June 2018 Paper 2 Foundation

Multiply top and bottom by 2 to get a denominator of 100:

$\frac{4}{50} = \frac{8}{100} = 8\%$

Look at the second decimal place: it is 9, which is 5 or more, so round the 5 up.

$1.59 \approx 1.6$

$3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$

The thousands digit is the fourth digit from the right in a whole number.

For example, $564\,000$: the digits are 5 (hundred thousands), 6 (ten thousands), 4 (thousands), then zeros.

(a) 1 cm = 10 mm, so $35 \times 10 = 350$ mm

(b) 1 litre = 1000 ml, so $7700 \div 1000 = 7.7$ litres

(c) 1 kg = 1000 g, so $0.32 \times 1000 = 320$ g

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The odd ones are 1, 3 and 9. Of these, 3 and 9 are multiples of 3.

So the numbers are 3 and 9.

Fix who comes first, then swap the other two.

Mohsin first: MYL, MLY

Yusuf first: YML, YLM

Luke first: LMY, LYM

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

Pens: $30 \div 6 = 5$ packs, $5 \times 82 = 410$p

Pencils: $30 \div 15 = 2$ packs, $2 \times 45 = 90$p

Rulers: $30 \div 10 = 3$ packs, $3 \times £1.25 = £3.75$

Pencil cases: $30 \times 37 = 1110$p

Total: $£4.10 + £0.90 + £3.75 + £11.10 = £19.85$

(a) Speed $= \frac{\text{distance}}{\text{time}} = 186 \div 3 = 62$ mph

(b) Distance $=$ speed $\times$ time $= 58 \times 4 = 232$ miles

(a) Check 21 to 29: $21 = 3 \times 7$, $25 = 5 \times 5$, $27 = 3 \times 9$, and the even ones divide by 2. Only 23 and 29 are prime.

(b) Yes. Any even number bigger than 2 can be divided by 2, so it has at least three factors and cannot be prime.

(a) $3x = 51$, so $x = 51 \div 3 = 17$

(b) $\frac{y}{4} = 3$, so $y = 3 \times 4 = 12$

(c) $2f + 7 = 18 \Rightarrow 2f = 11 \Rightarrow f = 5.5$

Total fans: $11 + 17 + 8 = 36$

Each fan is $360° \div 36 = 10°$

Burger $11 \times 10 = 110°$, pie $17 \times 10 = 170°$, hot dog $8 \times 10 = 80°$

Check: $110 + 170 + 80 = 360°$. Draw each sector with a protractor and label it.

Tickets that are not Laura's: $350 - 12 = 338$

$P(\text{not win}) = \frac{338}{350} = \frac{169}{175}$

Female: $45 - 22 = 23$

Male right-handed: $34 - 16 = 18$

Male left-handed: $22 - 18 = 4$

Female left-handed: $23 - 16 = 7$

Check: left-handed total $4 + 7 = 11 = 45 - 34$

(a) The marked equal sides meet at C, so the base angles are at A and B. Angle A $= 63°$, so $x = 180 - 63 - 63 = 54°$.

(b) The 57° angle and angle EGH lie on opposite sides of the line EG, between the parallel lines. That makes them alternate angles, not corresponding.

Buttons already accounted for: $20 \times 7 + 21 \times 3 + 22 \times 1 = 140 + 63 + 22 = 225$

Buttons left: $320 - 225 = 95$

Bags of 19: $95 \div 19 = 5$

Batches each ingredient allows:

Butter $900 \div 225 = 4$; sugar $1000 \div 110 \approx 9.1$; flour $1000 \div 275 \approx 3.6$; chocolate $225 \div 75 = 3$

Chocolate runs out first, after 3 batches.

$3 \times 30 = 90$ biscuits

Shape B is a mirror image of A, the same distance from the $y$-axis on the other side.

So it is a reflection in the $y$-axis ($x = 0$).

Curved edge: $\frac{1}{2} \times \pi \times 50 = 78.54$ m

Perimeter: $78.54 + 50 = 128.54$ m

Fence: $128.54 \times 29.86 = £3838.20$

Labour: $3 \times 180 = £540$

Total: $3838.20 + 540 = £4378.20$

(a) Add the powers: $m^{3+4} = m^7$

(b) Cube each part: $5^3 \times n^3 \times (p^3)^3 = 125n^3p^9$

(c) Divide the numbers and subtract the powers: $\frac{32}{4} = 8$, $q^{9-3} = q^6$, $r^{4-1} = r^3$, giving $8q^6r^3$

(a) $40 = 2^3 \times 5$ and $56 = 2^3 \times 7$

LCM $= 2^3 \times 5 \times 7 = 280$

(b) Take the lowest power of each shared prime: $2^2 \times 3 \times 5 = 60$

The line crosses the $y$-axis at $-6$, so $c = -6$.

From $(0, -6)$ to $(2, 0)$: up 6, across 2, so gradient $= 6 \div 2 = 3$.

$y = 3x - 6$

Price with VAT: $8500 \times 1.2 = £10\,200$

Monthly payments: $12 \times 531.25 = £6375$

Deposit: $10\,200 - 6375 = £3825$

Ratio: $3825 : 6375$. Divide both by 1275: $3 : 5$

(a) e.g. $x = -2$: $4 + 2 - 6 = 0$; $x = 1$: $1 - 1 - 6 = -6$; $x = 2$: $4 - 2 - 6 = -4$

(b) Plot $(-3, 6), (-2, 0), (-1, -4), (0, -6), (1, -6), (2, -4), (3, 0)$ and join with a smooth curve.

(c) Draw the line $y = -2$ and read off where it crosses the curve: $x \approx 2.6$ and $x \approx -1.6$

Original pressure: $70 \div 20 = 3.5$ N/cm²

New pressure: $80 \div 30 = 2.67$ N/cm²

Decrease: $3.5 - 2.67 = 0.83$

Percentage decrease: $\frac{0.83}{3.5} \times 100 \approx 24\%$

This is more than 20%, so Helen is wrong.

Base of triangle: $\sqrt{8.4^2 - 7.2^2} = \sqrt{18.72} = 4.327$ cm

Triangle area: $\frac{1}{2} \times 4.327 \times 7.2 = 15.58$ cm²

Volume: $15.58 \times 18 = 280.4 \approx 280$ cm³