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小红书号 1330516766
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小红书号 1330516766
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 文字应用题（率/总量） | 113 | 34 | 68 | 11 | A proposal for a construction project was included on a city election ballot, A TV news report … |
| 线性情境求值（率×量+初始） | 95 | 50 | 42 | 3 | The cost of renting a power washer is $44 for the first day and $22 for each additional day. Wh… |
| which equation represents（写方程） | 56 | 26 | 19 | 11 | A set designer is hammering nails along the top edge of a wall with a length of 3 x feet, where… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 解方程组（代入/消元） | 182 | 90 | 71 | 21 | \( x+5=11 \) \( y=3x^2+3 \) At what point ( x, y ) do the graphs of the equations in the given … |
| 方程组含参：交点/关系 | 19 | 11 | 8 | 0 | \( y=x-c \) \( y=-4\left(x-6\right)^2 \) In the given system of equations, c is a constant. The… |
| 解方程组：整体求值 x+y | 13 | 7 | 6 | 0 | y=5(x-2)^{2} y=10(x-2) A solution to the given system of equations is (x, y). What is one possi… |
| 方程组建模（which system） | 11 | 6 | 3 | 2 | A scientist makes batches of bricks using different sand-to-cement ratios to test how the sand-… |
| 应用题：设两元求解 | 4 | 1 | 2 | 1 | A movie theater sells two types of tickets, adult tickets for $12 and child tickets for $8. If … |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 整体代换求值 | 116 | 56 | 54 | 6 | If \( \frac{6}{7}p+42=84 \), what is the value of 7\( p \)?… |
| 解一元一次方程/分式方程 | 73 | 22 | 38 | 13 | \( \frac{x+1}{5x^{2}}=\frac{k}{x} \) In the given equation, k is a constant. The solution to th… |
| 多字母分式逐层求值 | 13 | 5 | 8 | 0 | In the figure shown, points A, B, C, and E lie on the circle, and AB < BC . Segment AC is perpe… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 最值应用（at least/at most） | 78 | 38 | 30 | 10 | A number x is at most 7 less than 6 times the value of y . If the value of y is 3. what is the … |
| 不等式建模（which inequality） | 63 | 22 | 36 | 5 | In December 2017, the lowest temperature recorded in a certain city was 10 degrees Fahrenheit (… |
| 不等式组与坐标平面（代点/求范围） | 35 | 16 | 13 | 6 | The shaded region shown in the graph represents all the solutions to which inequality?… |
| 三角不等式/其他不等式 | 19 | 13 | 4 | 2 | y > 9 x - 5 For which of the following tables are all the values of x and their corresponding v… |
| 解不等式/解集反推参数 | 1 | 1 | 0 | 0 | If \( x\ge-8 \) represents all solutions to the inequality \( ax-18\le14 \), where a is a const… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 解的个数判断 | 67 | 37 | 26 | 4 | y=5x y=2x+2 How many solutions does the given system of equations have?… |
| 无解：求参数/必真判断 | 64 | 46 | 16 | 2 | 5x=75y-125 One of the two equations in a system of linear equations is given. The system has no… |
| 无穷多解：求参数 | 33 | 20 | 12 | 1 | 16( x ＋4) =2( x + c ) +14 x In the given equation, c is a constant.The equation has infinitely … |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| x/y 截距计算 | 143 | 70 | 52 | 21 | The graph of the polynomial function f in the xy -plane, where y = f ( x ), has x -intercepts o… |
| 二次函数 y 截距+缩放模板 | 1 | 1 | 0 | 0 | The table shows three values of x and their corresponding values of y , where y = f(x) +4 and f… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 平行/垂直直线 | 131 | 57 | 64 | 10 | In the figure, parallel lines a and b are intersected by lines c , d , and e . If z = 54, y = 1… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 斜率计算/比较/含参 | 90 | 35 | 44 | 11 | What is the slope of the graph of \( y=\frac{1}{4}\left(27x+12\right)+7x \) in the \( xy \)-pla… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 确定线性函数式（斜率+点/两函数值） | 51 | 28 | 19 | 4 | For the linear function f , the graph of y = f(x) in the xy -plane has a slope of \( \frac{3}{4… |
