PART I · SHORT RESPONSE第一部分 · 短答题SAT-style MCQ + ON/BC short answer · 22 marksSAT 风格选择题 + 安/卑省考短答 · 共 22 分
Section A · Short ResponseA 部分 · 短答题
Mix of multiple-choice and short-answer items. For MCQs, circle the letter; show enough work in the margin that a marker could verify. For short-answer items, state units in every modeling context. No calculator on Q1–Q4; calculator permitted on Q5.本节包含选择题与短答题。选择题请圈出字母答案，并在空白处写下足以让阅卷人核对的过程。短答题在每个建模情境中都要写出单位。Q1–Q4 不可使用计算器；Q5 可用计算器。
The graph of $y = (x - 3)^{2} - 4$ is a parabola in the $xy$-plane. What are the coordinates of the vertex?$y = (x - 3)^{2} - 4$ 的图像是 $xy$ 平面内的一条抛物线。其顶点的坐标是什么？
A quadratic relation is given in standard form by $y = x^{2} - 8x + 11$.某二次关系以标准形式给出：$y = x^{2} - 8x + 11$。
(a)Convert the relation to vertex form by completing the square. State the vertex.用配方法将该关系化为顶点形式，并写出顶点。[3]
(b)State the axis of symmetry and the direction of opening.写出对称轴和开口方向。[2]
(c)State the $y$-intercept of the parabola.写出抛物线的 $y$ 轴截距。[1]
Q5MEDIUM中🇨🇦 BC卑BC Provincial-style卑诗省考风格§5 Completing the Square配方法 · BC PC11 quadratic functions二次函数[7 marks][7 分]
Consider the quadratic function $f(x) = 2x^{2} + 12x + 7$.考虑二次函数 $f(x) = 2x^{2} + 12x + 7$。
(a)Rewrite $f(x)$ in vertex form $f(x) = a(x - h)^{2} + k$ by completing the square. Show each step.用配方法将 $f(x)$ 改写为顶点形式 $f(x) = a(x - h)^{2} + k$，写出每一步。[3]
(b)State the vertex, axis of symmetry, and minimum value of $f$.写出 $f$ 的顶点、对称轴与最小值。[2]
(c)State the domain and the range of $f$ in interval notation.用区间记法写出 $f$ 的定义域与值域。[2]
PART II · EXTENDED RESPONSE第二部分 · 简答题AP-feeder FRQ + honors · 36 marksAP 衔接简答题 + 荣誉级 · 共 36 分
Section B · Extended ResponseB 部分 · 简答题
Show every algebraic step. State the chosen form (standard, vertex, or factored) before substituting. For factoring problems with $a \ne 1$, document either the AC-method grouping or the trial-and-error factor pair. No calculator on Q6–Q9 unless noted.每一步代数运算都要写出。在代入数值前先注明所用形式（标准式、顶点式或因式分解式）。对于 $a \ne 1$ 的因式分解题，需写出所用的 AC 分组法或试错法因式对。除特别说明外，Q6–Q9 不可使用计算器。
(a)Convert $g(x)$ to vertex form. State the vertex and indicate whether it is a maximum or a minimum.将 $g(x)$ 化为顶点形式，写出顶点，并指出该顶点为最大值还是最小值。[3]
(b)Convert $g(x)$ to factored form $g(x) = a(x - r_{1})(x - r_{2})$, and state the $x$-intercepts.将 $g(x)$ 化为因式分解形式 $g(x) = a(x - r_{1})(x - r_{2})$，并写出 $x$ 轴截距。[3]
(c)State the $y$-intercept and the axis of symmetry.写出 $y$ 轴截距与对称轴。[2]
Q7HARD难🇨🇦 BC卑BC Provincial-style卑诗省考风格§3 Factoring (a ≠ 1)因式分解（a ≠ 1） · BC PC11 polynomial factoring多项式因式分解[8 marks][8 分]
Solve each quadratic equation by factoring. Show the AC-method grouping or trial-and-error pair used for each. State the solution set in each case.用因式分解法求解下列二次方程。每题都要写出所用的 AC 分组法或试错法因式对，并写出解集。
