November 2018 Paper 3 Foundation

(i) $100 - 56.3 = 43.7$

(ii) One whole is $\frac{7}{7}$, so $\frac{7}{7} - \frac{2}{7} = \frac{5}{7}$

Per cent means out of 100, so $3\% = \frac{3}{100}$

$1.2 \times 1.2 = 1.44$, so $\sqrt{1.44} = 1.2$

$\frac{1}{8}$ of 720 means $720 \div 8 = 90$

(a) Six rectangular faces, so it is a cuboid.

(b) 4 edges on the top, 4 on the bottom and 4 upright edges: $4 + 4 + 4 = 12$

(a) Odd numbers are 1, 3, 5: that is 3 out of 6, so $\frac{3}{6} = \frac{1}{2}$. Put the cross in the middle.

(b) Numbers greater than 4 are 5 and 6, so the probability is $\frac{2}{6} = \frac{1}{3}$

Change 6 cm to metres: $6 \div 100 = 0.06$ m.

$1.88 + 0.06 = 1.94$ m (or $188 + 6 = 194$ cm).

One pen: $2.38 \div 2 = £1.19$, so 20 pens: $20 \times 1.19 = £23.80$

One folder: $5.60 \div 5 = £1.12$, so 20 folders: $20 \times 1.12 = £22.40$

Total: $23.80 + 22.40 = £46.20$

$£46.20 < £50$, so yes, Ben has enough (with £3.80 left).

(a) Shape E has exactly one pair of parallel sides, so it is a trapezium.

(b) Congruent shapes are exactly the same shape and size (they may be turned). C and D match.

Take each corner of the shape in turn and count its distance to the mirror line.

Plot the image corner the same distance on the other side, then join the corners up.

Men are 30%, so women are $100 - 30 = 70\%$

$70\%$ is 28, so $10\%$ is $28 \div 7 = 4$

$100\%$ is $4 \times 10 = 40$ people.

Each person is worth $360 \div 60 = 6°$

Peas: $24 \times 6 = 144°$; Carrots: $16 \times 6 = 96°$; Mushrooms: $20 \times 6 = 120°$

Check: $144 + 96 + 120 = 360°$. Draw the sectors with a protractor and label each one.

Books: $45 \times 1.20 = £54$

Candles: $34 \times 1.50 = £51$

Left for calendars: $150 - 54 - 51 = £45$

90p is £0.90, so $45 \div 0.90 = 50$ calendars.

(a) Probabilities add to 1: $1 - (0.2 + 0.4 + 0.1) = 0.3$

(b) The smallest probability is 0.1, which is for 4.

(c) Expected number of 1s: $0.2 \times 60 = 12$

A card with both marks is a multiple of 3 and of 5, so a multiple of 15.

Multiples of 15 up to 100: 15, 30, 45, 60, 75, 90.

That is 6 cards.

$450 : 15$

Divide both sides by 15: $30 : 1$

(a) By symmetry $DE = AB = 2x + 1$ and $CD = BC = x + 2$

Perimeter $= 4x + 2(2x + 1) + 2(x + 2) = 4x + 4x + 2 + 2x + 4 = 10x + 6$

The perimeter is 18, so $10x + 6 = 18$

(b) $10x = 12$, so $x = 1.2$

VAT: $20\%$ of $14\,200 = 2840$

Total cost: $14\,200 + 2840 = £17\,040$

After deposit: $17\,040 - 5000 = £12\,040$

Each payment: $12\,040 \div 10 = £1204$

(a) $x < 4$ does not include 4, so draw an open circle at 4 and an arrow pointing left.

(b) $y$ is more than 3 and at most 7: $4, 5, 6, 7$

(c) $3x + 5 \geqslant x + 17$

$2x + 5 \geqslant 17$

$2x \geqslant 12$, so $x \geqslant 6$

(a) The 4th figure is 7, so round up: $7357 \to 7360$

(b) Top: $\sqrt{17 + 16} = \sqrt{33} = 5.7445\ldots$

Bottom: $7.3^2 = 53.29$

$5.7445\ldots \div 53.29 = 0.1077981356$

Increase: $883 - 245 = 638$

Percentage increase: $\frac{638}{245} \times 100 = 260.4\%$

(a) $x = -3$: $9 - 3 - 4 = 2$; $x = -1$: $1 - 1 - 4 = -4$; $x = 2$: $4 + 2 - 4 = 2$; $x = 3$: $9 + 3 - 4 = 8$

(b) Plot all seven points and join with a smooth curve, dipping just below $-4$ between $x = -1$ and $x = 0$.

(c) The roots are where the curve crosses the $x$-axis: about $1.6$ or $-2.6$

(a) 2 students bought 20 to 24 books: $\frac{2}{40} \times 100 = 5\%$

(b) Frequencies 11, 8, 13, 6, 2 and midpoints 2, 7, 12, 17, 22

$11 \times 2 + 8 \times 7 + 13 \times 12 + 6 \times 17 + 2 \times 22 = 22 + 56 + 156 + 102 + 44 = 380$

Mean $\approx 380 \div 40 = 9.5$

(a) 1 min 54 s $= 114$ s

Time $= \frac{700}{475} \times 114 = 168$ s

$168$ s $= 2$ minutes $48$ seconds

(b) If she speeds up over a longer race, she will finish more quickly, so the real time is less than 2 min 48 s.

Angles A and B share $180 - 90 = 90°$ in the ratio $3 : 2$ (B : A)

One part $= 90 \div 5 = 18°$, so $A = 36°$ and $B = 54°$

AC is next to angle A and AB is the hypotenuse: $\cos 36° = \frac{14}{AB}$

$AB = \frac{14}{\cos 36°} = 17.3$ cm

The terms go up by 6, so start with $6n$.

$6n$ gives 6, 12, 18, 24. Each term is 1 less, so the nth term is $6n - 1$.