PART I · SHORT RESPONSE第一部分 · 短答题SAT-style MCQ + ON/BC short answer · 18 marksSAT 风格选择题 + 安/卑省考短答 · 共 18 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。
Which of the following is equivalent to the equation $4x - 3y = 12$ written in slope-intercept form?下列哪一项等价于方程 $4x - 3y = 12$ 的斜截式？
(A) $y = -\tfrac{4}{3} x + 4$
(B) $y = \tfrac{4}{3} x - 4$
(C) $y = 4 x - 12$
(D) $y = \tfrac{3}{4} x - 3$
Q3EASY易🇨🇦 ON安ON Provincial-style安大略省考风格§1 Rate of Change变化率 · MPM1D Linear Relations线性关系[4 marks][4 分]
A community pool is being drained. After $3$ minutes there are $4200$ litres of water left; after $11$ minutes there are $2600$ litres left. Assume the water level decreases at a constant rate.一个社区游泳池正在排水。$3$ 分钟后池中剩 $4200$ 升水；$11$ 分钟后剩 $2600$ 升。假设水位以恒定速率下降。
(a)Compute the rate of change of volume with respect to time. Include units.求体积关于时间的变化率，并写出单位。[2]
(b)Interpret the sign of the rate in the context of the situation.结合情境解释变化率符号的含义。[1]
(c)State one restriction on the variable $t$ (time) that arises from the situation.写出变量 $t$（时间）由该情境产生的一个限制条件。[1]
In the $xy$-plane, line $\ell$ passes through the points $(5, -8)$ and $(5, 17)$. Which of the following is an equation of line $\ell$?在 $xy$ 平面内，直线 $\ell$ 经过点 $(5, -8)$ 与 $(5, 17)$。下列哪一项是直线 $\ell$ 的方程？
(A) $y = 5$
(B) $y = -8$
(C) $x = 5$
(D) $y = \tfrac{25}{2} x$
Q5MEDIUM中🇨🇦 BC卑BC Provincial-style卑诗省考风格§3 Graphing作图 · FMPC10 linear functions一次函数[5 marks][5 分]
Consider the line with equation $3x + 4y = 12$.考虑方程为 $3x + 4y = 12$ 的直线。
(a)Determine the $x$-intercept and the $y$-intercept of the line.求该直线的 $x$ 轴截距与 $y$ 轴截距。[2]
(b)Sketch the line on coordinate axes, labelling both intercepts and one additional lattice point.在坐标系上画出该直线，标出两个截距及另一个格点。[2]
(c)State the slope of the line and classify the slope sign (positive, negative, zero, or undefined).写出直线的斜率，并判别斜率符号（正、负、零或不存在）。[1]
PART II · EXTENDED RESPONSE第二部分 · 简答题AP-feeder FRQ + honors · 35 marksAP 衔接简答题 + 荣誉级 · 共 35 分
Section B · Extended ResponseB 部分 · 简答题
Show every algebraic step. State the chosen form (point-slope, slope-intercept, standard) before substituting. For systems, record the method (substitution / elimination / row-reduction) and the line of work that justifies the answer. 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（点斜式、斜截式或标准式）。对于方程组，需注明所用方法（代入法 / 消元法 / 行简化）以及支撑答案的过程。除特别说明外，Q6–Q9 不可使用计算器。
Let $\ell_{0}$ be the line $2x + 5y = 10$ in the $xy$-plane.设 $\ell_{0}$ 为 $xy$ 平面内方程 $2x + 5y = 10$ 所表示的直线。
(a)Write $\ell_{0}$ in slope-intercept form and state its slope $m_{0}$.将 $\ell_{0}$ 化为斜截式，并写出其斜率 $m_{0}$。[2]
(b)Find the equation, in slope-intercept form, of the line through $(-3, 1)$ that is parallel to $\ell_{0}$.求过点 $(-3, 1)$ 且与 $\ell_{0}$ 平行的直线的斜截式方程。[2]
(c)Find the equation, in slope-intercept form, of the line through $(4, -2)$ that is perpendicular to $\ell_{0}$.求过点 $(4, -2)$ 且与 $\ell_{0}$ 垂直的直线的斜截式方程。[3]
