Year 7 OCR Maths: Unit Test Practice Paper Walkthrough | 七年级OCR数学：单元测试模拟卷解析

📚 Year 7 OCR Maths: Unit Test Practice Paper Walkthrough | 七年级OCR数学：单元测试模拟卷解析

This article provides a detailed walkthrough of a sample unit test for Year 7 OCR Mathematics. It covers key topics such as number operations, fractions, algebra, geometry, and statistics, offering step-by-step solutions and strategies to help students build confidence for their real assessment.

本文详细解析了一套七年级OCR数学单元测试模拟卷。内容涵盖整数运算、分数、代数、几何和统计等重点主题，通过逐步解题与策略讲解，帮助学生为真实测试建立信心。

1. Whole Number Addition and Subtraction | 整数加减法

Question: Calculate 4782 + 3259 and 7000 − 4567.

题目：计算 4782 + 3259 和 7000 − 4567。

For addition, line up the digits: 4782 + 3259. Add units: 2+9=11, write 1, carry 1. 加法部分，对齐数位：4782 + 3259。个位相加：2+9=11，写1进1。

Continue with tens: 8+5+carry1=14, write 4, carry 1. Hundreds: 7+2+carry1=10, write 0, carry 1. Thousands: 4+3+carry1=8. Result 8041. 继续加十位：8+5+进位1=14，写4进1。百位：7+2+进位1=10，写0进1。千位：4+3+进位1=8。结果为8041。

For subtraction, 7000 − 4567. Borrow: 7000 is 6 thousands, 9 hundreds, 9 tens, 10 units. Subtract: 10−7=3, 9−6=3, 9−5=4, 6−4=2. So 2433. 减法：7000 − 4567。借位：7000分解为6个千、9个百、9个十、10个一。计算：10−7=3，9−6=3，9−5=4，6−4=2。结果2433。

2. Negative Numbers | 负数运算

Question: Work out: (a) −5 + 3, (b) −2 − 7, (c) 4 − (−6).

题目：计算：(a) −5 + 3，(b) −2 − 7，(c) 4 − (−6)。

(a) Start at −5, move 3 steps right on the number line → −2. (a) 从 −5 开始，在数轴上向右移动3步 → −2。

(b) −2 − 7 means start at −2 and move 7 left → −9. (b) −2 − 7 表示从 −2 开始向左移动7步 → −9。

3. Multiplication and Division | 乘法与除法

Question: Calculate 237 × 46 and 896 ÷ 8.

题目：计算 237 × 46 和 896 ÷ 8。

Long multiplication: 237 × 46. Break 46 = 40 + 6. First, 237 × 6 = 1422. Then 237 × 40 = 9480. Add: 1422 + 9480 = 10902. 长乘法：237 × 46。拆分 46 = 40 + 6。首先 237 × 6 = 1422。然后 237 × 40 = 9480。相加得 10902。

Short division: 896 ÷ 8. 8 goes into 8 once → 1, remainder 0. Bring down 9 → 8 into 9 once, remainder 1. Bring down 6 → 8 into 16 exactly twice. Result 112. 短除法：896 ÷ 8。8除8得1余0；落下9，8除9得1余1；落下6，8除16得2。结果为112。

4. Fractions – Simplifying and Adding | 分数——化简与加法

Question: Simplify 18/24 and calculate 2/3 + 1/4.

题目：化简 18/24 并计算 2/3 + 1/4。

18/24: Divide numerator and denominator by their highest common factor, 6 → 18÷6=3, 24÷6=4 → 3/4. 18/24：分子分母同除以最大公因数6，得到 3/4。

2/3 + 1/4: Find common denominator 12. 2/3 = 8/12, 1/4 = 3/12. Sum = 11/12. 2/3 + 1/4：通分，公分母12。2/3 = 8/12，1/4 = 3/12，和为 11/12。

5. Decimals and Conversions | 小数与转换

Question: Multiply 4.7 × 2.3 and write 0.65 as a fraction in simplest form.

