 326

320 327

321 328

322 329

323 330

324 331

325 332

326 333

327 334

328 335

329 336

330 337

331 338

332 339

333 340

334 341

335 342

336 343

337 344

338 345

339 346

340 347

341 348

342 349

343 350

344 351

345 352

346 353

347 354

348 355

349 356

350 357

351 358

352 359

353 360

354 361

355 362

356 363

357 364

358 365

359 366

360 367

361 368

362 369

363 370

364 371

365 372

366 373

367 374

368 375

369 376

370 377

371 378

372 379

373 380

374 381

375 382

376 383

377 384

378 385

379 386

380 387

381 388

382 389

383 390

384 391

385 392

386 393

387 394

388 395

389 396

390 397

391 398

392 399

393 400

394 401

395 402

396 403

397 404

398 405

399 406

400 407

401 408

402 409

403 410

404 411

405 412

406 413

407 414

408 415

409 416

410 417

411 418

412 419

413 420

414 421

415 422

416 423

417 424

418 425

419 426

420 427

421 428

422 429

423 430

424 431

425 432

426 433

427 434

428 435

429 436

430 437

431 438

432 439

433 440

434 441

435 442

436 443

437 444

438 445

439 446

440 447

441 448

442 449

443 451

444 452

445 453

One-thousand-one algebra problems: That’s a lot of algebra problems.

It will take you seven days to do all of them, if you do 143 each day. Whew! It will take you 91 days to do all of them, if you manage to do 11 each day. And, of course, it will take you 1,001 days to do all the problems if you do just one each day. Whatever your game plan, this is still a lot of problems. You may want to start at the beginning and do each problem in turn, or you may want to jump around and do the problems in an order that suits you best. Either plan is doable. Either plan is fine. Just watch out for topics that build on one another — you may need the information from one skill to succeed in another.

Practice makes perfect. Unlike other subjects where you can just read or listen and absorb the information sufficiently, mathematics takes practice. The only way to figure out how the different algebraic rules work and interact with one another is to get into the problems — get your hands dirty, so to speak. Many problems appear to be the same, on the surface, but different aspects and challenges have been inserted to make the different problems unique. The concepts become more set in your mind when you work with the problems and have the properties confirmed with your solutions.

Yes, one-thousand-one algebra problems are a lot of problems. But you may find that this just whets your appetite for more. Enjoy!

This book has 1,001 algebra problems divided up among 23 chapters. Each chapter has many different sets of questions. The sets of questions are sometimes in a logical, sequential order, going from one part of a topic to the next and then to the next. Other times the sets of questions represent the different ways a topic can be presented. In any case, you’re given instructions on doing the problems. And sometimes you’re given a particular formula or format to use.

Instead of just having answers to each of the problems, you find a worked-out solution for each and every one. Flip to the back of the book for the step-by-step process needed to solve the problems. The solutions include verbal explanations inserted in the work where necessary. Sometimes an alternate procedure may be offered. Not everyone does algebra exactly the same way, but this book tries to provide the most understandable and success-promoting process to use when solving the algebra problems presented.

This workbook is divided into two main parts: questions and answers. But you probably figured that out already.

The questions chapters cover many different topics:

Basic operations: The first six chapters cover the types of numbers and the types of operations on those numbers that are essential to working in algebra. The natural numbers and whole numbers are fine for elementary arithmetic, but you need to broaden your horizons with signed numbers and decimals and fractions and exponential expressions. All these types of numbers are added, subtracted, multiplied, and divided. The rules for the different types of numbers have similarities and differences. The problems can help you come to grips with these situations and recognize what’s the same and what’s different.Also important in algebra are the operations involving radicals, absolute value, and factorial. And, tying together all the numbers and operations are the rules on how to deal with them: the order in which you perform the operations, and then the effect of grouping symbols on the whole process.

Algebraic expressions: An algebraic expression can consist of one or more terms — separated by addition and subtraction — or it can be in factored form. The factored form has everything connected by multiplication and division. Each of these forms is useful in some process or another, so it’s important to be able to change from one form to another and back again. Multiply out the factors if you want a listing of terms from highest exponent to lowest. Or, factor many terms to make them all just one if you want to solve for a root or reduce some fraction.You’ll find techniques for multiplying by one term or two — or more. There are some helpful tricks for raising binomials to higher powers. And then you find the factoring techniques — from rules of divisibility to factoring by grouping. One of the challenges of factoring expressions is deciding which technique to use. You find lots of practice to help you make those decisions.

Solving equations: What is the point of learning all those algebra basics and then going through the factoring process? One of the favorite and most common goals for all that practice is to use the techniques to solve an equation. Solving an equation means identifying the number or numbers you can replace the variable with to make a true statement.You’ll find factoring and the multiplication property of zero to be your first approach, and then you’ll also have the quadratic formula to use on some of the more challenging second-degree equations. Polynomials can be solved using synthetic division to help with the factoring. And then you have radical and absolute value equations — with their particular challenges. Finish the section off with inequalities, and you’ll have run the gamut of solving for what variables can represent.

Applications: Mention the words story problem , and you’ll see either a shudder or a brightening smile. People either love them or they don’t. But story problems (practical applications) are a main goal of learning to use algebra effectively.The practical applications found in this section of the workbook are broken into many different types. You find some that are based on an established formula: area, perimeter, simple interest, and so on. Other applications have to do with relationships between numbers or sizes of objects. The trick to doing those applications is understanding the wording, which is why you come armed with all the basics under your belt. Get to work on the work problems before you age too much with the age problems. Just write yourself a simple algebraic equation, and you’re almost finished.