November 2022 Paper 2 Foundation

Negative numbers get smaller the further they are from zero, so $-7$ is the smallest.

Order: $-7, -2, -1, 0, 7$

Per cent means out of 100, so $37\% = \frac{37}{100}$.

Odd numbers: 1, 3, 5, 7, 9, 11, 13

The 7th one is 13.

There are 10 mm in 1 cm.

$53 \times 10 = 530$ mm

To be even, the last digit must be 4 or 6.

The smallest start uses 3 first. Ending in 6 leaves 3, 4, 7: 3476. Ending in 4 leaves 3, 6, 7: 3674.

Smallest is 3476.

(a) Line the zero of the ruler up with A and read off at B: about 4.5 cm.

(b) The angle is obtuse, so read the larger scale on the protractor: about $110°$.

Distance: $12845 - 12468 = 377$ miles

Cost: $377 \times 13 = 4901$p

$4901 \div 100 = £49.01$

Cost $= 45 \times 7 = £315$

Label the horizontal axis with the five days and the vertical axis with a linear scale from 0 to 10.

Draw bars of equal width: Monday 9, Tuesday 10, Wednesday 8, Thursday 6, Friday 3.

(a) 07 20 to 08 00 is 40 minutes, then 08 00 to 08 09 is 9 more: 49 minutes.

(b) She reaches Blackrod at $08\,00 + 7 = 08\,07$, so she catches the 08 09 bus.

That bus reaches Bolton at 08 58, and $08\,58 + 15 = 09\,13$.

09 13 is before 09 20, so yes.

Children: $214 - 14 = 200$

Not wearing a hat: $100\% - 35\% = 65\%$

$0.65 \times 200 = 130$

(a) $132 \div 8 = 16.5$, and $16.5 \times 5 = 82.5$

(b) Use denominator 64: $\frac38 = \frac{24}{64}$, $\frac{9}{32} = \frac{18}{64}$, $\frac14 = \frac{16}{64}$, $\frac{21}{64}$.

Order: $\frac14, \frac{9}{32}, \frac{21}{64}, \frac38$

Offer 1: pay $2 \times 75 = 150$p for 3 bottles, which is 6 pints. $150 \div 6 = 25$p per pint.

Offer 2: pay $128 + 64 = 192$p for 2 bottles, which is 8 pints. $192 \div 8 = 24$p per pint.

The 4-pint offer is better value.

(a) $4c + 3c = 7c$ and $7d - d = 6d$, so $7c + 6d$.

(b) Divide by 5: $2m - 6 = 8$, so $2m = 14$ and $m = 7$.

(c) 3 boxes give $3x$ and 2 packets give $2y$: total $3x + 2y$.

(a) Use tens as the stem and units as the leaves, in order:

7 | 1 1 4 5 7
8 | 2 4 5 6 7 8 9
9 | 1 4 7 8
10 | 3

Key: 7 | 1 means 71

(b) There are 17 values, so the median is the $\frac{17+1}{2} = 9$th value: 86.

One pipe would take $4 \times 12 = 48$ hours to fill the lake.

Six pipes take $48 \div 6 = 8$ hours for the whole lake.

A quarter of the lake: $8 \div 4 = 2$ hours.

Midpoints: 155, 165, 175, 185, 195

$155\times8 + 165\times14 + 175\times24 + 185\times30 + 195\times4 = 14080$

$14080 \div 80 = 176$ cm

(a) The point at $(2, 1)$ is far away from the trend of the others.

(b) As rainfall goes up, sunshine goes down: negative correlation.

(c) Draw a line of best fit, go across from 7 hours to the line and down: about 3.5 mm.

Viewed from the right, the width comes from the depth of the plan (3 squares) and the height from the tallest point of the front elevation (5 squares).

Draw a rectangle 3 wide and 5 high. Visible edges where the sloping faces meet appear as horizontal lines across it.

(a) The terms go up by 6, so start with $6n$: 6, 12, 18, ... Each term is 1 more, so $6n + 1$.

(b) $8 - 6n = -58$

$6n = 66$, so $n = 11$.

11 is a whole number, so yes, $-58$ is the 11th term.

Rectangle ABCO: $11 \times 7 = 77$

Rectangle DEFO: $7 \times 9 = 63$

Triangle CDO: $\frac12 \times 11 \times 9 = 49.5$

Quarter circle: $\frac14 \times \pi \times 7^2 = 38.48...$

Total $= 227.98...\text{ m}^2$, and $227.98 \div 14 = 16.28...$ so 17 bags.

$17 \times 10.95 = £186.15$

$x$ is adjacent to $53°$ and 14.5 cm is the hypotenuse, so use cosine.

$x = 14.5 \cos 53° = 8.726...$

$x = 8.73$ (3 s.f.)

After year 1: $7000 \times 1.03 = 7210$

After year 2: $7210 \times 1.015 = £7318.15$

(a) The curve crosses the y-axis where $x = 0$: $y = 4$.

(b) The lowest point is at $(3, -5)$.

(c) Read where the curve crosses the x-axis: about $x = 0.8$ and $x = 5.2$.

(a) $1 \div 0.8 = 1.25$

(b) 2 s.f. here means to the nearest 100, so half of 100 is 50 either side.

$4700 - 50 = 4650$ and $4700 + 50 = 4750$

$4650 \le x < 4750$

After the increase the population is 109% of the 2018 figure.

$165680 \div 1.09 = 152000$