| 线性函数求值与比较 | 31 | 12 | 16 | 3 | For a particular car, the linear function f gives the predicted power, in brake horsepower (bhp… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 过点/三点共线求参数 | 46 | 29 | 17 | 0 | The function f is defined by f(x) = a^{x} - b , where a and b are constants.In the xy -plane, t… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 线性模型预测（两点定率外推） | 19 | 10 | 9 | 0 | A linear model estimates the population of a city from 1992 to 2016. The model estimates the po… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 公式变形 express in terms of | 109 | 51 | 51 | 7 | A conservation specialist hung artificial nesting structures each in the shape of a right recta… |
| 多项式等价与恒等系数 | 107 | 48 | 49 | 10 | An area of 56.00 square nautical miles is equivalent to k square kilometers. To the nearest ten… |
| 展开与合并同类项 | 77 | 37 | 33 | 7 | Which expression is equivalent to \( 14\left(x^2-6\right) \) ?… |
| 提公因式/因式分解 | 35 | 11 | 18 | 6 | Which expression is equivalent to 8 xy + 24 x^{2}y + 32 xy^{2} ?… |
| 改写求系数（rewritten as 型） | 17 | 9 | 7 | 1 | The scatterplot shows data set A , which consists of the weights y , in pounds, of a Labrador r… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 函数求值 f(a) | 100 | 37 | 51 | 12 | The function j is defined by \( j\left(x\right)=\frac{x}{7} \) . What is the value of j (42)?… |
| 反向求值：已知 f(x)=k 求 x | 60 | 26 | 26 | 8 | \( f(x)=18x^{2}-45x+16 \) The given equation defines the function \( f \) f . For what value of… |
| 由表格值确定函数式 | 30 | 17 | 10 | 3 | The roofs on the buildings of a public garden are designed to allow water to drain into the gar… |
| 图像平移/变换 | 25 | 11 | 12 | 2 | f(x) = ( x - 2)( x ＋4)( x - 3) In the xy -plane, when the graph of the function f , where y = f… |
| 定义域/值域/最值区间 | 10 | 6 | 4 | 0 | A 9-pound cat eats two types of canned cat food: chicken-flavored and duck-flavored. The recomm… |
| 复合/嵌套函数求值 | 6 | 5 | 1 | 0 | The function f is defined by f ( x )= | x - 6 x |. What value of a satisfies f ( 2 ) - f ( a )=… |
| 由文字关系构造函数（乘积/和） | 4 | 2 | 2 | 0 | The function \( f \) gives the product of a number, x , and a number that is 77 more than x . W… |
| 有理函数：无定义点 | 1 | 0 | 1 | 0 | The function g is defined as g(x) =\( \frac{2x-4}{(x+13)(x-5)} \) , when x=a,the function is un… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 解二次方程（求根/正解/求根公式） | 81 | 43 | 33 | 5 | \( \frac{x+1}{5x^2}=\frac{k}{x} \) In the given equation, \( k \) is a constant. The solution t… |
| 解（根）之和求参 | 48 | 22 | 24 | 2 | ( x - 21)^{2}= 1 What is the sum of the solutions to the given equation?… |
| 由根/零点构造方程或因式 | 26 | 15 | 9 | 2 | The quadratic function f has a factor of ( x +7.75) and a zero x = c , where c is a positive co… |
| 解（根）之积求参 | 14 | 14 | 0 | 0 | 56 x ^{2} +(56 s ＋ r ) x ＋ rs =0 ln the given equation, r and s are positive constants. The pro… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 指数函数求值/两点定倍率 | 51 | 30 | 17 | 4 | The function \( f \) is defined by \( f\left(x\right)=-39^x \). The function \( g \) is a decre… |
| 增长/衰减模型：建立与识别 | 37 | 23 | 13 | 1 | The amount of money owed on a certain type of loan has two components: the principal balance of… |
| 翻倍/半衰期周期模型 | 20 | 9 | 8 | 3 | The number of bacteria in a liquid medium doubles every day. There are 83,000 bacteria in the l… |
| 确定指数函数式 | 6 | 0 | 4 | 2 | The relationship between the variables x and y is defined by an exponential equation. When \( x… |
| 倍率与百分比互转 | 1 | 1 | 0 | 0 | The function \( f \) is defined by \( f(x)=56(0.19)^x \). For any positive integer n , the valu… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 恰一解 Δ=0：求参数（含完全平方数条件） | 46 | 34 | 12 | 0 | \( 18x^2-24x+c=0 \) In the given equation, \( c \) is a constant. The equation has exactly one … |
