November 2022 Paper 1 Foundation

The 3 is in the tenths column, so $0.3 = \frac{3}{10}$.

$3^2 = 3 \times 3 = 9$

Brackets first: $3 + 2 = 5$.

Then $20 \div 5 = 4$.

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

The ones between 8 and 14 are 10 and 12, so either answer works.

Multiply the numbers: $3 \times 5 = 15$.

Write the letters next to it: $15tw$.

Tickets: $33 + 2 \times 24.50 = 82$

Meals: $15 + 2 \times 10 = 35$

Total: $23 + 82 + 35 = £140$

Left: $200 - 140 = £60$

(a) A appears 5 times, more than any other letter, so the mode is A.

(b)(i) B appears 2 times out of 8: $\frac{2}{8} = \frac{1}{4}$, halfway between 0 and $\frac{1}{2}$.

(b)(ii) C appears once: $\frac{1}{8}$.

(a) $m - 3 = 4$, so $m = 4 + 3 = 7$.

(b) $3n + n = 4n$, so $4n = 24$ and $n = 24 \div 4 = 6$.

(a) The two angles go all the way round the point.

$y = 360 - 70 = 290$

(b) Angles at a point add up to $360°$.

(a) $23 \div 4 = 5.75$, so he can afford 5 whole jars (costing £20).

(b) At half price each jar is £2. $23 \div 2 = 11.5$, so he can buy 11 jars.

Twice 5 is 10, so he is not correct: he can buy 11.

(a)(i) The top side of A is 3 squares; in B it is 6 squares. $6 \div 3 = 2$.

(a)(ii) Draw lines through matching corners of B and A and extend them; they meet at the centre.

(b) Corner $(1, 4)$ of C maps to $(4, 1)$ of D: the coordinates swap. That is a reflection in $y = x$.

(a) Swimming: $\frac{1}{6} \times 120 = 20$ minutes

Gym: $20\% \times 120 = 24$ minutes

Café: $120 - 50 - 20 - 24 = 26$ minutes

(b) $50 + 20 + 24 = 94$ minutes after 1.30 pm is 3.04 pm, so she was 4 minutes late.

(a) The men bar for 2000 reaches 60.

(b) In 2010 the bar goes from 160 to 210: $210 - 160 = 50$ children.

(c) 2020: men and women together reach 200; children go from 200 to 280, so 80.

Ratio $80 : 200 = 2 : 5$

(a) Distance = speed × time $= 54 \times 1.5 = 81$ miles

(b) Real length $= 6 \times 25\,000 = 150\,000$ cm

$150\,000 \div 100 = 1500$ m, and $1500 \div 1000 = 1.5$ km

$P = (-3, -2)$ and $Q = (2, 4)$.

$x$: $\frac{-3 + 2}{2} = -0.5$

$y$: $\frac{-2 + 4}{2} = 1$

Midpoint $(-0.5, 1)$

Perimeter: $(x + 1) + (x - 1) + 2x + (2x - 5) = 6x - 5$

$6x - 5 = 52$, so $6x = 57$ and $x = 9.5$

$DC = 2x = 2 \times 9.5 = 19$ cm

(a) $100 - 30 = 70$ are not blue, so $P = \frac{70}{100}$.

(b) 2 parts = 30, so 1 part = 15. Green = $3 \times 15 = 45$.

(c) Red + yellow $= 100 - 30 - 45 = 25$. 25 is odd, so they cannot be equal.

One part: $240 \div 10 = 24$

Cola 120, lemonade 72, orange 48

Removed: $\frac{1}{2} \times 72 = 36$ and $\frac{1}{12} \times 48 = 4$

Left: $240 - 40 = 200$

$\frac{120}{200} \times 100 = 60\%$

$500 = 2 \times 250 = 2 \times 2 \times 125$

$125 = 5 \times 5 \times 5$

So $500 = 2^2 \times 5^3$

(a) $1 + 2 = 3$; $\frac{3}{5} + \frac{1}{4} = \frac{12}{20} + \frac{5}{20} = \frac{17}{20}$

Answer $3\frac{17}{20}$

(b) $2\frac{2}{3} = \frac{8}{3}$

$\frac{8}{3} \div 6 = \frac{8}{3} \times \frac{1}{6} = \frac{8}{18} = \frac{4}{9}$

Inside the bracket add the powers: $2^{-5} \times 2^8 = 2^{3}$

Square by multiplying the power: $(2^3)^2 = 2^6$

$4 \times 32 = 128$

There are $3 + 2 = 5$ decimal places in the question, so the answer is $0.00128$.

15 out of 80 people chose B.

$\frac{15}{80} \times 40\,000 = 7500$

(a)(i) Double $1 : 3$ to $2 : 6$ so $b$ is 6 in both. $a : b : c = 2 : 6 : 5$

(a)(ii) Total parts $2 + 6 + 5 = 13$, so $a$ is $\frac{2}{13}$.

(b) $p = 5n = 5 \times 2m = 10m$, so $m : p = 1 : 10$

Area $= 4 \times 2 = 8\text{ m}^2$

Pressure $= \frac{10\,000}{8} = 1250$ N/m$^2$

(a) $\frac{5x}{2} + 3 > 18$

$\frac{5x}{2} > 15$, so $5x > 30$ and $x > 6$

(b) Need two numbers that multiply to 9 and add to 10: 9 and 1.

$(x + 9)(x + 1)$