November 2023 Paper 2 Foundation

Factor pairs of 18: $1 \times 18$, $2 \times 9$, $3 \times 6$.

So the factors are 1, 2, 3, 6, 9 and 18. Any two of these, e.g. 2 and 9.

The 9 is in the tenths column, so $0.9 = \frac{9}{10}$.

There are 100 cm in 1 m.

$7 \times 100 = 700$ cm

Square the whole numbers: $4^2 = 16$, $5^2 = 25$, $6^2 = 36$, $7^2 = 49$.

Any of these works, e.g. 25.

50% means half.

$240 \div 2 = 120$

Pay per hour $=$ total pay $\div$ hours

$50 \div 4 = 12.5$, so £12.50 per hour.

(a) The solid has a circular base and comes to a point at the top, so it is a cone.

(b) Draw a triangle, draw an identical triangle slightly across and up from it, then join matching corners with three parallel lines.

Footballs: $5 \times 9.50 = 47.50$

Hockey sticks: 6 sticks is 3 lots of 2, so $3 \times 30 = 90$

Cricket bats: $2 \times 23 = 46$

Tennis balls: 4 balls cost $5$

Total $= 47.50 + 90 + 46 + 5 = £188.50$, which is less than £200, so he can buy everything.

Work systematically: fix the shirt, then go through the ties.

White: WP, WS, WC

Blue: BP, BS, BC

Grey: GP, GS, GC

That is $3 \times 3 = 9$ combinations.

Red : blue $= 24 : 40$

The highest common factor of 24 and 40 is 8.

$24 \div 8 = 3$ and $40 \div 8 = 5$, so the ratio is $3 : 5$.

(a) Only 1 of the 6 faces is a 3, so the probability is $\frac{1}{6}$: unlikely.

(b) The odd numbers are 1, 3 and 5, so 3 out of 6, which is $\frac{1}{2}$: evens.

Distance $=$ speed $\times$ time

$37 \times 3 = 111$ miles

(a) Area of a rectangle $=$ length $\times$ width $= 5 \times 4 = 20\text{ cm}^2$. Milo multiplied all four side lengths together, which uses each measurement twice.

(b) Area is measured in square units. An answer in cm is a length, so it should be in $\text{cm}^2$.

1 kg flour: $4.05 \div 3 = 1.35$

5 kg flour: $5 \times 1.35 = 6.75$, so 6 kg sugar costs $11.85 - 6.75 = 5.10$

1 kg sugar: $5.10 \div 6 = 0.85$

2 kg flour + 5 kg sugar $= 2 \times 1.35 + 5 \times 0.85 = 2.70 + 4.25 = £6.95$

Martha's share: $0.72 \times 120 = 86.40$

She keeps $100\% - 30\% = 70\%$ of it.

$0.7 \times 86.40 = £60.48$

Adults: $160 - 85 = 75$. Adult romance: $33 - 19 = 14$. Child adventure: $76 - 34 = 42$.

Adult horror: $75 - 14 - 34 - 7 = 20$, so 20 children chose thriller.

Child horror: $85 - 19 - 42 - 20 = 4$

Total horror: $20 + 4 = 24$

Use the tens-and-hundreds digits as the stem (16, 17, 18, 19) and the units as leaves.

16 | 0 2 8

17 | 2 2 3 7 8

18 | 0 0 3 4 6 8

19 | 1 7

Key: 16 | 0 means 160 cm. Check there are 16 leaves in total.

(a) Top: $9.8 + 6.8 = 16.6$. Bottom: $4.2 \times 2.1 = 8.82$

$16.6 \div 8.82 = 1.882086168\ldots$

(b) The third decimal place is 2, so round down: $1.88$

Triangle BCD is equilateral, so angle $DBC = 60°$ (angles in an equilateral triangle are equal).

Angle $BDE = 60°$ (alternate angles are equal, since CB is parallel to DE).

Angle $ABD = 90°$ (marked right angle).

Angles in a quadrilateral add up to $360°$: $x = 360 - 90 - 60 - 132 = 78°$

(a) Substitute each $x$ into $x^2 - x - 2$:

$x = -1$: $1 + 1 - 2 = 0$; $x = 0$: $-2$; $x = 2$: $4 - 2 - 2 = 0$; $x = 3$: $9 - 3 - 2 = 4$

(b) Plot the six points and join them with a smooth curve. The lowest point is between $x = 0$ and $x = 1$, just below $-2$.

Corners of A: $(1,5), (3,5), (1,2)$. Corners of B: $(-5,-1), (-5,-3), (-2,-1)$.

Each point $(a, b)$ goes to $(-b, -a)$, which is a reflection.

The mirror line is $y = -x$, so the answer is **reflection in the line $y = -x$**.

(a) $6y - 15 + 7y + 14 = 13y - 1$

(b) The HCF of $6x^2$ and $15x$ is $3x$: $6x^2 + 15x = 3x(2x + 5)$

(c) $f - 11 = 3g$, so $g = \frac{f - 11}{3}$

Income: $54 \times 7.50 = £405$

Costs: $100 + 120 + 80 = £300$

Profit: $405 - 300 = £105$

Percentage profit $= \frac{105}{300} \times 100 = 35\%$

Multiplier for 3.4% interest: $1.034$

$4500 \times 1.034^2 = 4811.202$, so £4811.20

Add $x$ to both sides: $6x - 14 = 52$

Add 14 to both sides: $6x = 66$

$x = 11$

Debbie has 4 parts $= 120$, so 1 part $= 30$ and the total is $9 \times 30 = 270$.

At first Errol has $2 \times 30 = 60$.

New ratio has $2 + 5 + 3 = 10$ parts, so 1 part $= 27$ and Errol now has $3 \times 27 = 81$.

Chris gave Errol $81 - 60 = £21$

The return bearing differs by $180°$.

$147 + 180 = 327°$

Volume $= \pi \times 15^2 \times 43 = 30\,394.9\ldots\text{ cm}^3$

$1000\text{ cm}^3 = 1$ litre, so this is $30.3949\ldots$ litres.

Time $= 30.3949 \div 0.47 = 64.67\ldots$, so 65 minutes

AB is opposite the $49°$ angle and BC (28 cm) is adjacent, so use tan.

$AB = 28 \times \tan 49° = 32.21\ldots$

So $AB = 32.2$ cm (3 s.f.)

Multiply the first equation by 3: $9x + 3y = -13.5$

Subtract the second: $5x = -10$, so $x = -2$

Substitute: $3(-2) + y = -4.5$, so $y = 1.5$