June 2024 Paper 1 Foundation

The thousands digit is 8 and the next digit is 4.

Since $4 < 5$, round down: $18\,475 \approx 18\,000$.

Multiply by 100: $0.3 \times 100 = 30$, so $0.3 = 30\%$.

The marked angle is bigger than $180^\circ$ but less than $360^\circ$, so it is a reflex angle.

Write each with two decimal places: 0.21, 0.20, 0.03, 0.10, 0.16.

Order: $0.03,\ 0.1,\ 0.16,\ 0.2,\ 0.21$.

$8 \times 8 = 64$, so $\sqrt{64} = 8$.

Cakes: $4 \times £1.30 = £5.20$

Spent: $£10 - £1.80 = £8.20$

Two tins: $£8.20 - £5.20 = £3.00$

One tin: $£3.00 \div 2 = £1.50$

Draw a dual bar chart: days along the horizontal axis, hours (0 to 10) up the vertical axis.

For each day draw two bars side by side, e.g. Wednesday: Lena 6, Pavel 7.

Add a key showing which bar is Lena and which is Pavel, and label the vertical axis 'Hours'.

Angles at a point add up to $360^\circ$.

$x = 360 - 220 - 90 = 50^\circ$

(a) $13 \times 2 = 26$, $26 - 10 = 16$

(b) Work backwards: $28 + 10 = 38$, $38 \div 2 = 19$

(c) Solve $2x - 10 = x$ to get $x = 10$. Check: $10 \times 2 = 20$, $20 - 10 = 10$.

Cows : sheep $= 24 : 36$

Divide both by the HCF, 12: $2 : 3$

(a) Negative ÷ negative is positive: $-12 \div -4 = 3$

(b) $2^5 = 2\times2\times2\times2\times2 = 32$

(c) $30 \div (3+2) - 4 = 30 \div 5 - 4 = 6 - 4 = 2$

Triangle perimeter: $30 + 36 + 14 = 80$ cm

Rectangle perimeter: $80 \div 4 = 20$ cm

Two widths: $2 \times 4 = 8$ cm, so two lengths $= 12$ cm

Length $= 12 \div 2 = 6$ cm

(a) Every note is worth more than £5, so the probability is $1$.

(b) Each type is worth 20p: twenty 1p coins and ten 2p coins, so 30 coins.

$P(1\text{p}) = \frac{20}{30} = \frac{2}{3}$

$273 \times 50 = 13\,650$

$273 \times 4 = 1\,092$

$13\,650 + 1\,092 = 14\,742$

(a) 15 values, so the median is the 8th: $64$ minutes.

(b) Range $= 81 - 45 = 36$ minutes.

(c) Adults' median 64 < children's median 75, so on average the adults took less time.

Cost per battery:

4-pack: $180 \div 4 = 45$p

8-pack: $320 \div 8 = 40$p

12-pack: $600 \div 12 = 50$p

The pack of 8 is best value.

$2(4x - 5) = 18$

$4x - 5 = 9$

$4x = 14$

$x = 3.5$

Any non-zero number to the power 0 equals 1, so $10^0 = 1$.

Corner $(-3, 1)$ of A moves to $(2, -3)$ on B.

That is 5 right and 4 down, with no turning or flipping.

Translation by $\begin{pmatrix}5\\-4\end{pmatrix}$

The terms go up by 4, so start with $4n$.

$4n$ gives 4, 8, 12, ... Each term is 3 less, so the nth term is $4n - 3$.

(a) $3\frac{4}{5} - 1\frac{2}{3} = \frac{57}{15} - \frac{25}{15} = \frac{32}{15} = 2\frac{2}{15}$

(b) $35 - 24 = 11$, so $\frac{35}{24} = 1\frac{11}{24}$. Kevin wrote 9 instead of 11 in the numerator.

(a) Area $= 10 \times 8 - 4 \times 3 = 80 - 12 = 68\text{ m}^2$

Paint: $3 \times 2.5 = 7.5$ litres, covering $7.5 \times 10 = 75\text{ m}^2$

$75 > 68$, so yes, she has enough.

(b) With 11 m² per litre it covers $82.5\text{ m}^2$, even more, so the answer does not change.

(a) $P'$ is everything not in $P$: $10, 11, 13, 14, 16, 17$

(b) $P \cup Q = \{10, 12, 14, 15, 18\}$, which is 5 of the 9 numbers.

Probability $= \frac{5}{9}$

(a) Round: $513 \approx 500$ km and $0.81 \approx 0.8$ euros.

$500 \div 10 = 50$ lots of 10 km, $50 \times 0.8 = 40$ euros.

(b) Underestimate: both values were rounded down.

(a) The line crosses the $y$-axis at 3.

From $(0, 3)$ to $(2, 6)$: gradient $= \frac{6-3}{2-0} = \frac{3}{2}$

$y = \frac{3}{2}x + 3$

(b) Parallel lines have the same gradient, e.g. $y = 5x + 1$.

Empty jars: $\frac{3}{8} \times 400 = 150$

S : M $= 3 : 4$ and M : L $= 1 : 2 = 4 : 8$, so S : M : L $= 3 : 4 : 8$

Small empty: $\frac{3}{15} \times 150 = 30$

Percentage: $\frac{30}{400} \times 100 = 7.5\%$

After a 30% reduction the sale price is 70% of the normal price.

$70\% = £280$, so $10\% = £40$ and $100\% = £400$.

$x + 11 \le 5 - \frac{1}{2}x$

$\frac{3}{2}x \le -6$

$x \le -4$