November 2021 Paper 2 Foundation

Per cent means out of 100, so $31\% = \frac{31}{100}$.

There are 100 cm in 1 m, so $3 \times 100 = 300$ cm.

Compare whole-number parts first: 0.12 and 0.21 are less than 1.

Then compare tenths: $0.12 < 0.21$ and $1.02 < 1.20$.

Order: 0.12, 0.21, 1.02, 1.20

(a) Four lots of $m$ make $4m$.

(b) $12p \div 4 = 3p$ because $12 \div 4 = 3$.

Each 5 m becomes 1 cm.

$35 \div 5 = 7$ cm and $20 \div 5 = 4$ cm.

Draw a rectangle 7 cm long and 4 cm wide.

(a) $5 \times 5 = 25$, so 25 is square.

(b) $8 \times 3 = 24$, so 24 is a multiple of 8.

Flour in A and B together: $2500 - 940 = 1560$ g.

They are equal, so bag A has $1560 \div 2 = 780$ g.

Frequencies read from the chart: 6, 4, 5, 8, 7, 5.

Total throws: $6+4+5+8+7+5 = 35$.

Each student: $35 \div 5 = 7$ throws.

Multiplication comes before addition (BIDMAS).

$3 \times 4 = 12$, then $2 + 12 = 14$, not 20.

The part goes on top and the whole on the bottom: $\frac{17}{30}$.

Take each corner of A and count its distance to the mirror line.

Plot the image point the same distance on the other side, then join the points.

(a) $13.82 \div 4.06 = 3.40394\ldots$

$\sqrt{3.40394\ldots} = 1.844977205\ldots$

(b) The third decimal is 4, so round down: 1.84

(i) Angles on a straight line total $180^\circ$.

$x = 180 - 75 - 84 = 21$

(ii) Angles on a straight line add up to $180^\circ$.

(a) At 2 hours the pay is £30, so $30 \div 2 = £15$ per hour.

(b) $15 \times 36 = £540$

Convert to decimals:

$\frac{5}{8} = 0.625$, $\frac{2}{3} = 0.667$, $\frac{4}{9} = 0.444$, $\frac{3}{5} = 0.6$

Order: $\frac{4}{9}, \frac{3}{5}, \frac{5}{8}, \frac{2}{3}$

(a) Black is a right angle, $90^\circ$, for 135 cars, so $1^\circ$ is $135 \div 90 = 1.5$ cars.

White: $80 \times 1.5 = 120$ cars.

(b) Total cars: $360 \times 1.5 = 540$

$P(\text{grey}) = \frac{50}{540} = \frac{5}{54}$

Men: $60 - 38 = 22$. Men who text: $22 - 15 = 7$.

Text in total: $0.6 \times 60 = 36$.

Women who text: $36 - 7 = 29$. Women who email: $38 - 29 = 9$.

Known lengths: $3\times5 + 2.5\times8 + 1.5\times14 + 1\times10 = 15 + 20 + 21 + 10 = 66$ m.

Left for 2 m planks: $92 - 66 = 26$ m.

Number of planks: $26 \div 2 = 13$.

Rachel: $\frac{2}{5} \times 600 = £240$. Left: $600 - 240 = £360$.

Samina: $\frac{1}{4} \times 360 = £90$.

Tom: $360 - 90 = £270$.

Equal share: $600 \div 3 = £200$. Tom already gets more, so he is not correct.

(a) Dividing: subtract the powers, $5 - 2 = 3$, giving $c^3$.

(b) Power of a power: multiply, $4 \times 3 = 12$, giving $d^{12}$.

(a) The open circle at $-1$ means $-1$ is not included, and the arrow points right: $x > -1$.

(b) Filled circle at $-3$ (included) and open circle at 4 (not included), with a line joining them.

(a) $60 = 2^2 \times 3 \times 5$ and $84 = 2^2 \times 3 \times 7$.

HCF $= 2^2 \times 3 = 12$.

(b) $24 = 2^3 \times 3$ and $40 = 2^3 \times 5$.

LCM $= 2^3 \times 3 \times 5 = 120$.

(a) 20 km in 15 minutes. There are four lots of 15 minutes in an hour, so $20 \times 4 = 80$ km/h.

(b) Stop: flat line at 20 km from 10 15 to 10 25.

In 20 minutes at 75 km/h: $75 \times \frac{20}{60} = 25$ km.

Draw a line from (10 25, 20) to (10 45, 45).

(a) $x=-1$: $1 + 2 + 2 = 5$. $x=1$: $1 - 2 + 2 = 1$. $x=2$: $4 - 4 + 2 = 2$. $x=4$: $16 - 8 + 2 = 10$.

(b) Plot $(-2,10), (-1,5), (0,2), (1,1), (2,2), (3,5), (4,10)$ and join with a smooth curve.

(c) Draw the line $y = 4$. It crosses the curve at about $x = -0.7$ and $x = 2.7$.

Hypotenuse: $\sqrt{8^2 + 10^2} = \sqrt{164} = 12.806\ldots$ mm.

Outer edges: 8, 10, part of the first hypotenuse ($12.806 - 10 = 2.806$), the second hypotenuse $12.806$, and 8.

Perimeter $= 8 + 10 + 2.806 + 12.806 + 8 = 41.6$ mm (3 s.f.)

(a) $BC$ is opposite $56^\circ$ and 12 is adjacent, so use tan.

$BC = 12 \tan 56^\circ = 17.79\ldots = 17.8$ cm

(b) 15 is adjacent and 18 is the hypotenuse, so use cos.

$x = \cos^{-1}\left(\frac{15}{18}\right) = 33.557\ldots = 33.6^\circ$

Find two numbers that multiply to $-18$ and add to $-7$: $+2$ and $-9$.

$(x + 2)(x - 9) = 0$

$x = -2$ or $x = 9$

The sale price is $100\% - 15\% = 85\%$ of the normal price.

$272\,000 \div 0.85 = £320\,000$