June 2022 Paper 1 Foundation

There are 10 mm in 1 cm.

$40 \times 10 = 400$ mm

Adding the same term four times gives four lots of it: $e+e+e+e = 4e$

Take each corner of the triangle in turn.

Count how many squares it is from the mirror line, then plot the new corner the same distance on the other side.

Join the new corners to make the image.

16 007 has 1 ten-thousand, 6 thousands, 0 hundreds, 0 tens and 7 ones.

So the 6 is worth $6000$.

Write each as a decimal: $\frac{1}{2} = 0.5$, $0.55$, $45\% = 0.45$

Smallest to largest: $0.45, 0.5, 0.55$

So: 45%, $\frac{1}{2}$, 0.55

Saturday has 4 symbols and each symbol stands for 2 hours.

$4 \times 2 = 8$ hours

Amount spent: $20 - 6 = 14$ pounds

Each candle costs £2: $14 \div 2 = 7$

Simon buys 7 candles.

(a) Draw a bar up to 35 above May and a bar up to 20 above June, the same width as the others.

(b) The vertical scale goes up 5 cm per square, so half a square is $5 \div 2 = 2.5$ cm.

February's bar is at $15 + 2.5 = 17.5$ cm, not 15.5 cm.

(a) Each new pattern adds one square to each arm. Pattern 5 has arms 5 squares long, sharing the corner square: 9 squares.

(b) The numbers go up by 2 each time: 1, 3, 5, 7, 9, 11

Start at $-15$ and go up 42 degrees.

$-15 + 42 = 27$

Highest temperature: $27^\circ$C

Units used: $89\,198 - 88\,738 = 460$ kWh

Cost: $460 \times 16 = 4600 + 2760 = 7360$p

$7360\text{p} = £73.60$

(a) $\frac{1}{6} = \frac{2}{12}$, so $\frac{5}{12} + \frac{2}{12} = \frac{7}{12}$

(b) $\frac{3}{10} \times \frac{5}{8} = \frac{15}{80}$

Divide top and bottom by 5: $\frac{3}{16}$

(a) 4 red out of 15 sweets: $P(\text{red}) = \frac{4}{15}$

(b) Probabilities add to 1: $1 - 0.3 = 0.7$

$y = 6 \times 4 - 5$

$y = 24 - 5 = 19$

(a) Round each number: $92 \approx 90$ and $1.63 \approx 2$

$90 \times 2 = 180$

(b) $29.6$ is $2.96 \times 10$ and $32$ is $3.2 \times 10$, so the answer is $9.472 \times 100 = 947.2$

(a) Time $= 50 \div 40 = 1.25$ hours

$0.25 \times 60 = 15$, so 1 hour 15 minutes.

07 30 + 1 h 15 min = 08 45

(b) Going faster over the same distance takes less time, so he arrives earlier.

(a) Adults: 32, so children: $72 - 32 = 40$

Adults failed: $32 - 20 = 12$

Children passed: $40 - 6 = 34$

(b) 12 adults failed out of 72 people: $\frac{12}{72} = \frac{1}{6}$

25 scones is $25 \div 10 = 2.5$ times the recipe.

$40 \times 2.5 = 100$ g of sugar

$10\%$ of 240 is 24, so $20\%$ is $48$

$240 + 48 = 288$

The top strip of B matches the unshaded part of A: $1 - \frac{5}{8} = \frac{3}{8}$

The bottom strip of B matches the unshaded part of C: $1 - \frac{9}{11} = \frac{2}{11}$

Shaded part of B: $1 - \frac{3}{8} - \frac{2}{11} = \frac{88 - 33 - 16}{88} = \frac{39}{88}$

Use the tens digit as the stem and the units digit as the leaf, then put the leaves in order:

1 | 7 9

2 | 5 5 6 7 7 7 8 9

3 | 3 7 7

4 | 5 7

Key: 2 | 5 means 25 years

The plan is a circle 6 cm across, so the radius is 3 cm.

The front elevation is 5 cm tall, so the height is 5 cm.

$V = \pi r^2 h = \pi \times 3^2 \times 5 = 45\pi$ cm³

$7x - 27 < 8$

Add 27: $7x < 35$

Divide by 7: $x < 5$

$124 = 2 \times 62$

$62 = 2 \times 31$, and 31 is prime.

So $124 = 2 \times 2 \times 31 = 2^2 \times 31$

Cars: $160 \div 10 = 16$, $16 \times 3 = 48$

Electric: $48 \div 8 = 6$

Diesel: $25\%$ of 48 $= 12$

Petrol: $48 - 6 - 12 = 30$

(a) Move the decimal point 3 places left: $0.00163$

(b) $438\,000 = 4.38 \times 100\,000 = 4.38 \times 10^5$

(c) $4 \times 6 = 24$ and $10^3 \times 10^{-5} = 10^{-2}$

$24 \times 10^{-2} = 2.4 \times 10^{-1}$

Hexagon interior angle: $180 - 360 \div 6 = 120^\circ$

Pentagon interior angle: $180 - 360 \div 5 = 108^\circ$

Angles round a point add to $360^\circ$: $x = 360 - 120 - 108 = 132^\circ$

(a) $x = -1$: $1 + 3 + 1 = 5$; $x = 2$: $4 - 6 + 1 = -1$; $x = 3$: $9 - 9 + 1 = 1$; $x = 4$: $16 - 12 + 1 = 5$

(b) Plot $(-1,5), (0,1), (1,-1), (2,-1), (3,1), (4,5)$ and join with a smooth curve.

(c) The curve crosses $y = 0$ at about $x = 0.4$ and $x = 2.6$

Volumes: $3^3 = 27$ cm³ and $4^3 = 64$ cm³

Densities: $81 \div 27 = 3$ g/cm³ and $128 \div 64 = 2$ g/cm³

Ratio: $3 : 2$

This is one of the exact trig values to learn: $\sin 30^\circ = \frac{1}{2} = 0.5$