CAEC Mathematics Preparation Course: Patterns and relations

1. السؤال 1 من 17

   What is the next number in the pattern 4, 9, 14, 19, …?

   • A25
   • B24
   • C23
   • D29
   أظهر الإجابة

   الإجابة: B. 24

   Each term is 5 more than the one before: 19 + 5 = 24.

2. السؤال 2 من 17

   What is the next number in the pattern 3, 6, 12, 24, …?

   • A36
   • B48
   • C30
   • D27
   أظهر الإجابة

   الإجابة: B. 48

   Each term is multiplied by 2: 24 × 2 = 48.

3. السؤال 3 من 17

   The table shows how a savings account grows by the same amount each week. If the pattern continues, how much will be in the account in week 8?

   Week	Balance
   1	$150
   2	$175
   3	$200
   4	$225

   • A$1,400.00
   • B$225.00
   • C$325.00
   • D$350.00
   أظهر الإجابة

   الإجابة: C. $325.00

   The balance goes up $25 each week. Week 8 = $150 + 7 × $25 = $325.00.

4. السؤال 4 من 17

   A tile pattern uses 5 tiles in figure 1, 8 tiles in figure 2 and 11 tiles in figure 3. How many tiles are in figure 20?

   • A65
   • B100
   • C60
   • D62
   أظهر الإجابة

   الإجابة: D. 62

   Each figure adds 3 tiles, so figure n uses 3n + 2 tiles. Figure 20 uses 3 × 20 + 2 = 62 tiles.

5. السؤال 5 من 17

   A taxi charges a $4.00 flat fee plus $2.10 per kilometre. Which equation gives the cost C for a trip of d kilometres?

   • AC = 2.10 + 4.00d
   • BC = 6.10d
   • CC = 4.00d − 2.10
   • DC = 4.00 + 2.10d
   أظهر الإجابة

   الإجابة: D. C = 4.00 + 2.10d

   The fixed fee is added once, and the rate is multiplied by the distance: C = 4.00 + 2.10d.

6. السؤال 6 من 17

   A taxi charges C = 4.00 + 2.10d dollars for a trip of d kilometres. A ride costs $25.00. How long was the trip?

   • A10 km
   • B11.9 km
   • C21 km
   • D13.8 km
   أظهر الإجابة

   الإجابة: A. 10 km

   25 = 4 + 2.10d. Subtract 4: 21 = 2.10d. Divide: d = 21 ÷ 2.10 = 10 km.

7. السؤال 7 من 17

   Distance is d = rt, where r is the speed and t is the time. Which formula gives the time t?

   • At = d − r
   • Bt = d × r
   • Ct = r ÷ d
   • Dt = d ÷ r
   أظهر الإجابة

   الإجابة: D. t = d ÷ r

   Divide both sides of d = rt by r to get t = d ÷ r.

8. السؤال 8 من 17

   The formula F = 1.8C + 32 changes Celsius to Fahrenheit. What is 25 °C in Fahrenheit?

   • A77 °F
   • B45 °F
   • C102.6 °F
   • D57 °F
   أظهر الإجابة

   الإجابة: A. 77 °F

   Multiply first, then add: 1.8 × 25 = 45, and 45 + 32 = 77 °F.

9. السؤال 9 من 17

   The formula C = (F − 32) ÷ 1.8 changes Fahrenheit to Celsius. What is 50 °F in Celsius?

   • A32.4 °C
   • B−4.2 °C
   • C10 °C
   • D18 °C
   أظهر الإجابة

   الإجابة: C. 10 °C

   Do the brackets first: 50 − 32 = 18. Then 18 ÷ 1.8 = 10 °C.

10. السؤال 10 من 17

    Simple interest is I = Prt. A loan of $1,500 for 2 years cost $90 in interest. What was the yearly interest rate r?

    • A3%
    • B30%
    • C1.5%
    • D6%
    أظهر الإجابة

    الإجابة: A. 3%

    Rearrange: r = I ÷ (P × t) = 90 ÷ (1,500 × 2) = 0.03, which is 3%.

11. السؤال 11 من 17

    A plumber charges a $75 call-out fee plus $90 per hour. Your bill is $300. How many hours did the plumber work?

    • A3.3 hours
    • B4.2 hours
    • C2.0 hours
    • D2.5 hours
    أظهر الإجابة

    الإجابة: D. 2.5 hours

    300 = 75 + 90h. Subtract 75: 225 = 90h. Divide: h = 225 ÷ 90 = 2.5 hours.

12. السؤال 12 من 17

    Gym A charges a $40 joining fee and $25 a month. Gym B has no joining fee and charges $35 a month. Which equation finds the number of months m when both gyms cost the same?

    • A40m + 25 = 35m
    • B25m = 40 + 35m
    • C40 + 25m = 35
    • D40 + 25m = 35m
    أظهر الإجابة

    الإجابة: D. 40 + 25m = 35m

    Each side is the total cost after m months: Gym A is 40 + 25m and Gym B is 35m. Set them equal.

13. السؤال 13 من 17

    Two gym plans cost the same after m months when 40 + 25m = 35m. Solve for m.

    • AAfter 8 months
    • BAfter 1.6 months
    • CAfter 10 months
    • DAfter 4 months
    أظهر الإجابة

    الإجابة: D. After 4 months

    Subtract 25m from both sides: 40 = 10m, so m = 4. After 4 months both gyms cost $140.

14. السؤال 14 من 17

    A print shop charges C = 0.15n + 12 dollars for n flyers. How many flyers can you get for $87?

    • A75
    • B580
    • C660
    • D500
    أظهر الإجابة

    الإجابة: D. 500

    87 = 0.15n + 12. Subtract 12: 75 = 0.15n. Divide: n = 75 ÷ 0.15 = 500 flyers.

15. السؤال 15 من 17

    Ana is older than Ben. Ben is older than Cal. Dee is younger than Cal. Who is the youngest?

    • ACal
    • BDee
    • CBen
    • DAna
    أظهر الإجابة

    الإجابة: B. Dee

    Put them in order from oldest: Ana, Ben, Cal, Dee. Dee is the youngest.

16. السؤال 16 من 17

    Each shelf holds 12 boxes. You have 75 boxes to store. How many shelves do you need?

    • A8
    • B7
    • C6
    • D6.25
    أظهر الإجابة

    الإجابة: B. 7

    75 ÷ 12 = 6.25. Six shelves hold only 72 boxes, so you must round up to 7 shelves.

17. السؤال 17 من 17

    Three friends share a $96 bill. Sam pays $12 more than each of the other two, who pay the same amount. How much does Sam pay?

    • A$40.00
    • B$44.00
    • C$32.00
    • D$28.00
    أظهر الإجابة

    الإجابة: A. $40.00

    Let x be what each of the other two pays: x + x + (x + 12) = 96, so 3x = 84 and x = 28. Sam pays $28 + $12 = $40.00.

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

الاختبار الحقيقي: 55% on each CAEC test