| 二次无实数解：参数范围 | 25 | 21 | 3 | 1 | \( x^2+38x+c=0 \) In the given equation, c is a constant, The equation has no real solutions if… |
| 至少一解：分离参数求最值 | 1 | 1 | 0 | 0 | \( y=x-c \) \( y=-4\left(x-10\right)^2 \) The system above has at least 1 solution. What is the… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 顶点/对称轴/最值 | 35 | 23 | 10 | 2 | Function f is a quadratic function. The graph of y = f ( x ) in the xy -plane has a vertex at (… |
| 二次建模：抛体最大高度 | 6 | 2 | 4 | 0 | An object is launched from a height of 121 feet above the ground. A quadratic function \( f \) … |
| 抛物线截距/开口/必真判断 | 1 | 1 | 0 | 0 | The parabola shown intersects the y-axis at the point ( x , y ). What is the value of y ?… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 绝对值方程求解/整体求值 | 41 | 25 | 8 | 8 | The equation 4| x -6|= k , where k is a constant, has exactly one solution. which of the follow… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 指数法则运算（乘/除/幂） | 15 | 9 | 5 | 1 | Which expression is equivalent to \( \left(5x^6\right)\left(x^3\right) \) ?… |
| 根式与分数指数互化 | 14 | 13 | 1 | 0 | -9 x ( x ＋9) = 90 One solution to the given equation can be written as \( x=-\frac{s+\sqrt{t}}{… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 结构判断：常数/系数是否直接显示（最值/截距） | 24 | 22 | 2 | 0 | The functions f and g are defined by the equations shown, where a and b are integer constants, … |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 百分数基础计算 | 224 | 111 | 95 | 18 | A scientist analyzed a soil sample with a mass of 900 grams and determined that it contained 18… |
| 百分比链（a% of b, b% of c） | 48 | 31 | 16 | 1 | The table summarizes the number of objects in each group. The number of objects in group C is p… |
| 混合浓度问题 | 20 | 9 | 10 | 1 | During an experiment, the temperature, in degrees Celsius (ºC), of a mixture was recorded to th… |
| 折扣/税费/利息 | 16 | 10 | 6 | 0 | A clothing store buys shirts at a wholesale price of 4.00 dollars each and resells them each at… |
| 连续涨跌（倍率连乘） | 6 | 5 | 1 | 0 | The value of an autographed baseball increased by 178 % from the end of 2012 to the end of 2013… |
| 反求涨跌幅 p% | 3 | 2 | 0 | 1 | The price of an item increased by p % from $90 to $93. What is the value of p ?… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 长度/面积/体积单位换算 | 151 | 73 | 65 | 13 | A triangular prism has a height of 9 centimeters ( cm ) and a volume of 234 \( cm^{3} \) . What… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 均值：加权/合并/反求 | 60 | 29 | 31 | 0 | Data set A: 2, 3, 4, 5,5 Data set B: 2, 3, 4, 10 Which of the following statements best compare… |
| 标准差/极差比较 | 26 | 16 | 10 | 0 | Which of the following choices has the least standard deviation?… |
| 中位数 | 23 | 15 | 4 | 4 | A science class studied the feeding behavior of the birds that visited a bird feeder each schoo… |
| 均值 vs 中位数比较判断 | 20 | 18 | 1 | 1 | A data set of the orbital periods, rounded to the nearest whole number of Earth days, for 13 of… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 单位价格/率的应用 | 84 | 39 | 35 | 10 | One gallon of sealant costs $29 and will cover 300 square feet of a surface. A deck has a total… |
| 配比与比率方程 | 31 | 15 | 12 | 4 | The graph shows the estimated concentration of a certain strain of bacteria, in millions of cel… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 相似图形/立体缩放 | 76 | 38 | 36 | 2 | The table gives the areas and perimeters of two similar rectangles, where n is a constant. What… |
| 比例尺（地图/模型） | 2 | 1 | 1 | 0 | A grove has 6 rows of birch trees and 5 rows of maple trees. Each row of birch trees has 8 tree… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 散点图读图/趋势/拟合线 | 68 | 24 | 39 | 5 | The scatterplot shows the relationship between the length of eruption y , in hours, and the num… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 概率计算与反求 | 33 | 8 | 20 | 5 | The table gives the distribution of favorite core subject and grade level for 80 students. If a… |
