June 2023 Paper 2 Foundation

The hundreds digit is 1 and the next digit is 8, which is 5 or more, so round up.

$6184 \to 6200$

The 7 is in the tenths column, so $0.7 = \frac{7}{10}$.

There are 100 cm in 1 m, so $9 \times 100 = 900$ cm.

Multiply the numbers: $3 \times 4 = 12$, and keep the letter.

$3 \times 4t = 12t$

Multiples of 25 are 25, 50, 75, 100, ...

Only 100 is in the list ($25 \times 4 = 100$).

(a) A normal dice has no 7, so rolling a 7 is impossible: probability $0$.

(b) Even numbers are 2, 4 and 6, so the probability is $\frac{3}{6} = \frac{1}{2}$, halfway along the scale.

(a) Put the ruler's 0 on A and read off at C: about $9.3$ cm.

(b) Place the protractor's centre on B, line up one side with 0 and read the scale that starts at 0: about $106^\circ$. It is obtuse, so the answer must be over $90^\circ$.

(c) Two equal sides ($QP = QR$) means the triangle is isosceles.

Total map distance: $8 + 16 = 24$ cm

Each cm is 4 km: $24 \times 4 = 96$ km

(a) The terms go up by 5, so the next term is $23 + 5 = 28$.

(b) The second term is 8 and the fourth is 18.

$8 : 18$, divide both by 2: $4 : 9$

(a) Go up from 4 hours to the line and across: £6.

(b) Go across from £9 to the line and down: 6 hours.

$08\,00 + 6$ hours $= 14\,00$ (2 pm)

Multiply each weight by how many people have it:

$40 + 100 + 240 + 350 + 240 + 90 = 1060$ kg

$1060 < 1200$, so the total is less than 1200 kg.

(a) The horizontal edge of A becomes the vertical edge of B, so the mirror line is diagonal. Draw the line that is the same distance from each corner of A as from the matching corner of B.

(b) Reflecting in the $x$-axis flips the shape down, so the image should be below the $x$-axis (between $y = -2$ and $y = -4$). Alex flipped it across the $y$-axis instead.

50 is $\frac{1}{16}$ of the total, so the total is 16 lots of 50.

$16 \times 50 = 800$

Change the packet to cm: 8 cm by 6 cm by 2 cm.

Along each edge: $72 \div 8 = 9$, $48 \div 6 = 8$, $24 \div 2 = 12$

$9 \times 8 \times 12 = 864$

(Check: $82944 \div 96 = 864$.)

Dice, less than 3: scores 1 and 2, so $\frac{2}{6} = \frac{8}{24}$

Spinner, greater than 5: 6, 7 and 8, so $\frac{3}{8} = \frac{9}{24}$

$\frac{9}{24} > \frac{8}{24}$, so the spinner is more likely.

45 minutes $= \frac{45}{60} = 0.75$ hours, so the time is $1.75$ hours.

Distance = speed × time $= 56 \times 1.75 = 98$ km

Total seats $= 3 \times 380 = 1140$

A and B together: $350 + 250 = 600$

Cinema C: $1140 - 600 = 540$

(a) Packs: $180 \div 12 = 15$. Cost: $15 \times £3 = £45$

(b) Total volume: $24 \times 330 = 7920$ ml

Cost of 1 ml: $700 \div 7920 = 0.0884$p, so 100 ml costs $8.84$p

To the nearest penny: 9p

(a) No car: $240 - 150 = 90$. Of these, 65 have a bicycle, so $90 - 65 = 25$ do not.

Car owners with a bicycle: $110 - 65 = 45$; without: $150 - 45 = 105$.

(b) $\frac{45}{150} \times 100 = 30\%$

(a) Top: $25 - \sqrt{43.87} = 18.3765...$

Bottom: $6 + 2.1^2 = 10.41$

$18.3765... \div 10.41 = 1.765279230...$

(b) Reciprocal $= 1 \div 0.625 = 1.6$

$60 = 2 \times 30 = 2 \times 2 \times 15 = 2 \times 2 \times 3 \times 5$

So $60 = 2^2 \times 3 \times 5$

The ratio $1 : 2$ has $1 + 2 = 3$ parts.

$48 \div 3 = 16$, so there are 16 red and 32 blue.

Helen is wrong: 24 red would be half, which is a $1 : 1$ ratio.

(a) $n$ is less than 5, so the greatest integer is $4$.

(b) Filled circle at $-4$ (it is included), empty circle at $1$ (not included), and a line joining them.

(c) $\frac{2}{5}g - 4 < 6$

$\frac{2}{5}g < 10$

$2g < 50$

$g < 25$

Triangle: $\frac{1}{2} \times 8 \times 6x = 24x$

Rectangle: $5(4x - 1) = 20x - 5$

$24x = 20x - 5 + 10$

$4x = 5$, so $x = 1.25$

(Check: triangle 30, rectangle 20.)

Paper and glass: $0.57 \times 800 = 456$ kg

Ratio $12 : 7$ has 19 parts: $456 \div 19 = 24$

Glass: $7 \times 24 = 168$ kg

Rounding to 1 d.p. means the value is within $0.05$ of $12.7$.

Lower bound: $12.7 - 0.05 = 12.65$

Upper bound: $12.7 + 0.05 = 12.75$

$12.65 \le d < 12.75$

Tamsin: $150\,000 \times 1.04^2 = £162\,240$

Rachel: $160\,000 \times 1.015^2 = £164\,836$

$164\,836 > 162\,240$, so Rachel's house is worth more.

$y = x^2 - 4x$ is a U-shaped curve through the origin: B

$y = x + 3$ slopes up and crosses the $y$-axis above O: D

$y = x^3 - 2$ is the S-shaped cubic: E

$y = \frac{1}{x}$ has two separate branches: C

$y = 5 - 2x$ slopes down: A