Math Quiz interactive exercise for Grade 4/Year 5 - Free Printable

Let's solve each question step by step and explain the reasoning.

---

Q1) Complete these sentences.

a) A number with more than two factors is called a _________ number.
✔ Composite
*Explanation:* A composite number has more than two factors (e.g., 6 has factors 1, 2, 3, 6). Numbers with only two factors (1 and itself) are prime.

b) A number with only two factors is called a _________ number.
✔ Prime
*Explanation:* Prime numbers have exactly two factors: 1 and the number itself (e.g., 5 → 1 and 5).

---

Q2) Matchstick Patterns

We are given three patterns made of squares using matchsticks:

- Pattern 1: 7 matchsticks
- Pattern 2: 12 matchsticks
- Pattern 3: 17 matchsticks

#### a) Complete the table and calculate the number of matchsticks in the fourth pattern.

| Pattern number | 1 | 2 | 3 | 4 |
|----------------|---|---|---|---|
| Number of matchsticks | 7 | 12 | 17 | ? |

Let’s look at the difference between terms:
- 12 - 7 = 5
- 17 - 12 = 5

So, the pattern increases by 5 each time.

Therefore:
- 4th pattern = 17 + 5 = 22

✔ Answer: 22

---

#### b) What is the term-to-term rule?

The sequence goes: 7, 12, 17, 22,...

Each term increases by 5.

✔ Term-to-term rule: Add 5

---

#### c) How many matchsticks are in the 10th pattern?

We can use the formula for an arithmetic sequence:

> $ \text{nth term} = a + (n - 1)d $

Where:
- $ a = 7 $ (first term)
- $ d = 5 $ (common difference)
- $ n = 10 $

$$
\text{10th term} = 7 + (10 - 1) \times 5 = 7 + 9 \times 5 = 7 + 45 = 52
$$

✔ Answer: 52

---

Q3) Find the value of:

a) $ 6^2 = $
$ 6^2 = 6 \times 6 = 36 $
✔ 36

b) Tenth square number =
Square numbers: $ 1^2 = 1, 2^2 = 4, 3^2 = 9, ..., 10^2 = 100 $
✔ 100

---

Q4) Given the first term and the term-to-term rule, write down the first four terms.

- First term: 8
- Rule: add 3

So:
- 1st: 8
- 2nd: 8 + 3 = 11
- 3rd: 11 + 3 = 14
- 4th: 14 + 3 = 17

✔ Answer: 8, 11, 14, 17

---

✔ Final Answers Summary:

---

Q1)
a) Composite
b) Prime

Q2)
a) 22
b) Add 5
c) 52

Q3)
a) 36
b) 100

Q4)
8, 11, 14, 17

---

Let me know if you'd like this formatted as a printable answer sheet!