Q7MEDIUM中🇨🇦 ON安ON Provincial-style安大略省考风格§4 Equations from a Table由数值表写方程 · MCR3U A1.2 / A1.7[8 marks][8 分]
The table below records a linear relation between $x$ and $y$.下表记录了 $x$ 与 $y$ 之间的某线性关系。
(a)Solve the system by elimination, showing the row operation you apply.用消元法求解，注明所用的行变换。[3]
(b)Solve the same system by substitution and confirm that both methods give the same ordered pair.再用代入法求解，验证两种方法所得有序对一致。[3]
(c)Briefly justify why replacing one equation by the sum of itself and a multiple of the other does not change the solution set (cite the reasoning behind HSA-REI.C.5).简要论证：用其中一个方程与另一方程的倍数之和代替原方程，为何不改变解集（援引 HSA-REI.C.5 背后的推理）。[2]
(d)State the geometric meaning of the answer in terms of the two lines.从两条直线的角度说明答案的几何意义。[1]
Q9HARD难Honors荣誉级🇺🇸 US美🇨🇦 BC卑🇨🇦 ON安AP-feeder FRQAP 衔接简答题§7 Matrix Row-Reduction矩阵行简化 · HSA-REI.C.8/9 (+) / BC PC12 / ON MCV4U[11 marks][11 分]
Consider the $3 \times 3$ system $\begin{cases} \;\;\,x + 2y + z = 9 \\ 2x - y + z = 3 \\ \;\;\,x + y - z = 0 \end{cases}.$考虑 $3 \times 3$ 方程组 $\begin{cases} \;\;\,x + 2y + z = 9 \\ 2x - y + z = 3 \\ \;\;\,x + y - z = 0 \end{cases}.$
(a)Write the augmented matrix $[A \,|\, \mathbf{b}]$ of the system.写出该方程组的增广矩阵 $[A \,|\, \mathbf{b}]$。[1]
(b)Apply elementary row operations to bring the matrix to row-echelon form. Record each operation in the standard notation $R_{i} \to R_{i} + k R_{j}$ beside the step.应用初等行变换将矩阵化为行阶梯形。每一步旁用标准记号 $R_{i} \to R_{i} + k R_{j}$ 注明所用变换。[5]
(c)Back-substitute to obtain $(x, y, z)$.回代求出 $(x, y, z)$。[3]
(d)Verify your answer by substituting back into each of the three original equations.将答案代回原方程组的三个方程进行验证。[2]
PART III · MODELING / APPLIED第三部分 · 建模与应用Universal · 28 marks通用题型 · 共 28 分
Section C · Modeling and ApplicationsC 部分 · 建模与应用
Name your variables (with units) before writing equations. Set up your system, 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）。列出方程组、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 student club is producing custom T-shirts to sell at a school fair. The printing service charges a one-time setup fee of US$90 plus US$6.50 per shirt. The club plans to sell each shirt for US$12.某学生社团准备印制定制 T 恤在校园市集上出售。印刷商一次性收取 US$90 的开版费，外加每件 US$6.50。社团计划每件售价 US$12。
(a)Let $n$ be the number of shirts produced and sold. Write a linear cost function $C(n)$ and a linear revenue function $R(n)$.设 $n$ 为生产并售出的 T 恤件数。写出线性成本函数 $C(n)$ 与线性收入函数 $R(n)$。[2]
(b)Interpret the slope and the intercept of $C(n)$ in the context of the situation (Common Core HSF-LE.B.5).结合情境解释 $C(n)$ 的斜率与截距的实际含义（共同核心 HSF-LE.B.5）。[2]
(c)Find the break-even quantity $n^{*}$ algebraically.用代数方法求盈亏平衡数量 $n^{*}$。[2]
(d)State the smallest whole number of shirts the club must sell to make a profit, and give the profit at that quantity.写出社团要盈利至少需售出的最少整件数，并给出此时的利润。[2]
