June 2019 Paper 2 Foundation

$0.75$ means 75 hundredths: $\frac{75}{100}$.

Divide top and bottom by 25: $\frac{75}{100} = \frac{3}{4}$

Negative numbers are smaller than zero, and $-3$ is further below zero than $-1$.

So the order is $-3, -1, 0, 2, 4$

Factor pairs of 15: $1 \times 15$ and $3 \times 5$.

So the factors are 1, 3, 5 and 15; any two of these will do, e.g. 3 and 5.

There are 1000 g in 1 kg, so divide by 1000.

$1756 \div 1000 = 1.756$ kg

One million is $1\,000\,000$ (six zeros).

Two million is $2\,000\,000$

Two coffees: $2 \times 2.75 = 5.50$

Total spent: $5.50 + 2.90 = 8.40$, so £8.40

Change: $10 - 8.40 = 1.60$, so £1.60

£1.60 is more than £1.50, so Dave is correct.

Each boat holds 7 people, so $y$ boats hold $7 \times y$ people.

In algebra we write this as $7y$.

(a) Write the number first, then the letters: $7ab$

(b) $y$ multiplied by itself three times is $y^3$

(c) Top: $e \times e \times e \times f = e^3 f$. Bottom: $e \times e \times f \times f = e^2 f^2$

Cancel two $e$s and one $f$: $\frac{e^3 f}{e^2 f^2} = \frac{e}{f}$

(a)(i) 3 circles: $3 \times 8 = 24$

(a)(ii) 2 circles and a quarter: $2 \times 8 + 2 = 18$

(b) Wednesday is 1 part and Thursday 8 parts, so 9 parts make 36: $36 \div 9 = 4$

Wednesday 4, Thursday $8 \times 4 = 32$

Draw half a circle for Wednesday ($4 = \frac{1}{2} \times 8$) and 4 full circles for Thursday ($32 \div 8 = 4$).

$14 < 21$

$4 + 7 = 11$ and $103 - 92 = 11$, so they are equal.

$2^2 = 4$ and $2 \times 2 = 4$, so they are equal.

$-3$ is nearer zero than $-5$, so $-3 > -5$

$P = 7 \times 5 + 3 \times (-4)$

$= 35 + (-12)$

$= 23$

(a) From 07 15 to 07 22 is 7 minutes.

(b) The 07 22 train reaches London at 09 00.

07 22 to 08 00 is 38 minutes; 08 00 to 09 00 is 1 hour.

Journey time: 1 hour 38 minutes (98 minutes).

Across the length there are 6 squares side by side, so each side is $12 \div 6 = 2$ cm.

Down the width there are 5 squares, so the width is $5 \times 2 = 10$ cm.

Divide both sides by 2.25:

$4.5 \div 2.25 = 2$ and $2.25 \div 2.25 = 1$

So the ratio is $2 : 1$

Area of the garden: $90 \times 60 = 5400$ m²

Grass is $100\% - 40\% = 60\%$ of it.

$0.6 \times 5400 = 3240$ m²

(a) As decimals: A 0.33, B 0.033, C $0.333...$, D 0.3

Least likely is B; most likely is C.

(b) P(Tails) $= 1 - \frac{1}{3} = \frac{2}{3}$, which is not $\frac{1}{3}$, so Julie is wrong.

(c) $4000 \times 0.033 = 132$

Banana: $\frac{60}{100} \times 84 = 50.4$

Yogurt: $\frac{150}{100} \times 87 = 130.5$

Total: $50.4 + 130.5 = 180.9$ calories

Machine A: 6 parts per 10 min is $6 \times 6 = 36$ per hour.

$36 \times 12 = 432$

Machine B: 13 parts per 15 min is $13 \times 4 = 52$ per hour.

$52 \times 10 = 520$

Total: $432 + 520 = 952$

Scale 1 : 30, so divide real lengths by 30.

$180 \div 30 = 6$ cm and $150 \div 30 = 5$ cm

With compasses set to 6 cm, draw an arc centred on A. The table must be outside this arc.

Draw a line parallel to BC, 5 cm in from it. The table must be on the A side of this line.

Shade the part of the kitchen that is outside the arc and beyond the line from BC.

(a) $14n - 11n > 6$, so $3n > 6$ and $n > 2$.

(b) Subtract 3 from every part: $-2 - 3 < x \le 4 - 3$, so $-5 < x \le 1$.

Draw an open circle at $-5$ (not included), a filled circle at $1$ (included) and join them.

Make a table of values using $y = 2x - 3$:

| $x$ | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| $y$ | −7 | −5 | −3 | −1 | 1 | 3 | 5 |

Plot the points and join them with a single ruled line from $(-2,-7)$ to $(4,5)$.

(i) $\frac{10}{30} = \frac{1}{3}$ of the sample chose the theme park.

$\frac{1}{3} \times 195 = 65$

(ii) Assume the 30 students represent the whole group fairly. If they do not, the true number could be quite different from 65.

Volume $= 30 \times 19 \times 6 = 3420\text{ cm}^3$

Water $= \frac{2}{3} \times 3420 = 2280\text{ cm}^3 = 2280\text{ ml}$

$2280 \div 275 = 8.29...$

Only 8 cups can be completely filled.

AC is the hypotenuse (16 cm) and AB is opposite the 38° angle.

$\sin 38^\circ = \frac{AB}{16}$

$AB = 16 \sin 38^\circ = 9.850... = 9.85\text{ cm}$

The display began 8.3, so the digits after 8.3 have been cut off (truncated), not rounded.

The smallest value is 8.3 and $y$ can get as close as you like to 8.4 without reaching it.

$8.3 \le y < 8.4$

Abby : Ben = 2 : 7. Chloe and Denesh each get $1.5 \times 2 = 3$ parts.

Total parts $= 2 + 7 + 3 + 3 = 15$

One part $= 360 \div 15 = £24$

Ben gets $7 \times 24 = £168$

(a) Move the decimal point 3 places right to get 5.62, so $0.00562 = 5.62 \times 10^{-3}$.

(b) $1.452 \times 10^3$: move the point 3 places right to get $1452$.

(a) Add the two previous terms: $9 + 15 = 24$, then $15 + 24 = 39$

(b) $a,\ a,\ 2a$, then $a + 2a = 3a$, $2a + 3a = 5a$, $3a + 5a = 8a$

The 6th term is $8a$.

$2\mathbf{b} = \begin{pmatrix}6\\4\end{pmatrix}$

$\mathbf{a} - 2\mathbf{b} = \begin{pmatrix}4 - 6\\5 - 4\end{pmatrix} = \begin{pmatrix}-2\\1\end{pmatrix}$