(b)Use the discriminant to classify the number and type of roots (two distinct real, one repeated real, or two non-real complex roots).利用判别式判断根的个数与类型（两个不同实根、一个重实根，或两个非实复根）。[1]
(c)Solve the equation using the quadratic formula. Give exact answers in simplified radical form.用求根公式求解方程，以化简的根式形式给出精确答案。[4]
(d)Using function notation $f(x) = 3x^{2} - 7x - 2$, evaluate $f(0)$ and explain what it represents on the graph.用函数记号 $f(x) = 3x^{2} - 7x - 2$，求 $f(0)$ 的值，并说明它在图像上的几何意义。[2]
Consider the family of quadratic equations $x^{2} - 4x + c = 0$, where $c$ is a real parameter.考虑二次方程族 $x^{2} - 4x + c = 0$，其中 $c$ 为实参数。
(a)Express the discriminant $\Delta$ as a function of $c$.将判别式 $\Delta$ 表示为 $c$ 的函数。[1]
(b)Find the value(s) of $c$ for which the equation has exactly one real solution (a double root). State that root.求方程恰有一个实数解（重根）时 $c$ 的取值，并写出该根。[2]
(c)State the range of values of $c$ for which the equation has two distinct real solutions, and the range for which it has two non-real complex solutions.写出使方程有两个不同实数解的 $c$ 取值范围，以及使其有两个非实复数解的取值范围。[3]
(d)Take $c = 13$ and solve the equation using the quadratic formula. Express the two complex solutions in the form $a + bi$, and verify that they are complex conjugates of each other (cite the reasoning behind HSN-CN.A.7).取 $c = 13$，用求根公式求解方程。将两个复数解表示为 $a + bi$ 形式，并验证它们互为共轭复数（援引 HSN-CN.A.7 背后的推理）。[4]
(e)Interpret part (d) geometrically: describe what the absence of real roots tells you about the graph of $y = x^{2} - 4x + 13$ relative to the $x$-axis.对 (d) 作几何解释：说明无实根这一事实对图像 $y = x^{2} - 4x + 13$ 相对于 $x$ 轴的位置说明了什么。[1]
PART III · MODELING / APPLIED第三部分 · 建模与应用Universal · 32 marks通用题型 · 共 32 分
Section C · Modeling and ApplicationsC 部分 · 建模与应用
Name your variables (with units) before writing equations. Set up your model, solve, and conclude with a one-sentence answer in context. Calculator permitted throughout Part III.在写方程前，先定义变量名（含单位）。建立模型、求解，并以一句结合情境的话作答。第三部分全程可用计算器。
A model rocket is launched vertically upward from a platform $2$ m above the ground with an initial speed of $30$ m/s. Its height above the ground, in metres, after $t$ seconds is modeled by $h(t) = -4.9 t^{2} + 30 t + 2$.一枚模型火箭从距地面 $2$ m 高的平台上以初速度 $30$ m/s 竖直向上发射。其在 $t$ 秒后距地面的高度（米）由模型 $h(t) = -4.9 t^{2} + 30 t + 2$ 描述。
(a)State the initial height $h(0)$ and interpret it in context.写出初始高度 $h(0)$，并结合情境解释其含义。[2]
(b)Determine the time at which the rocket reaches its maximum height, and the maximum height. Round each to the nearest tenth.求火箭达到最大高度的时刻及最大高度，结果保留一位小数。[3]
(c)Determine the time at which the rocket strikes the ground. Round to the nearest tenth of a second.求火箭落地的时刻，结果保留到 $0.1$ 秒。[3]
(d)State the practical (situational) domain and range of $h(t)$ in interval notation. Interpret HSF-IF.B.4 in context: list one increasing interval and one decreasing interval.用区间记法写出 $h(t)$ 在实际情境下的定义域与值域。结合情境解读 HSF-IF.B.4：写出一个递增区间和一个递减区间。[2]
