November 2021 Paper 3 Foundation

Per cent means out of 100, so divide by 100.

$45 \div 100 = 0.45$

Find pairs that multiply to 35: $1 \times 35$ and $5 \times 7$.

So the factors are 1, 5, 7 and 35. Any two of these will do, e.g. 5 and 7.

Add the 2 hours first: 8.05 am → 10.05 am.

Then add 40 minutes: 10.05 am → 10.45 am.

To find $\frac{1}{6}$ of an amount, divide by 6.

$66 \div 6 = 11$

Measure the length of AB with a ruler.

Halve that length, measure that far from A along the line, and mark a cross there.

(a) Write the number first and drop the multiplication signs: $4ab$.

(b) Collect the $x$ terms: $4x - x = 3x$.

Collect the numbers: $3 + 5 = 8$.

So the answer is $3x + 8$.

Work systematically: take each letter from bag A in turn and pair it with each letter from bag B.

E: EJ, EK

F: FJ, FK

G: GJ, GK

That gives $3 \times 2 = 6$ outcomes.

Planes: $2 \times 600 = 1200$

Hotel: $7 \times 120 = 840$

Theme park: $2 \times 250 = 500$

Total: $1200 + 840 + 500 = 2540$ dollars, and $2540 > 2500$.

Put in the given values: total 56, plastic total 32, blue total 14, blue plastic 5, red not plastic 8, red total 12.

Red plastic: $12 - 8 = 4$. Blue not plastic: $14 - 5 = 9$.

Black total: $56 - 12 - 14 = 30$. Black plastic: $32 - 4 - 5 = 23$.

Black not plastic: $30 - 23 = 7$. Not plastic total: $56 - 32 = 24$.

$300 \div 4.85 = 61.85...$

She cannot buy part of a book, and 62 books would cost more than £300, so round down.

She can buy 61 books.

(a) $3 \times 60 = 180$ minutes, and $196 - 180 = 16$.

So 196 minutes is 3 hours 16 minutes.

(b) Speed = distance ÷ time, so the speed is $\frac{x}{2}$ miles per hour.

(a) Measure the distance on the map: about 2.5 cm.

$2.5 \times 20 = 50$ km

(b) $5 \times 1200 = 6000$ cm on the ground.

$6000 \div 100 = 60$ m

(a) There are $2 + 3 = 5$ parts, and land is 2 of them.

$\frac{2}{5} \times 100 = 40\%$

(b) Water is $100 - 20 = 80\%$.

Land : water $= 20 : 80 = 1 : 4$

The land is $1 - \frac{13}{15} = \frac{2}{15}$ of the cost.

$600 \div 15 = 40$

$40 \times 2 = 80$, so the land cost £80 million.

Add the angles: $23 + 145 + 23 + 69 = 260°$.

Angles around a point must add up to $360°$, so these results cannot be right.

The shape keeps the same angles but gets bigger, so it is an enlargement.

AB is 1 unit and AD is 4 units, so the scale factor is 4.

Point A stays still at $(1, 1)$, so that is the centre.

Enlargement, scale factor 4, centre $(1, 1)$.

(a) $y \times y + y \times 5 = y^2 + 5y$

(b) The highest common factor of 4 and 6 is 2: $2(2a - 3)$

(c) $10x - 8 = 21$, so $10x = 29$ and $x = 2.9$

(d) $4 \times 5 = 20$, $e^2 \times e = e^3$, $f \times f^3 = f^4$, giving $20e^3f^4$

1 m = 100 cm, so a 1 m by 1 m square is 100 cm by 100 cm.

$100 \times 100 = 10\,000$ cm²

The big square has side $3 + 5 = 8$ cm, so its area is $64$ cm².

Each corner triangle has area $\frac{1}{2} \times 3 \times 5 = 7.5$ cm².

Shaded area $= 64 - 4 \times 7.5 = 34$ cm².

(Or: side$^2 = 3^2 + 5^2 = 34$.)

Use the tens digit as the stem and the units digit as the leaf.

Put the leaves in order:

1 | 5 7 8 9 9

2 | 0 2 2 4 5 5 8

3 | 2 3 5

Key: 2 | 5 means 25 cm. Check there are 15 leaves.

(a) The point far from the others is at $(100, 18)$.

(b) Draw a line of best fit through the main trend and read up from 370: about 13.8 mg/m³.

(c) No. One outlier does not remove the pattern; the other points still show positive correlation.

Total parts: $9 + 2 + 1 = 12$

Cheese: $6000 \div 12 \times 2 = 1000$ g

$1000 \div 175 = 5.714...$ lots of 175 g

$5.714... \times 2.25 = £12.857...$, so about £12.86

(a) Move the digits 5 places: $4.5 \times 10^5 = 450\,000$

(b) $0.007 = 7 \times 10^{-3}$

(c) $4200 + 530 = 4730 = 4.73 \times 10^3$

Company A: 1 min 40 s $= \frac{5}{3}$ min, so the rate is $8 \div \frac{5}{3} = 4.8$ litres per minute.

Time A $= 2400 \div 4.8 = 500$ min.

Company B: $2.2 \times 4.54 = 9.988$ litres per minute.

Time B $= 2400 \div 9.988 = 240.29$ min.

Difference $= 500 - 240.29 = 259.7$, about 260 minutes.

Each term is the sum of the two before, so the fifth term is $3a + 5a = 8a$.

$a + 2a + 3a + 5a + 8a = 19a$

$19a = 228$, so $a = 12$.

(a) The probabilities add to 1: $1 - 0.05 - 0.15 = 0.8$ for green and pink together.

Green is 0.2 more than pink: $2p + 0.2 = 0.8$, so pink $= 0.3$ and green $= 0.5$.

(b) $0.15$ of the counters are blue: $18 \div 0.15 = 120$.

Quarter circle: $\frac{1}{4} \times \pi \times 8^2 = 50.265...$ cm²

Triangle $OPR$: $\frac{1}{2} \times 8 \times 8 = 32$ cm²

Segment $= 50.265... - 32 = 18.265...$

So the area is $18.3$ cm² (3 s.f.).

For positive $x$, $y$ is positive and gets smaller as $x$ grows, so draw a curve in the top-right quadrant.

For negative $x$, $y$ is negative, so draw the matching curve in the bottom-left quadrant.

The curves get close to the axes but never touch them, and there is no point at $x = 0$.