{"id":1420,"date":"2026-01-28T18:52:51","date_gmt":"2026-01-28T08:52:51","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1420"},"modified":"2026-01-28T18:52:51","modified_gmt":"2026-01-28T08:52:51","slug":"year11-math-3-2-1-algebra-and-functions-warm-up-workbook","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1420","title":{"rendered":"Year11 MATH 3-2-1 Algebra and Functions warm-up workbook"},"content":{"rendered":"\n

Unit 1<\/h4>\n\n\n\n

1. Algebra and Functions<\/h3>\n\n\n\n

Focus: Quadratics, polynomials, and function notation.<\/em><\/p>\n\n\n\n

    \n
  1. Factorise x<\/mi>2<\/mn><\/msup>\u2212<\/mo>7<\/mn>x<\/mi>+<\/mo>10<\/mn><\/mrow>x^2 – 7x + 10<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  2. Solve for x<\/mi>x<\/annotation><\/semantics><\/math>: 2<\/mn>x<\/mi>2<\/mn><\/msup>+<\/mo>5<\/mn>x<\/mi>\u2212<\/mo>3<\/mn>=<\/mo>0<\/mn><\/mrow>2x^2 + 5x – 3 = 0<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  3. If f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>3<\/mn>x<\/mi>2<\/mn><\/msup>\u2212<\/mo>2<\/mn>x<\/mi><\/mrow>f(x) = 3x^2 – 2x<\/annotation><\/semantics><\/math>, find f<\/mi>(<\/mo>\u2212<\/mo>2<\/mn>)<\/mo><\/mrow>f(-2)<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  4. Determine the domain<\/strong> and range<\/strong> of f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>x<\/mi>\u2212<\/mo>4<\/mn><\/mrow><\/msqrt><\/mrow>f(x) = \\sqrt{x – 4}<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  5. Complete the square for x<\/mi>2<\/mn><\/msup>+<\/mo>6<\/mn>x<\/mi>+<\/mo>1<\/mn><\/mrow>x^2 + 6x + 1<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  6. Simplify x<\/mi>2<\/mn><\/msup>\u2212<\/mo>9<\/mn><\/mrow>x<\/mi>+<\/mo>3<\/mn><\/mrow><\/mfrac>\\frac{x^2 – 9}{x + 3}<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  7. Find the coordinates of the turning point for y<\/mi>=<\/mo>(<\/mo>x<\/mi>\u2212<\/mo>2<\/mn>)<\/mo>2<\/mn><\/msup>+<\/mo>5<\/mn><\/mrow>y = (x – 2)^2 + 5<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  8. Solve the simultaneous equations: y<\/mi>=<\/mo>2<\/mn>x<\/mi>+<\/mo>1<\/mn><\/mrow>y = 2x + 1<\/annotation><\/semantics><\/math> and y<\/mi>=<\/mo>x<\/mi>2<\/mn><\/msup>\u2212<\/mo>2<\/mn><\/mrow>y = x^2 – 2<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  9. Describe the transformation of y<\/mi>=<\/mo>x<\/mi>2<\/mn><\/msup><\/mrow>y = x^2<\/annotation><\/semantics><\/math> to y<\/mi>=<\/mo>\u2212<\/mo>(<\/mo>x<\/mi>+<\/mo>3<\/mn>)<\/mo>2<\/mn><\/msup><\/mrow>y = -(x + 3)^2<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n
  10. State the remainder when P<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>x<\/mi>3<\/mn><\/msup>\u2212<\/mo>2<\/mn>x<\/mi>2<\/mn><\/msup>+<\/mo>4<\/mn><\/mrow>P(x) = x^3 – 2x^2 + 4<\/annotation><\/semantics><\/math> is divided by (<\/mo>x<\/mi>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow>(x – 1)<\/annotation><\/semantics><\/math>.<\/li>\n<\/ol>\n\n\n\n

    Answers:<\/strong><\/p>\n\n\n\n

      \n
    1. (<\/mo>x<\/mi>\u2212<\/mo>5<\/mn>)<\/mo>(<\/mo>x<\/mi>\u2212<\/mo>2<\/mn>)<\/mo><\/mrow>(x – 5)(x – 2)<\/annotation><\/semantics><\/math> | 2. x<\/mi>=<\/mo>0.5<\/mn>,<\/mo>x<\/mi>=<\/mo>\u2212<\/mo>3<\/mn><\/mrow>x = 0.5, x = -3<\/annotation><\/semantics><\/math> | 3. 16 | 4. Domain: $[<\/mo>4<\/mn>,<\/mo>\u221e<\/mi>)<\/mo><\/mrow>[4, \\infty)<\/annotation><\/semantics><\/math>, Range: [<\/mo>0<\/mn>,<\/mo>\u221e<\/mi>)<\/mo><\/mrow>[0, \\infty)<\/annotation><\/semantics><\/math> | 5. (<\/mo>x<\/mi>+<\/mo>3<\/mn>)<\/mo>2<\/mn><\/msup>\u2212<\/mo>8<\/mn><\/mrow>(x + 3)^2 – 8<\/annotation><\/semantics><\/math> | 6. x<\/mi>\u2212<\/mo>3<\/mn><\/mrow>x – 3<\/annotation><\/semantics><\/math> | 7. (<\/mo>2<\/mn>,<\/mo>5<\/mn>)<\/mo><\/mrow>(2, 5)<\/annotation><\/semantics><\/math> | 8. (<\/mo>3<\/mn>,<\/mo>7<\/mn>)<\/mo><\/mrow>(3, 7)<\/annotation><\/semantics><\/math> and (<\/mo>\u2212<\/mo>1<\/mn>,<\/mo>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow>(-1, -1)<\/annotation><\/semantics><\/math> | 9. Reflected over x-axis, translated 3 units left | 10. P<\/mi>(<\/mo>1<\/mn>)<\/mo>=<\/mo>3<\/mn><\/mrow>P(1) = 3<\/annotation><\/semantics><\/math>.<\/li>\n<\/ol>\n\n\n\n

      <\/p>\n","protected":false},"excerpt":{"rendered":"

      Unit 1 1. Algebra and Functions Focus: Quadratics, polynomials, and function notation. Answers:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1420","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1420"}],"version-history":[{"count":3,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1420\/revisions"}],"predecessor-version":[{"id":1440,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1420\/revisions\/1440"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}