A chemistry technician needs $24$ litres of a $35\%$ alcohol solution for a lab. The stockroom has two solutions on hand: a $20\%$ alcohol solution and a $50\%$ alcohol solution. Let $x$ be the litres of $20\%$ solution and $y$ be the litres of $50\%$ solution used.某化学实验员实验需配制 $24$ 升 $35\%$ 浓度的酒精溶液。库房里现有两种溶液：$20\%$ 与 $50\%$ 的酒精溶液。设 $x$ 为所用 $20\%$ 溶液的升数，$y$ 为所用 $50\%$ 溶液的升数。
(a)Write an equation that records the total volume constraint.写出表示总体积约束的方程。[1]
(b)Write an equation that records the total alcohol constraint.写出表示总酒精量约束的方程。[2]
(c)Solve the system by substitution or elimination. Show every step.用代入法或消元法求解方程组，写出每一步过程。[4]
(d)Verify your answer by computing the percentage of alcohol in the resulting mixture.通过计算所得混合液的酒精百分比，验证答案。[2]
(e)Write a one-sentence concluding statement that includes both quantities with units.用一句话作答，并写出两个量及其单位。[1]
Two cyclists, Maya and Jin, leave the same trailhead and ride along the same straight forest road. Maya starts at $9{:}00$ a.m. and rides at a constant speed of $18$ km/h. Jin starts $30$ minutes later, at $9{:}30$ a.m., and rides at a constant speed of $24$ km/h. Let $t$ be the time, in hours, measured from $9{:}00$ a.m., and let $d$ be the distance, in kilometres, from the trailhead.两名骑行者 Maya 与 Jin 从同一林道入口出发，沿同一条笔直林间道路骑行。Maya 上午 $9{:}00$ 出发，以 $18$ km/h 的恒定速度骑行。Jin 晚 $30$ 分钟出发，即上午 $9{:}30$ 出发，以 $24$ km/h 的恒定速度骑行。设 $t$ 为从 $9{:}00$ 起经过的时间（小时），$d$ 为距入口的距离（公里）。
(a)Write a linear equation $d_{M}(t)$ giving Maya's distance from the trailhead at time $t \ge 0$.写出 Maya 在时刻 $t \ge 0$ 距入口的线性方程 $d_{M}(t)$。[2]
(b)Write a linear equation $d_{J}(t)$ giving Jin's distance from the trailhead at time $t \ge 0.5$, and explain the domain restriction.写出 Jin 在时刻 $t \ge 0.5$ 距入口的线性方程 $d_{J}(t)$，并解释定义域的限制。[3]
(c)Determine, by inspection or by solving the system $d_{M}(t) = d_{J}(t)$, the time at which Jin catches up to Maya. State the time as both a value of $t$ (in hours) and a clock time.通过观察或求解方程 $d_{M}(t) = d_{J}(t)$，确定 Jin 追上 Maya 的时间。同时以 $t$ 值（小时）与钟表时间两种方式作答。[3]
(d)Sketch both lines on a single set of $(t, d)$ axes for $0 \le t \le 3$, marking the point of intersection and Jin's $t$-intercept. Label which line is which.在同一坐标系 $(t, d)$ 上画出两条直线，范围 $0 \le t \le 3$，标出交点与 Jin 的 $t$ 轴截距，并标注每条线代表谁。[2]
🇺🇸 US Common Core美国共同核心HSF-LE.A.1 · HSF-LE.A.2 · HSF-LE.B.5 · HSF-IF.B.6 · HSA-REI.B.3 · HSA-REI.C.5/6 · HSA-REI.C.8/9 (+)
🇨🇦 Ontario安大略MPM1D Linear Relations · MPM1D Analytic Geometry · MPM2D Using Linear Systems to Solve Problems · MCR3U A1.2, A1.5, A1.7MPM1D 线性关系 · MPM1D 解析几何 · MPM2D 用线性方程组解题 · MCR3U A1.2、A1.5、A1.7
🇨🇦 British Columbia不列颠哥伦比亚FMPC 10 Big Idea #3 · Content: linear functions, systems of linear equations, arithmetic sequences · PC12 (matrix, honors)FMPC 10 大概念 #3 · 内容：一次函数、线性方程组、等差数列 · PC12（矩阵，荣誉级）
Full 3-column Syllabus Map lives in ../Study Guides/Unit_1_Linear_Functions_and_Systems.html.完整的三列大纲对照表见 ../Study Guides/Unit_1_Linear_Functions_and_Systems.html。