题目：计算 4.7 × 2.3，并将 0.65 化简为最简分数。

4.7 × 2.3: Think of 47 × 23 then place decimal. 47×23 = 1081 (47×20=940, 47×3=141, sum=1081). Two decimal places total, so 10.81. 4.7 × 2.3：看作 47×23 再点小数点。47×23=1081。因数共两位小数，结果为 10.81。

0.65 as fraction: 65/100. Simplify by dividing by 5 → 13/20. 0.65 化为分数：65/100，分子分母同除以5得 13/20。

6. Algebraic Expressions | 代数表达式

Question: (a) If a = 3 and b = 5, evaluate 2a + 3b. (b) Simplify 4x + 2y − x + 3y.

题目：(a) 若 a = 3，b = 5，求 2a + 3b 的值。(b) 化简 4x + 2y − x + 3y。

(a) Substitute: 2×3 + 3×5 = 6 + 15 = 21. (a) 代入：2×3 + 3×5 = 6 + 15 = 21。

(b) Combine like terms: 4x − x = 3x, 2y + 3y = 5y → 3x + 5y. (b) 合并同类项：4x − x = 3x，2y + 3y = 5y → 3x + 5y。

7. Solving Linear Equations | 解线性方程

Question: Solve: (a) 3x + 4 = 19, (b) 5y − 7 = 2y + 8.

题目：解方程：(a) 3x + 4 = 19，(b) 5y − 7 = 2y + 8。

(a) Subtract 4 from both sides: 3x = 15, then divide by 3: x = 5. (a) 两边减4：3x = 15，再除以3：x = 5。

(b) Subtract 2y from both sides: 3y − 7 = 8, add 7: 3y = 15, divide by 3: y = 5. (b) 两边减2y：3y − 7 = 8，加7：3y = 15，除以3：y = 5。

8. Angle Facts | 角的基本计算

Question: (a) On a straight line, one angle is 72°. Find the other angle. (b) In a triangle, two angles are 48° and 73°. Find the third angle.

题目：(a) 在一条直线上，一个角是72°，求另一个角。(b) 三角形中两个角分别为48°和73°，求第三个角。

(a) Angles on a straight line add to 180°: 180° − 72° = 108°. (a) 直线上的角互补：180° − 72° = 108°。

(b) Angles in a triangle sum to 180°: 180° − (48° + 73°) = 180° − 121° = 59°. (b) 三角形内角和180°：180° − (48° + 73°) = 59°。

9. Area and Perimeter | 面积与周长

Question: A rectangle measures 8 cm by 5 cm. Find its area and perimeter. A triangle has base 10 cm and height 6 cm; find its area.

题目：矩形长8 cm、宽5 cm，求面积和周长。三角形底10 cm、高6 cm，求面积。

Rectangle area = length × width = 8 × 5 = 40 cm². Perimeter = 2×(8+5) = 26 cm. 矩形面积 = 长×宽 = 40 cm²。周长 = 2×(8+5) = 26 cm。

Triangle area = ½ × base × height = ½ × 10 × 6 = 30 cm². 三角形面积 = ½ × 底 × 高 = ½ × 10 × 6 = 30 cm²。

10. Statistics – Bar Chart and Mean | 统计——条形图与平均数

Question: The frequency table shows pets owned by students: Cat (8), Dog (12), Fish (5), Other (3). Draw a bar chart and find the mean number of pets per student if there are 28 students.

题目：频数表显示学生饲养宠物的数量：猫8人，狗12人，鱼5人，其他3人。画出条形图，并计算28名学生每人平均拥有宠物数（假设每人最多一种宠物）。

Bar chart: categories on horizontal axis, frequency on vertical axis. Draw bars of heights 8, 12, 5, 3 respectively. 条形图：横轴为种类，纵轴为频数。画出高度分别为8、12、5、3的条形。

Total pets = 8+12+5+3 = 28. Since there are 28 students and each has one pet in this survey, mean = 28 ÷ 28 = 1 pet per student. 宠物总数 = 28。因为28名学生每人都拥有一种宠物（根据此调查），平均每人1只。

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Year 7 OCR Maths: Unit Test Practice Paper Walkthrough | 七年级OCR数学：单元测试模拟卷解析