CAEC Mathematics Preparation Course: Data management and probability

1. السؤال 1 من 17

   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
   أظهر الإجابة

   الإجابة: B. 39

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

2. السؤال 2 من 17

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

   • A80
   • B85
   • C26
   • D400
   أظهر الإجابة

   الإجابة: A. 80

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

3. السؤال 3 من 17

   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
   أظهر الإجابة

   الإجابة: B. 9

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

4. السؤال 4 من 17

   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
   أظهر الإجابة

   الإجابة: 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. السؤال 5 من 17

   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
   أظهر الإجابة

   الإجابة: B. 20 °C

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

6. السؤال 6 من 17

   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
   أظهر الإجابة

   الإجابة: 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. السؤال 7 من 17

   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
   أظهر الإجابة

   الإجابة: C. $7.00

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

8. السؤال 8 من 17

   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%
   أظهر الإجابة

   الإجابة: D. 25%

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

9. السؤال 9 من 17

   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
   أظهر الإجابة

   الإجابة: B. 146.25

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

10. السؤال 10 من 17

    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
    أظهر الإجابة

    الإجابة: C. $570.00

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

11. السؤال 11 من 17

    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
    أظهر الإجابة

    الإجابة: 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. السؤال 12 من 17

    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
    أظهر الإجابة

    الإجابة: A. 19

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

13. السؤال 13 من 17

    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
    أظهر الإجابة

    الإجابة: B. 1/2

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

14. السؤال 14 من 17

    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
    أظهر الإجابة

    الإجابة: 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. السؤال 15 من 17

    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
    أظهر الإجابة

    الإجابة: A. 1/12

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

16. السؤال 16 من 17

    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%
    أظهر الإجابة

    الإجابة: A. 4%

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

17. السؤال 17 من 17

    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%
    أظهر الإجابة

    الإجابة: A. 2%

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

لوحة المفاتيح: 1–4 للإجابة، وEnter للسؤال التالي.

الاختبار الحقيقي: 55% on each CAEC test