June 2023 Paper 1 Foundation

Per cent means out of 100, so divide by 100.

$38 \div 100 = 0.38$

The shape is split into 10 equal triangles and 3 of them are shaded.

So the fraction shaded is $\frac{3}{10}$.

Compare the whole-number parts first: only 0.5 starts with 0.

So the smallest is $0.5$.

Start at $-9$ on a number line and move 5 to the right.

$-9 + 5 = -4$

Add 2 to both sides.

$p = 3 + 2 = 5$

The labelled line starts at the centre and stops at the circle.

A line like that is a radius. A diameter goes right across the circle through the centre, so the 'Diameter' label is wrong.

Find the factor pairs of 20: $1 \times 20$, $2 \times 10$, $4 \times 5$.

So the factors are 1, 2, 4, 5, 10, 20. Any three of these will do, e.g. 2, 4, 5.

(a) Angles around a point add up to $360^\circ$.

$x = 360 - 50 = 310^\circ$

(b) An obtuse angle is between $90^\circ$ and $180^\circ$. $50^\circ$ is less than $90^\circ$, so it is an acute angle.

(a) $B$ is 5 across and 2 up: $(5, 2)$.

(b) Go 4 right and 2 down, and mark $C$.

(c) $A = (-3, 4)$. Midpoint $= \left(\frac{-3+5}{2}, \frac{4+2}{2}\right) = (1, 3)$

(d) $y = -4$ is the horizontal line through every point with $y$-coordinate $-4$.

Large plates: $6 \times £2 = £12$

Each small plate is half price: $80\text{p} \div 2 = 40\text{p}$, so $6 \times 40\text{p} = £2.40$

Total $= £12 + £2.40 = £14.40$

$£14.40 < £15$, so yes, he has enough (with 60p left over).

(a) $700 - 452 = 248$

(b) Round to 1 s.f.: $300 \times £10 = £3000$ and $400 \times £20 = £8000$

Estimate $= £3000 + £8000 = £11\,000$

(c) Overestimate: all four numbers were rounded up, so the true total is smaller.

Add them: $13 + 5 + 4 + 9 + 3 + 8 = 42$

Divide by how many there are: $42 \div 6 = 7$

(a) $\frac{15a}{3} = 5a$

(b) $b$ terms: $5b - 7b = -2b$. $c$ terms: $4c + c = 5c$.

So $19 - 2b + 5c$

(c) The highest common factor of 8 and 6 is 2: $8d - 6 = 2(4d - 3)$

(a) $100 - 73 = 27\%$

(b) Total parts $= 2 + 5 = 7$, so adults are $\frac{2}{7}$.

(c) Friday: $0.7 \times 500 = 350$ children

Saturday: $720 \div 8 \times 5 = 450$ children

$450 > 350$, so no, Kasim is wrong.

Multiply tops and bottoms: $\frac{6 \times 5}{7 \times 12} = \frac{30}{84}$

Divide top and bottom by 6: $\frac{5}{14}$

60 biscuits is $60 \div 20 = 3$ times as many.

Flour: $250 \times 3 = 750$ g

Yellow and green together: $200 - 38 - 52 = 110$

Yellow: $110 \div 2 = 55$

Percentage: $\frac{55}{200} \times 100 = 27.5\%$

Each bag has 5 apples, so $b$ bags hold $5b$.

Each crate has 28 apples, so $c$ crates hold $28c$.

$T = 5b + 28c$

The terms go up by 8, so start with $8n$: 8, 16, 24, ...

Each term of the sequence is 13 less: $8 - 13 = -5$.

nth term $= 8n - 13$

Multiply both numbers by 100: $8.46 \div 0.15 = 846 \div 15$

$15 \times 56 = 840$, remainder 6, and $6 \div 15 = 0.4$

So the answer is $56.4$

Make improper fractions: $7\frac{3}{8} = \frac{59}{8}$, $2\frac{1}{2} = \frac{20}{8}$

$\frac{59}{8} - \frac{20}{8} = \frac{39}{8} = 4\frac{7}{8}$

A cube has 6 equal faces: $150 \div 6 = 25$ cm²

Edge length: $\sqrt{25} = 5$ cm

Volume: $5 \times 5 \times 5 = 125$ cm³

Plot each frequency above the middle of its class: 2.5, 7.5, 12.5, 17.5, 22.5.

Points: $(2.5, 8), (7.5, 24), (12.5, 13), (17.5, 11), (22.5, 4)$

Join them in order with a ruler. Do not join the last point back to the first.

(a) Odd: 1, 3, 5, 7, 9. Square: 1, 4, 9.

In both: 1, 9. Odd only: 3, 5, 7. Square only: 4. Neither: 2, 6, 8, 10.

(b) $B'$ means not square: $10 - 3 = 7$ numbers, so $P = \frac{7}{10}$

(a) As age increases, weight increases: positive correlation.

(b) Draw a line of best fit. Go across from 5.8 kg to the line, then down to the age axis.

This gives about 3.5 months.

20% of the price is £240.

10% is £120, so 100% is $120 \times 10 = £1200$

Volume = base area × height, so base area $= 1200 \div 40 = 30$ cm²

Pressure $= \frac{90}{30} = 3$ newtons/cm²

The solution is where the two lines meet, at $(6, -2)$.

Check: $2 - 2(-2) = 6$ ✓ and $2(-2) = -4 = 3(6) - 22$ ✓

So $x = 6$, $y = -2$.

Multiplying: add the powers, $-6 + 9 = 3$, so the top is $4^3$.

Dividing by $4^1$: subtract the powers, $4^{3-1} = 4^2 = 16$

This is one of the exact trig values to learn.

$\cos 60^\circ = \frac{1}{2}$

Follow the branches: home on Monday (0.2), then office on Friday (0.3).

Multiply along the branches: $0.2 \times 0.3 = 0.06$