November 2018 Paper 1 Foundation

Compare the tenths digit first: 0.02, 0.152, 0.2, 0.37, 0.4

So the order is 0.02, 0.152, 0.2, 0.37, 0.4

Multiply by 100: $0.6 \times 100 = 60$, so it is 60%.

The factors of 10 are 1, 2, 5 and 10.

The only one in the list is 5.

7829 lies between 7000 and 8000.

The hundreds digit is 8, which is 5 or more, so round up to 8000.

(a) Multiply first: $3 \times 5 = 15$, then $15 + 7 = 22$

(b) $2^3 = 2 \times 2 \times 2 = 8$

(c) $35 = 7 \times 5$ and $2 + 3 = 5$, so $7 \times (2 + 3) = 35$

Both cats together eat $2 \times \frac{1}{4} = \frac{1}{2}$ tin a day.

For 14 days: $14 \times \frac{1}{2} = 7$ tins.

$7 < 8$, so yes, Sue has bought enough.

Key: one square = 4 trees.

Apple 3 squares = 12, cherry $1\frac{1}{4}$ squares = 5, pear $1\frac{1}{2}$ squares = 6.

Plum $= 30 - (12 + 5 + 6) = 7$ trees.

$7 \div 4 = 1\frac{3}{4}$, so draw one full square and three quarters of a square.

(a) Go across to $-2$, then down to $-1$: $(-2, -1)$

(b) Go 2 right and 3 up and mark B.

(c) Every point on $x = -4$ has $x$-coordinate $-4$, so draw the vertical line through $-4$ on the $x$-axis.

$2g = 2 \times 9 = 18$

$3h = 3 \times 4 = 12$

$18 + 12 = 30$

Try primes $p$ and check whether $32 - p$ is prime:

$32 - 3 = 29$ (prime) ✓

$32 - 13 = 19$ (prime) ✓

So 3 and 29 (or 13 and 19).

(a) $\frac{10}{16} = \frac{5}{8}$, not $\frac{3}{4}$. The others all simplify to $\frac{3}{4}$.

(b) $\frac{5}{6} = \frac{10}{12}$

$\frac{1}{12} + \frac{10}{12} = \frac{11}{12}$

(a) At 0 miles the line starts at £10, so the fixed charge is £10.

(b) The line rises from £10 to £100 over 60 miles, which is £1.50 per mile.

20 miles more costs $20 \times 1.5 = £30$ more (e.g. 20 miles £40, 40 miles £70).

Let Ryan's score be 1.

Azmol $= 4 \times 1 = 4$, Kim $= 4 \div 2 = 2$.

Azmol : Ryan : Kim $= 4 : 1 : 2$

Angle $BAD = 100°$ (marked on the diagram).

Angle $ADC = 180 - 75 = 105°$ (angles on a straight line add up to 180°).

Angle $BCD = 50°$ (vertically opposite angles are equal).

Angle $ABC = 360 - 100 - 50 - 105 = 105°$ (angles in a quadrilateral add up to 360°).

$AB = AD$, so triangle $ABD$ is isosceles and angles $ABD$ and $ADB$ are equal. Since angle $ABC$ = angle $ADC$, angles $CBD$ and $CDB$ are also equal, so $CB = CD$.

Two pairs of equal adjacent sides, so $ABCD$ is a kite.

(a) Orange juice limits it: $300 \div 5 = 60$ ml per part.

Lemonade needed $= 2 \times 60 = 120$ ml (he has 200 ml, so enough).

Total $= 7 \times 60 = 420$ ml.

(b) No: he still only needs 120 ml of lemonade, and 160 ml is enough.

For similar shapes every length is multiplied by the same scale factor.

$12 \div 8 = 1.5$ but $10 \div 6 = 1.67$, so the rectangles are not similar. Jim is wrong.

(a) Men $= 80 - 48 = 32$. Men who like coffee $= 32 - 8 = 24$.

Women who like coffee $= 61 - 24 = 37$. Women who do not $= 48 - 37 = 11$.

(b) 61 people like coffee and 37 of them are women: $\frac{37}{61}$

Food Mart: $£5 \times 0.8 = £4$ for 400 g, so $400 \div 4 = 100$ g per £1.

Jan's Store: $400 \times 1.3 = 520$ g for £5, so $520 \div 5 = 104$ g per £1.

104 > 100, so Jan's Store is better value.

A 180° turn about $(1, 0)$ sends $(x, y)$ to $(2 - x, -y)$.

$(-3, 5) \to (5, -5)$, $(-2, 5) \to (4, -5)$, $(-2, 3) \to (4, -3)$, $(-3, 4) \to (5, -4)$

Plot and join these points.

$3^7 \times 3^{-2} = 3^{7 + (-2)} = 3^5$

$3^5 \div 3^3 = 3^{5 - 3} = 3^2 = 9$

(a) $v^2 = 12^2 + 2 \times (-3) \times 18 = 144 - 108 = 36$

$v = \sqrt{36} = 6$

(b) $v^2 - u^2 = 2as$

$s = \frac{v^2 - u^2}{2a}$

Managers get $0.4 \times 2100 = £840$, so salesmen get $2100 - 840 = £1260$.

Each salesman: $1260 \div 7 = £180$.

Shared equally: $2100 \div 10 = £210$.

25% more than £180 is $180 \times 1.25 = £225$.

$£210 \ne £225$, so the salesman is wrong (it is only about 16.7% more).

(a) One tap alone would take $120 \times 5 = 600$ minutes.

Three taps: $600 \div 3 = 200$ minutes.

(b) Assume each tap gives water at the same rate, and that rate stays constant.

(a) Round 213 to 200 mph.

1 hour $= 60 \times 60 = 3600$ seconds.

Time for 1 mile $= 3600 \div 200 = 18$ seconds.

(b) Overestimate: 200 is slower than the real speed, so the real time is shorter.

Multiply the first equation by 3: $15x + 3y = 63$

Add $x - 3y = 9$: $16x = 72$, so $x = 4.5$

$5(4.5) + y = 21 \Rightarrow y = 21 - 22.5 = -1.5$

Check: $4.5 - 3(-1.5) = 9$ ✓

Quarter circle, radius 20: $\frac{1}{4}\pi \times 20^2 = 100\pi$

Semicircle, radius 10: $\frac{1}{2}\pi \times 10^2 = 50\pi$

Shaded $= 100\pi - 50\pi = 50\pi$

Square $= 20 \times 20 = 400$

$\frac{50\pi}{400} = \frac{\pi}{8}$

(a) First bag: green $= 1 - \frac{3}{10} = \frac{7}{10}$

Second bag (independent of the first): red $\frac{5}{9}$, green $\frac{4}{9}$ on both branches.

(b) $\frac{3}{10} \times \frac{5}{9} = \frac{15}{90} = \frac{1}{6}$

Interior + exterior = 180°, so $x + 11x = 180$.

$12x = 180 \Rightarrow x = 15°$ (exterior angle)

Number of sides $= 360 \div 15 = 24$