November 2024 Paper 3 Foundation

In 3721 the 7 is in the hundreds column.

So it is worth $7 \times 100 = 700$.

To find $\frac{1}{6}$ of 96, divide by 6.

$96 \div 6 = 16$

Factor pairs of 16: $1 \times 16$, $2 \times 8$, $4 \times 4$.

So the factors are 1, 2, 4, 8 and 16. Any two of these, e.g. 2 and 8.

The most negative number is the smallest.

$-7 < -3 < 0 < 4 < 6$

$1.5 \times 1.5 = 2.25$

So $\sqrt{2.25} = 1.5$

(a) $4x = 20$, so $x = 20 \div 4 = 5$

(b) $y = 24 - 7 = 17$

(c) $w = 4 \times 2 = 8$

(a) The shape has exactly one pair of parallel sides (top and bottom), so it is a trapezium.

(b) Draw along one horizontal grid line and one vertical grid line from the same point, then join their ends. The grid lines meet at $90°$.

(a) Paint: $2 \times 24.95 = £49.90$

Planks: $232.50 \div 7.75 = 30$

Total: $119.96 + 49.90 + 232.50 + 14.95 = £417.31$

(b) $892.48 + 4.47 + 240 - 365.50 = £771.45$

Children: $\frac{2}{5} \times 200 = 80$, adults: $200 - 80 = 120$

Vegetarian children: $0.35 \times 80 = 28$

Vegetarian adults: $0.45 \times 120 = 54$

Not vegetarian: $200 - 28 - 54 = 118$

(a) The 07 46 reaches Salford at 08 05: that is 14 + 5 = 19 minutes.

(b)(i) He must reach Manchester by $09\,00 - 8$ min $= 08\,52$. The 08 17 from Lostock arrives at 08 45. Leave home 6 minutes earlier: 08 11.

(ii) The next Lostock train (09 17) reaches Manchester at 09 45, after 09 15, so he still needs the 08 17. No effect.

(a) Read across from 10 miles: 16 km.

(b) From the graph, 25 km $\approx 15.5$ miles, so 50 km $\approx 31$ miles.

Total: $17 + 31 = 48$ miles

Each pack has 6 apples, so $x$ packs give $6x$ apples.

Each bag has 7 oranges, so $y$ bags give $7y$ oranges.

Total: $6x + 7y$

Crate in cm: $300 \times 100 \times 150$

$300 \div 20 = 15$, $100 \div 10 = 10$, $150 \div 75 = 2$

Boxes: $15 \times 10 \times 2 = 300$

(Check with volumes: $4\,500\,000 \text{ cm}^3 \div 15\,000 \text{ cm}^3 = 300$ boxes)

Weekdays: $5 \times 6 = 30$ hours, $30 \times 8 = £240$

Weekend rate: $1.5 \times 8 = £12$ per hour

Weekend: $(4 + 3) \times 12 = £84$

Total: $240 + 84 = £324$

(a) $\sum fx = 48 + 63 + 150 + 121 + 24 = 406$

Mean $= 406 \div 41 = 9.90... \approx 9.9$ years

(b) No. 15 is how many children there are, not an age. The modal age is 10.

(a) $126 = 2 \times 63 = 2 \times 7 \times 9 = 2 \times 3^2 \times 7$

(b) $210 = 2 \times 3 \times 5 \times 7$

Common primes: $2 \times 3 \times 7 = 42$

Midpoints: 130, 150, 170, 190, 210

Plot (130, 12), (150, 28), (170, 30), (190, 22), (210, 8).

Join neighbouring points with straight lines. Do not join the last point back to the first.

(a) Move the decimal point 5 places right: $3.402 \times 10^5 = 340\,200$

(b) Move the point 1 place right to get 8.026, so the power is $-1$: $8.026 \times 10^{-1}$

Put the compass point on B and draw an arc crossing BA and BC.

From each crossing point, draw equal arcs that meet inside the angle.

Rule a line from B through where the arcs meet. Leave all arcs visible.

(a) Not winning: $1 - 0.3 = 0.7$. Each pair of branches is 0.3 (wins) and 0.7 (does not win).

(b) $0.7 \times 0.7 = 0.49$

One part: $240 \div 8 = 30$, so 90 pens and 150 pencils.

Cost: $90 \times 9 + 150 \times 6 = 1710$p

Income: $90 \times 11 + 150 \times 10 = 2490$p

Profit: $2490 - 1710 = 780$p

$\frac{780}{1710} \times 100 = 45.6\%$

School A has 23 scores, so the median is the 12th: 57.

Range: $79 - 30 = 49$

Median: A (57) is higher than B (56), so A did slightly better on average.

Range: A (49) is higher than B (47), so A's scores were more spread out.

The calculator display began 10.2, so the number was cut off (truncated), not rounded.

It could be anything from 10.2 up to but not including 10.3:

$10.2 \le t < 10.3$

AB is opposite the $62°$ angle and BC (7.6 cm) is adjacent.

$\tan 62° = \frac{AB}{7.6}$

$AB = 7.6 \times \tan 62° = 14.29... \approx 14.3$ cm

(a) Multiply the numbers: $2 \times 7 = 14$. Add the powers: $x^{3+2} = x^5$, $y^{5+1} = y^6$.

So $14x^5y^6$

(b) Multiply the powers: $2 \times -3 = -6$, so $m^{-6}$

Multiplier: $1 + 0.018 = 1.018$

After 3 years: $4500 \times 1.018^3 = 4747.40...$

Interest: $4747.40 - 4500 = £247.40$

The line crosses the $y$-axis at 3, so $c = 3$.

It passes through $(0, 3)$ and $(1, 1)$: $y$ goes down 2 for each 1 across, so $m = -2$.

$y = -2x + 3$