June 2018 Paper 1 Foundation

Look at the hundreds digit of 6324: it is 3, which is less than 5.

So round down to 6000.

(a) Negatives come first, and $-6$ is smaller than $-5$: $-6, -5, 0, 6, 12$

(b) Write each with three decimal places: 0.078, 0.780, 0.870, 0.708.

Order: $0.078, 0.708, 0.78, 0.87$

Per cent means out of 100, so $20\% = \frac{20}{100}$.

This simplifies to $\frac{1}{5}$.

Simplify each: $\frac{4}{16} = \frac{1}{4}$, $\frac{2}{8} = \frac{1}{4}$, $\frac{15}{60} = \frac{1}{4}$, but $\frac{3}{9} = \frac{1}{3}$.

So the odd one out is $\frac{3}{9}$.

Multiples of 7: 7, 14, 21, ...

7 is odd, so the first even one is 14.

(a) $3 \times 4t = 12t$

(b) $8a - 3a = 5a$, then $5a + 2a = 7a$

(a) Certain means probability 1, which is D.

(b) Unlikely means between 0 and a half, which is B.

(c) Green $= 12 - (3 + 1 + 2) = 6$

Yellow or green $= 2 + 6 = 8$ counters

$P = \frac{8}{12} = \frac{2}{3}$

1 kg costs $54 \div 3 = £18$

2 kg cost $2 \times 18 = £36$

(a) A line from the centre to the edge is a radius.

(b) A line that touches the circle at just one point is a tangent.

Total $= 1280 + 640 + 220 = £2140$

Each share $= 2140 \div 4 = £535$

(a) 12 is even, but $3 \times 4 = 12$, so 3 is an odd factor of 12.

(b) 23 is odd, but its digit 2 is even.

(a) The desktop section in 2015 reaches 100.

(b) Laptops: $260 - 100 = 160$, $340 - 120 = 220$, $440 - 160 = 280$

Total $= 160 + 220 + 280 = 660$

(c) Tablets: $320 - 260 = 60$ in 2015 up to $780 - 440 = 340$ in 2017, a rise of 280. Tablets grew most.

(d) No: we know how many were sold, not the profit on each item.

Left after two pieces: $240 - 2 \times 45 = 150$ cm

$150 \div 40 = 3.75$

Only whole pieces count, so 3.

Gavin saves 28%.

Harry spends $\frac{3}{4}$, so saves $\frac{1}{4} = 25\%$.

Isabel saves $\frac{3}{3+7} = \frac{3}{10} = 30\%$.

30% is the biggest, so Isabel saves the most.

10% of 160 $= 16$

5% $= 16 \div 2 = 8$

15% $= 16 + 8 = 24$ g

(a) $P = 4 \times 5 + 3 \times (-2) = 20 - 6 = 14$

(b) $4e \times e = 4e^2$ and $4e \times 2 = 8e$, so $4e^2 + 8e$

(c) Divide by 3: $m - 4 = 7$, so $m = 11$

Nuts: $\frac{1}{4}$, no nuts: $1 - \frac{1}{4} = \frac{3}{4}$

Ratio $\frac{1}{4} : \frac{3}{4} = 1 : 3$

$A = \{15, 20, 25\}$, $B = \{15, 17, 19, 21, 23, 25\}$

(a) Union is everything in either: 15, 17, 19, 20, 21, 23, 25

(b) Intersection is in both: 15 and 25, the odd multiples of 5.

(a) Whole numbers: $2 + 1 = 3$. Fractions: $\frac{1}{7} + \frac{1}{4} = \frac{4}{28} + \frac{7}{28} = \frac{11}{28}$

Answer $3\frac{11}{28}$

(b) $1\frac{1}{5} = \frac{6}{5}$, then $\frac{6}{5} \times \frac{4}{3} = \frac{24}{15} = \frac{8}{5} = 1\frac{3}{5}$

Flats : bungalows $= 8 : 5$, and $50 \div 5 = 10$, so flats $= 8 \times 10 = 80$

Houses : flats $= 7 : 4$, and $80 \div 4 = 20$, so houses $= 7 \times 20 = 140$

5 kg $= 5000$ g, so $5000 \div 250 = 20$ bags

Takings $= 20 \times 65\text{p} = £13$

Profit $= 13 - 10 = £3$

Percentage profit $= \frac{3}{10} \times 100 = 30\%$

(a) Round: $3000$ miles, $15$ mph

Hours $= 3000 \div 15 = 200$

Days $= 200 \div 8 = 25$

(b) A higher speed means fewer hours, so he would need fewer days.

(a) From the front you see a triangle: base 6 cm, height 4 cm, apex above the middle of the base.

(b) Each sloping face: $\frac{1}{2} \times 6 \times 5 = 15\text{ cm}^2$

Four faces: $4 \times 15 = 60$. Base: $6 \times 6 = 36$

Total $= 60 + 36 = 96\text{ cm}^2$

Width $= 38 - 6 = 32$, covering four square widths, so each side is $32 \div 4 = 8$.

C is two sides right of A: $x = 6 + 2 \times 8 = 22$

C is two sides below B: $y = 36 - 2 \times 8 = 20$

So $C = (22, 20)$

Make a table with $y = 1 - 4x$:

$x$: −3, −2, −1, 0, 1, 2, 3

$y$: 13, 9, 5, 1, −3, −7, −11

Plot the points and join them with a ruler.

$2\mathbf{a} = \begin{pmatrix} 10 \\ 4 \end{pmatrix}$

$2\mathbf{a} + \mathbf{b} = \begin{pmatrix} 10 + (-1) \\ 4 + 7 \end{pmatrix} = \begin{pmatrix} 9 \\ 11 \end{pmatrix}$