| 条件概率（given that） | 22 | 9 | 9 | 4 | At a convention center, there are a total of 225 visitors. Each visitor is located in either ro… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 频数表/直方图/图表读取 | 51 | 17 | 25 | 9 | The bar graph shows the distribution of flower type for the 700 flowers that a florist has in s… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 误差范围与样本量 | 9 | 7 | 2 | 0 | A research manager selected 2 random samples of ovens of a certain type to estimate the average… |
| 抽样偏差/结论推广/实验设计 | 6 | 3 | 2 | 1 | To investigate the effect of magnesium supplementation on the sleep quality of adults, a resear… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 三角形内角与外角 | 143 | 70 | 63 | 10 | A total of 3 squares each have side length r . A total of 6 equilateral triangles each have sid… |
| 相似/全等判定（补充信息） | 29 | 14 | 11 | 4 | In triangle ABC and triangle DEF , sides AB and DE each have a side length of 10 inches, and an… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 圆方程（配方/圆心半径） | 71 | 31 | 39 | 1 | A circle in the xy -plane has its center at ( -7, 3 ) and has a radius of 9 . An equation of th… |
| 半径/周长/面积计算 | 44 | 21 | 20 | 3 | Circle N has a radius of 6 millimeters (mm). Circle M has an area of \( 121π mm^{2} \) . What i… |
| 弧长/扇形/圆心角 | 18 | 9 | 8 | 1 | A circle has diameters \( AC \) and \( BD \) . The circumference of the circle is 84π, and the … |
| 切线性质 | 5 | 5 | 0 | 0 | A circle in the xy -plane has its center at \( \left(-2,\ 2\right) \) . Line t is tangent to th… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 直角三角形求三角比 | 69 | 21 | 45 | 3 | A business consultant charges $408 for the first hour and $204 for each additional hour of work… |
| 单位圆与弧度 | 34 | 8 | 24 | 2 | An angle has a measure of \( \frac{13π}{6} \) radians. What is the measure of the angle in degr… |
| 互余角 sin/cos 转换 | 11 | 5 | 6 | 0 | In right triangle RST , the sum of the measures of angle R and angle S is 90 degrees. The valne… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 棱柱/棱锥体积与表面积 | 30 | 20 | 10 | 0 | A right square pyramid has a surface area of 75,264 square inches. which includes a base area o… |
| 圆锥/圆柱/球体积与斜高 | 24 | 12 | 12 | 0 | A hemisphere is half of a sphere. If a hemisphere has a radius of 59 inches, which of the follo… |
| 体积/表面积综合 | 12 | 5 | 7 | 0 | w(t)=600-3t The function w models the volume of water, in milliliters, in a container t seconds… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 矩形/正方形/组合图形面积 | 46 | 23 | 18 | 5 | In the figure, \( LQ \) intersects \( MP \) at point R , and \( LM \) is parallel to \( PQ \) .… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 平行线与角度/多边形内角 | 45 | 16 | 20 | 9 | A rectangular fence covers an rectangle area of 40 square plots. Each square plot has an area o… |
| 考法 | 题量 | Hard | Medium | Easy | 例题（Hard 优先） |
|---|---|---|---|---|---|
| 函数值 f(a)=b 的实际意义 | 64 | 24 | 40 | 0 | An acceptable noise criterion rating for the background noise in a laundry room is 50. For a no… |
| 斜率/变化率系数的实际意义 | 49 | 20 | 28 | 1 | H = 2.408L + 23.16 A group of biology students conducted an experiment to study the relationshi… |
| 其他解释判断类 | 33 | 14 | 16 | 3 | A school swim team sold shirts to raise money.The team raised $13 from each short-sleeved shirt… |
| y 截距/初始值的实际意义 | 15 | 6 | 8 | 1 | Kenny engages in up to 3 types of exercise each week for a total of 6 hours while training for … |
| 顶点/最值的实际意义 | 13 | 7 | 6 | 0 | The function\( f\left(x\right)=\frac{1}{8}\left(x-6\right)^2+4 \) gives a toy car's height abov… |