CAEC Mathematics Preparation Course：Data management and probability

1. 第1题，共17题

   The table shows the hours one employee worked last week. How many hours did they work in total?

   Day	Hours worked
   Monday	7.5
   Tuesday	8
   Wednesday	6
   Thursday	9.5
   Friday	8

   • A7.8
   • B39
   • C29.5
   • D9.5
   显示答案

   答案: B. 39

   Add all five days: 7.5 + 8 + 6 + 9.5 + 8 = 39 hours.

2. 第2题，共17题

   A learner's practice scores are 72, 85, 90, 64 and 89. What is the mean score?

   • A80
   • B85
   • C26
   • D400
   显示答案

   答案: A. 80

   Mean = total ÷ number of values = 400 ÷ 5 = 80.

3. 第3题，共17题

   A store sold shoes in these sizes today: 8, 9, 9, 10, 9, 11, 8, 9, 10. What is the mode?

   • A10
   • B9
   • C11
   • D8
   显示答案

   答案: B. 9

   The mode is the value that appears most often. Size 9 appears 4 times.

4. 第4题，共17题

   Six deliveries took 12, 15, 9, 20, 18 and 11 minutes. What is the median time?

   • A14.5 minutes
   • B14.2 minutes
   • C13.5 minutes
   • D12 minutes
   显示答案

   答案: C. 13.5 minutes

   Sort first: 9, 11, 12, 15, 18, 20. With an even count, the median is the mean of the middle two: (12 + 15) ÷ 2 = 13.5.

5. 第5题，共17题

   The low temperatures for five days were −12 °C, −5 °C, 3 °C, 8 °C and −2 °C. What is the range?

   • A10 °C
   • B20 °C
   • C15 °C
   • D4 °C
   显示答案

   答案: B. 20 °C

   Range = highest − lowest = 8 − (−12) = 8 + 12 = 20 °C.

6. 第6题，共17题

   Five homes on a street sold for $410,000, $425,000, $430,000, $445,000 and $1,900,000. Which measure best shows a typical price?

   • AThe median
   • BThe range
   • CThe mean
   • DThe highest price
   显示答案

   答案: A. The median

   The $1,900,000 sale is an outlier that pulls the mean up. The median ($430,000) is not affected by it.

7. 第7题，共17题

   Five workers earn $16, $17, $17, $18 and $52 per hour. By how much is the mean wage higher than the median wage?

   • A$24.00
   • B$17.00
   • C$7.00
   • D$35.00
   显示答案

   答案: C. $7.00

   Mean = 120 ÷ 5 = $24. Median = $17. The outlier ($52) makes the mean $7.00 higher.

8. 第8题，共17题

   The table shows a security company's service calls. What was the percent increase from January to February?

   Month	Service calls
   January	120
   February	150
   March	135
   April	180

   • A30%
   • B15%
   • C20%
   • D25%
   显示答案

   答案: D. 25%

   Change = 150 − 120 = 30. Percent increase = 30 ÷ 120 × 100 = 25%. Always divide by the starting value.

9. 第9题，共17题

   The table shows a security company's service calls. What was the mean number of calls per month?

   Month	Service calls
   January	120
   February	150
   March	135
   April	180

   • A585
   • B146.25
   • C142.5
   • D180
   显示答案

   答案: B. 146.25

   Total = 120 + 150 + 135 + 180 = 585. Mean = 585 ÷ 4 = 146.25 calls.

10. 第10题，共17题

    A circle graph of a household budget is shown as this table. Take-home pay is $3,800 a month. How much goes to food?

    Category	Share of monthly take-home pay
    Housing	35%
    Food	15%
    Transportation	12%
    Savings	10%
    Other	28%

    • A$1,330.00
    • B$5,700.00
    • C$570.00
    • D$380.00
    显示答案

    答案: C. $570.00

    Food is 15%: 0.15 × $3,800 = $570.00.

11. 第11题，共17题

    The table shows hours studied and test scores for six learners. What relationship does the data show?

    Learner	Hours studied	Score (%)
    A	2	52
    B	4	61
    C	5	66
    D	7	74
    E	9	83
    F	10	88

    • AScores stay the same no matter the hours
    • BA negative relationship: more study hours go with lower scores
    • CA positive relationship: more study hours go with higher scores
    • DNo relationship between hours and scores
    显示答案

    答案: C. A positive relationship: more study hours go with higher scores

    As hours go up, scores also go up. On a scatterplot the points would rise from left to right, which is a positive relationship.

12. 第12题，共17题

    A histogram of employee ages is shown as this table. How many employees are 30 or older?

    Age group	Number of employees
    20–29	6
    30–39	9
    40–49	7
    50–59	3

    • A19
    • B25
    • C16
    • D9
    显示答案

    答案: A. 19

    Add the groups from 30 up: 9 + 7 + 3 = 19.

13. 第13题，共17题

    A bag holds 3 red, 5 blue and 2 green marbles. You pick one without looking. What is the probability it is blue?

    • A1/5
    • B1/2
    • C1/3
    • D5/8
    显示答案

    答案: B. 1/2

    Probability = favourable ÷ total = 5 ÷ 10 = 1/2.

14. 第14题，共17题

    You roll a fair six-sided die once. What is the probability of rolling a 2 or a 5?

    • A1/36
    • B2/3
    • C1/3
    • D1/6
    显示答案

    答案: C. 1/3

    You cannot roll both at once, so the events are mutually exclusive. Add: 1/6 + 1/6 = 2/6 = 1/3.

15. 第15题，共17题

    You flip a coin and roll a six-sided die. What is the probability of getting heads and a 6?

    • A1/12
    • B2/3
    • C1/8
    • D1/6
    显示答案

    答案: A. 1/12

    The events are independent, so multiply: 1/2 × 1/6 = 1/12.

16. 第16题，共17题

    A bus is late on 20% of days. Each day is independent. What is the probability it is late on both Monday and Tuesday?

    • A4%
    • B20%
    • C40%
    • D16%
    显示答案

    答案: A. 4%

    Independent events: multiply. 0.20 × 0.20 = 0.04, which is 4%.

17. 第17题，共17题

    A raffle sells 500 tickets and draws one winning ticket. You buy 4 tickets and your friend buys 6. What is the probability that one of you wins?

    • A2%
    • B0.0096%
    • C0.8%
    • D1.2%
    显示答案

    答案: A. 2%

    Only one ticket wins, so the events are mutually exclusive. Add: 4/500 + 6/500 = 10/500 = 2%.

键盘：按1–4作答，按 Enter 进入下一题。

真实考试：55% on each CAEC test