📚 GCSE OCR Mathematics: Last-Minute Revision Notes | GCSE OCR 数学：考前冲刺笔记
As the GCSE OCR Mathematics exam approaches, a focused revision of key concepts and formulas can boost your confidence and performance. This concise guide covers essential topics across Number, Algebra, Geometry, Statistics and Probability, with quick-reference notes and tips.
在 GCSE OCR 数学考试临近之际，针对关键概念和公式进行聚焦复习能提升你的信心和表现。这份简明指南涵盖数、代数、几何、统计与概率等核心主题，提供速查笔记与技巧。
1. Number Basics | 数字基础
Understand prime numbers, factors and multiples. A prime number has exactly two factors: 1 and itself. The highest common factor (HCF) and lowest common multiple (LCM) are essential for simplifying fractions and solving problems involving repeated events.
理解质数、因数和倍数。质数只有两个因数：1 和它本身。最大公因数 (HCF) 和最小公倍数 (LCM) 对于约分及解决重复事件问题至关重要。
Apply the order of operations strictly: Brackets, Indices, Division and Multiplication (left to right), Addition and Subtraction (left to right). For example, 3 + 4 × 2 = 3 + 8 = 11, not 14.
严格遵循运算顺序：括号、指数、乘除（从左到右）、加减（从左到右）。例如，3 + 4 × 2 = 3 + 8 = 11，而不是 14。
Rounding and estimation: use decimal places (d.p.) and significant figures (s.f.). When checking an answer, round each number to one significant figure to get a quick estimate. Know how to round up or down based on the next digit.
四舍五入与估算：使用小数位数 (d.p.) 和有效数字 (s.f.)。检查答案时，可将每个数四舍五入到一位有效数字快速估算。掌握根据后一位数字决定进位或舍去。
2. Fractions, Decimals & Percentages | 分数、小数与百分比
Convert fluently between fractions, decimals and percentages. 1/2 = 0.5 = 50%. To change a fraction to a decimal, divide the numerator by the denominator. To turn a decimal into a percentage, multiply by 100. Remember that percentages can be greater than 100%.
熟练地在分数、小数和百分比之间转换。1/2 = 0.5 = 50%。分数转小数，用分子除以分母。小数转百分比乘以 100。记住百分比可以超过 100%。
Operations with fractions: addition and subtraction require a common denominator. Multiplication: multiply numerators and denominators. Division: multiply by the reciprocal. Simplify your answer where possible.
分数的运算：加减法需找到公分母。乘法：分子乘分子，分母乘分母。除法：乘倒数。可能时化简答案。
Percentage increase and decrease: increase = original × (1 + r/100), decrease = original × (1 – r/100). For reverse percentages, divide by the multiplier. If a price including 20% VAT is £96, the original price = £96 ÷ 1.2 = £80.
百分比增减：增加后 = 原值 × (1 + r/100)，减少后 = 原值 × (1 – r/100)。逆向百分比：除以倍数。如果含 20% 增值税的价格为 96 英镑，原价 = 96 ÷ 1.2 = 80 英镑。
3. Standard Form & Surds | 标准形式与根式
Standard form is written as a × 10ņ where 1 ≤ a < 10 and n is an integer. For very large numbers, n is positive; for very small numbers, n is negative. When multiplying, add the powers; when dividing, subtract the powers.
标准形式写作 a × 10ņ，其中 1 ≤ a < 10，n 为整数。极大数 n 为正，极小数 n 为负。乘法时指数相加，除法时指数相减。
Surds in exact form: √a × √b = √(ab). Simplify by extracting square factors, e.g. √75 = √(25×3) = 5√3. Rationalise denominators by multiplying numerator and denominator by the conjugate, e.g. 3/(√2 – 1) × (√2+1)/(√2+1).
根式的精确形式：√a × √b = √(ab)。通过提取平方因子化简，如 √75 = √(25×3) = 5√3。分母有理化：分子分母同乘共轭式，如 3/(√2 – 1) × (√2+1)/(√2+1)。
Exact calculations with surds and π are often required. Leave answers in simplified radical form unless stated otherwise.
考试常要求用根式和 π 得出精确结果。除非特别说明，答案保持最简根式形式。
(a × 10ņ) × (b × 10&mcedil;) = (a b) × 10ņ⊃&plusm;&mcedil;
4. Algebra Foundation | 代数基础
Simplify expressions by collecting like terms, e.g. 3x + 5y – 2x = x + 5y. Expand single brackets: a(b + c) = ab + ac. Expand double brackets carefully: (x + p)(x + q) = x² + (p+q)x + pq.
合并同类项化简表达式，如 3x + 5y – 2x = x + 5y。单项括号展开：a(b + c) = ab + ac。双项括号展开：(x + p)(x + q) = x² + (p+q)x + pq。
Factorise by taking out the highest common factor, e.g. 6x² + 9x = 3x(2x + 3). Difference of two squares: a² – b² = (a – b)(a + b). Factorising quadratics: for x² + bx + c, find two numbers that multiply to c and add to b.
提公因式分解：6x² + 9x = 3x(2x + 3)。平方差公式：a² – b² = (a – b)(a + b)。二次三项式分解：对于 x² + bx + c，找两数积为 c、和为 b。
Solving linear equations: isolate the variable using inverse operations. If fractions appear, multiply every term by the common denominator. Always check the solution by substituting back.
解一元一次方程：通过逆运算分离变量。出现分数时各项同乘分母。务必代入原方程检验。
a² – b² = (a – b)(a + b)
5. Graphs & Functions | 图像与函数
Straight-line graphs are given by y = mx + c. Here m is the gradient (steepness) and c is the y-intercept. Parallel lines have equal gradients; perpendicular lines satisfy m1 × m2 = -1.
直线图像由 y = mx + c 表示，m 为斜率，c 为 y 轴截距。平行线斜率相同；垂直线斜率之积为 -1。
Quadratic graphs are parabolas. Find x-intercepts by solving ax² + bx + c = 0. The turning point can be found by completing the square or using x = -b/(2a). The shape depends on the sign of a: positive a gives a U-shape; negative a gives an inverted U.
二次函数图像为抛物线。令 ax² + bx + c = 0 求 x 轴截距。通过配方法或 x = -b/(2a) 求顶点。开口方向由 a 的符号决定：a 正开口向上，a 负开口向下。
Graph transformations: f(x) + a moves the graph up by a; f(x + a) shifts it left by a; -f(x) reflects it in the x-axis; f(-x) reflects it in the y-axis. Stretches are also examinable.
图像变换：f(x) + a 向上平移 a；f(x + a) 向左平移 a；-f(x) 关于 x 轴反射；f(-x) 关于 y 轴反射。拉伸变换也在考试范围内。
6. Ratio, Proportion & Rates | 比率、比例与变化率
Simplify ratios by dividing all parts by their HCF. To divide a quantity in a given ratio, find the total number of parts, then multiply the value of one part. For example, divide £72 in ratio 3 : 5 → total 8 parts, one part = £9, so £27 and £45.
Published by TutorHao | GCSE Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply