November 2022 Paper 3 Foundation

Give each number three decimal places: 0.410, 0.500, 0.460, 0.408.

Now compare: 0.408 < 0.410 < 0.460 < 0.500, so the order is 0.408, 0.41, 0.46, 0.5

In 12 345 the digits are: 1 ten-thousand, 2 thousands, 3 hundreds, 4 tens, 5 ones.

So the 2 is worth 2000.

$\frac{4}{5} = \frac{8}{10} = 0.8$

Look at the first decimal place: 19.4949. It is 4, which is less than 5, so round down.

Answer: 19

Check each number: $18 = 3 \times 6$, and none of 5, 11, 22 or 29 divides exactly by 3.

Answer: 18

(a) Months above 16°C: May, Jun, Jul, Aug, Sep, Oct, so 6 months (April is exactly 16°C, not above).

(b) May and October are both at 20°C.

Large bars: $208 \div 4 = 52$, worth $52 \times £1 = £52$

Small bars: $208 - 52 = 156$, worth $156 \times £0.60 = £93.60$

Total: $£52 + £93.60 = £145.60$

(a) $121 - 19 = 102$

(b) Total $= 143 + 121 + 45 + 19 = 328$

Mean $= 328 \div 4 = 82$

(a) A is 1 left of O and 2 up, so A is $(-1, 2)$.

(b) Go 1 right, then 4 up, and mark B.

(c) $y = -3$ is the horizontal line where every point has y-coordinate −3.

The differences are $20 - 16 = 4$ and $16 - 13 = 3$.

If the differences keep falling by 1, next subtract 2 then 1: $13 - 2 = 11$, $11 - 1 = 10$.

Rule: the number you take away goes down by 1 each time.

Volume $= 8 \times 5 \times 4 = 160\text{ cm}^3$

Let Amol have 1 sweet. Gemma has $6 \times 1 = 6$. Harry has $6 \div 2 = 3$.

Ratio: $1 : 6 : 3$

(a) $x = 360 - 120 - 120 - 80 = 40°$ because the angles in a quadrilateral add up to 360°.

(b) $80 + 60 + 50 = 190°$. Angles in a triangle must add up to 180°, so the diagram cannot be right.

(a) Across from 850 g to the line, then down: 30 ounces.

(b) 80 is off the graph, so use 20 ounces: 20 ounces ≈ 567 g.

$80 = 4 \times 20$, so $4 \times 567 \approx 2268$ g.

Carrots: $1.74 \div 3 = £0.58$ per kg, so 2 kg cost $£1.16$

Onions: $2.36 - 1.16 = £1.20$ for 2.5 kg, so $1.20 \div 2.5 = £0.48$ per kg

4 kg: $4 \times 0.48 = £1.92$, which is less than £2, so yes.

Total $= 90 + 105 + 105 = 300$ potatoes, so each potato is $360 \div 300 = 1.2°$.

Correct angles: $90 \times 1.2 = 108°$, $105 \times 1.2 = 126°$ twice. Salim's sectors are clearly not these sizes (one is a right angle), so they are wrong.

Also, the sectors are not labelled with the types of potato.

(a) The 4th figure is 6, so round the 5 up: 87 600

(b) Top: $(3.2 + 3.7) \times 4.9 = 6.9 \times 4.9 = 33.81$

Bottom: $5.3 - 2.8 = 2.5$

$33.81 \div 2.5 = 13.524$

The shape has vertices $(-4,-2)$, $(-1,-2)$, $(-1,-4)$, $(-2,-4)$.

A 90° anticlockwise turn about O sends $(x, y)$ to $(-y, x)$.

New vertices: $(2,-4)$, $(2,-1)$, $(4,-1)$, $(4,-2)$.

(a) The line is flat from 08 30 to 08 45: 15 minutes.

(b) At 08 50 the graph is at about 4.6 km.

(c) She travels 4 km in 20 minutes. 20 minutes $= \frac{1}{3}$ hour.

Speed $= 4 \div \frac{1}{3} = 12$ km/h

Scale factor: $25 \div 10 = 2.5$

Butter $80 \times 2.5 = 200$ g, flour $350 \times 2.5 = 875$ g, sugar $30 \times 2.5 = 75$ g, eggs $2 \times 2.5 = 5$

Compare: butter $200 - 100 = 100$ g more, sugar $75 - 50 = 25$ g more, eggs $5 - 4 = 1$ more. Flour is fine (875 g < 1 kg).

$p = 3a - 9$

Add 9: $p + 9 = 3a$

Divide by 3: $a = \frac{p + 9}{3}$

The ratio 3 : 5 has $3 + 5 = 8$ parts.

One part $= 120 \div 8 = 15$, giving $45$ and $75$.

Rob divided by 3 and by 5 separately instead of by 8.

German: $200 - 104 - 70 = 26$, so boys choosing German $= 26 - 18 = 8$

Boys: 90, of which 60 chose French and 8 chose German.

Boys choosing Spanish $= 90 - 60 - 8 = 22$

One tank: $\pi \times 40^2 \times 160 \approx 804\,248\text{ cm}^3$

Four tanks: $\approx 3\,216\,991\text{ cm}^3 \approx 3217$ litres

Fertiliser is 1 part in 101: $3217 \div 101 \approx 31.85$ litres

$31.85 < 32$, so yes, she has enough.

AC = 5 matches DF = 20, so the scale factor is $20 \div 5 = 4$.

(a) EF matches BC: $4 \times 4 = 16$ cm

(b) AB matches DE: $22 \div 4 = 5.5$ cm

(a) Not winning the sports quiz: $1 - 0.3 = 0.7$. Not winning the music quiz: $1 - 0.35 = 0.65$ on both pairs of branches.

(b) $P(\text{both}) = 0.3 \times 0.35 = 0.105$

(a) $1\text{ m}^3 = 100^3 = 1\,000\,000\text{ cm}^3$, so $8000 \div 1\,000\,000 = 0.008\text{ m}^3$

(b) $180$ km $= 180\,000$ m, and 1 hour $= 3600$ s

$180\,000 \div 3600 = 50$ m/s

Total for everyone: $50 \times 167.6 = 8380$ cm

Total for men: $20 \times 182 = 3640$ cm

Women: $(8380 - 3640) \div 30 = 4740 \div 30 = 158$ cm

(a) Move the decimal point 4 places left: 0.000675

(b) $2.56 \times 10^6 \times 4.12 \times 10^{-3} = 10\,547.2$

$10\,547.2 \div (1.6 \times 10^{-2}) = 659\,200 = 6.592 \times 10^5$

(a)(i) $\begin{pmatrix}2\\3\end{pmatrix} + \begin{pmatrix}-1\\2\end{pmatrix} = \begin{pmatrix}1\\5\end{pmatrix}$

(ii) $2\mathbf{a} = \begin{pmatrix}4\\6\end{pmatrix}$, so $2\mathbf{a} - \mathbf{c} = \begin{pmatrix}4-4\\6-1\end{pmatrix} = \begin{pmatrix}0\\5\end{pmatrix}$

(b) $\mathbf{d}$ goes 3 right and 2 down, so $2\mathbf{d}$ goes 6 right and 4 down from P.