A small bakery currently sells $200$ croissants per day at a price of CA$3.00 each. A market study estimates that, for every CA$0.10 increase in price, daily sales will drop by $5$ croissants. Let $x$ be the number of CA$0.10 price increases.某小烘焙店目前每天以每件 CA$3.00 的价格售出 $200$ 个牛角包。一项市场研究估计，价格每上涨 CA$0.10，日销量会下降 $5$ 个牛角包。设 $x$ 为 CA$0.10 涨价的次数。
(a)Write a linear expression for the new price per croissant, $P(x)$, and a linear expression for the new daily quantity sold, $Q(x)$.写出每个牛角包的新单价 $P(x)$ 的线性表达式，以及新日销量 $Q(x)$ 的线性表达式。[2]
(b)Write the daily revenue $R(x) = P(x) \cdot Q(x)$ in expanded standard form.将每日营收 $R(x) = P(x) \cdot Q(x)$ 展开写成标准形式。[2]
(c)Determine the value of $x$ that maximizes daily revenue, and compute the maximum revenue.求使每日营收最大化的 $x$ 值，并计算最大营收。[4]
(d)State the optimal price per croissant and the optimal daily quantity.写出每个牛角包的最优单价与最优日销量。[2]
(e)State one restriction on the variable $x$ that arises from the situation (e.g. a non-negativity or whole-number constraint), and justify it briefly.写出变量 $x$ 由该情境产生的一个限制条件（例如非负性或取整数约束），并简要论证。[1]
(a)Factor the corresponding quadratic expression $2x^{2} - 5x - 12$, and state the roots of $2x^{2} - 5x - 12 = 0$.将对应的二次表达式 $2x^{2} - 5x - 12$ 因式分解，并写出 $2x^{2} - 5x - 12 = 0$ 的根。[3]
(b)Construct a sign chart showing the sign of $2x^{2} - 5x - 12$ on each interval determined by its roots. Label each interval with its sign.作符号表，列出 $2x^{2} - 5x - 12$ 在由其根划分的各区间上的符号，并在每个区间上标明符号。[3]
(c)State the solution set of the inequality $2x^{2} - 5x - 12 < 0$ in interval notation.用区间记法写出不等式 $2x^{2} - 5x - 12 < 0$ 的解集。[2]
(d)Without redoing the sign chart, state the solution set of the related inequality $2x^{2} - 5x - 12 \ge 0$ in interval notation.不重新作符号表，用区间记法写出相关不等式 $2x^{2} - 5x - 12 \ge 0$ 的解集。[1]
(e)A small park's profit, in hundreds of dollars, on a busy day depends on the daily admission price $x$ (in dollars) via $\Pi(x) = -2x^{2} + 5x + 12$. Use your sign-chart reasoning from (b) to state the range of admission prices $x \ge 0$ for which the park earns a strictly positive profit.某小型公园在繁忙日的利润（以百美元计）依赖于每日门票价格 $x$（以美元计），关系为 $\Pi(x) = -2x^{2} + 5x + 12$。利用 (b) 中的符号表推理，写出使公园利润严格为正的门票价格范围 $x \ge 0$。[2]
🇺🇸 US Common Core美国共同核心HSA-SSE.A.1 · HSA-SSE.B.3a · HSA-CED.A.1 · HSA-REI.B.4 · HSF-IF.B.4 · HSF-IF.C.7a · HSF-IF.C.8a · HSN-CN.A.7 (+)
🇨🇦 British Columbia不列颠哥伦比亚PC11 Big Idea "Quadratic relationships are prevalent" · Content: quadratic functions and equations, polynomial factoring, linear and quadratic inequalities (sign analysis)PC11 大概念 "二次关系普遍存在" · 内容：二次函数与方程、多项式因式分解、一次与二次不等式（符号分析）
Full 3-column Syllabus Map lives in ../Study Guides/Unit_2_Quadratic_Functions_and_Equations.html.完整的三列大纲对照表见 ../Study Guides/Unit_2_Quadratic_Functions_and_Equations.html。