Comprehensive mental maths quiz designed for 5th-grade students to practice a variety of mathematical concepts.

Here are the solutions to the mental maths quiz, worked out step by step.

1) $0.6 \times 4$
* Think of this as $6 \times 4$, which is $24$.
* Since there is one decimal place in $0.6$, put the decimal point back in the answer.
* $2.4$

2) Which two numbers are prime? (17, 14, 15, 18, 19, 10)
* A prime number has only two factors: 1 and itself.
* 14, 18, and 10 are even, so they divide by 2. Not prime.
* 15 divides by 5 ($3 \times 5 = 15$). Not prime.
* 17 cannot be divided by anything else. It is prime.
* 19 cannot be divided by anything else. It is prime.
* The primes are 17 and 19.

3) How many acute angles?
* An acute angle is smaller than a right angle (smaller than a square corner).
* Looking at the triangle, the bottom-left angle is a right angle ($90^\circ$).
* The other two angles are sharp and small.
* There are 2 acute angles.

4) Perimeter of a square with sides 50cm
* A square has 4 equal sides.
* $50 + 50 + 50 + 50 = 200$.
* Or $50 \times 4 = 200$.
* The perimeter is 200 cm.

5) Which numbers are divisible by 5? (32, 51, 45, 20, 18)
* Numbers divisible by 5 must end in a 0 or a 5.
* 45 ends in 5.
* 20 ends in 0.
* The answers are 45 and 20.

6) Add together $\frac{2}{10}, \frac{3}{10}$ and $\frac{4}{10}$
* Since the bottom numbers (denominators) are all the same, just add the top numbers.
* $2 + 3 + 4 = 9$.
* Keep the 10 on the bottom.
* The answer is $\frac{9}{10}$.

7) $9278 = 9008 + \_\_\_$
* Subtract 9008 from 9278 to find the missing part.
* $9278 - 9008 = 270$.
* The answer is 270.

8) Name of the shape
* The shape has 4 sides that look equal in length.
* It does not have right angles (square corners), so it is not a square or rectangle.
* It is not a trapezium because opposite sides are parallel.
* The name is rhombus.

9) Round 3.48 to the nearest whole number
* Look at the first digit after the decimal point: 4.
* Because 4 is less than 5, we round down.
* The answer is 3.

10) Cooking time for a 2kg chicken
* Base time: 15 minutes.
* Extra time: 25 minutes for every 500g.
* First, find how many 500gs are in 2kg. Since 1kg is two 500gs, 2kg is four 500gs ($500, 1000, 1500, 2000$).
* Multiply the extra time: $4 \times 25 \text{ minutes} = 100 \text{ minutes}$.
* Total minutes: $15 + 100 = 115 \text{ minutes}$.
* Convert to hours: 115 minutes is 1 hour (60 mins) and 55 minutes left over.
* Answer: 1 h 55 min.

11) Cost of 10 raffle tickets at £1.60 each
* Multiply $1.60 \times 10$.
* When multiplying by 10, move the decimal point one spot to the right.
* Answer: £16.00 (or £16).

12) $\frac{1}{4}$ of 32 subtract $\frac{1}{3}$ of 18
* First part: $\frac{1}{4}$ of 32 is $32 \div 4 = 8$.
* Second part: $\frac{1}{3}$ of 18 is $18 \div 3 = 6$.
* Subtract them: $8 - 6 = 2$.
* Answer: 2.

13) Value of $2x + 1$ if $x = 6$
* Replace $x$ with 6.
* $2 \times 6 + 1$.
* $12 + 1 = 13$.
* Answer: 13.

14) Change from £10
* Total spent: $£4.30 + £2.50 = £6.80$.
* Change: $£10.00 - £6.80$.
* $10 - 6 = 4$, then take away the extra 80p.
* $4.00 - 0.80 = 3.20$.
* Answer: £3.20.

15) Fraction of girls
* The whole class is 1 (or $\frac{5}{5}$).
* Boys are $\frac{2}{5}$.
* Girls are the rest: $\frac{5}{5} - \frac{2}{5} = \frac{3}{5}$.
* Answer: $\frac{3}{5}$.

16) Arrival time
* Start time: 7:40 am.
* Journey: 45 minutes.
* Add 20 minutes to get to 8:00 am.
* You have 25 minutes left to add ($45 - 20 = 25$).
* 8:00 am + 25 minutes = 8:25 am.
* Answer: 8:25 am.

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Final Answer:
1) 2.4
2) 17 and 19
3) 2
4) 200 cm
5) 45 and 20
6) $\frac{9}{10}$
7) 270
8) rhombus
9) 3
10) 1 h 55 min
11) £16
12) 2
13) 13
14) £3.20
15) $\frac{3}{5}$
16) 8:25 am