November 2020 Paper 1 Foundation

Give every number three decimal places: 0.320, 0.400, 0.350, 0.309.

Now compare: 0.309 < 0.320 < 0.350 < 0.400, so the order is 0.309, 0.32, 0.35, 0.4.

Check each number: $18 = 3 \times 6$. None of 5, 11, 22 or 29 divides exactly by 3.

So the multiple of 3 is 18.

Look at the first decimal digit: 6, which is 5 or more.

So round up: 4.666 becomes 5.

$\frac{3}{4} = 3 \div 4 = 0.75$

(One quarter is 0.25, so three quarters is $3 \times 0.25 = 0.75$.)

In 8765 the digits are 8 thousands, 7 hundreds, 6 tens and 5 ones.

So the 7 is worth 700.

(a) 4 of the 8 equal sections are C, so $P(C) = \frac{4}{8} = \frac{1}{2}$. Put the cross in the middle of the scale.

(b) No section shows D, so it is impossible: put the cross at 0.

Monday shows $1\frac{1}{2}$ ovals for 18 eggs, so one oval is $18 \div 1.5 = 12$ eggs.

Tuesday: $24 \div 12 = 2$ ovals.

Wednesday: $27 \div 12 = 2\frac{1}{4}$ ovals (two whole ovals and a quarter).

Key: one oval represents 12 eggs.

(a) A is 2 across and 3 up: $(2, 3)$.

(b) B is on the y-axis, 1 below the origin: $(0, -1)$.

(c) Go 2 left, then 1 up, and mark C there.

(a) There are $3 + 4 = 7$ parts and 3 are red, so the fraction is $\frac{3}{7}$.

(b) Divide both sides by 12: $12 \div 12 = 1$, $30 \div 12 = 2.5$.

So the ratio is $1 : 2.5$.

Large: $\frac{1}{4}$ of 12 = 3, so small = $12 - 3 = 9$.

Large weight: $3 \times 70 = 210$ g. Small weight: $9 \times 50 = 450$ g.

Total: $210 + 450 = 660$ grams.

Take each corner in turn. Count how many squares it is from the mirror line, then plot the image the same distance on the other side.

The corner nearest the line (2 squares away) stays 2 squares away; the far edge (4 squares away) goes 4 squares to the left. Join the new corners.

(a) $7 \times 2 = 14$, then $14 - 3 = 11$.

(b) Work backwards with inverses: $41 + 3 = 44$, then $44 \div 2 = 22$.

(a) Put the protractor on the north line at A and measure clockwise to the line AB: about $25°$, written $025°$.

(b) AB measures about 5 cm on the map.

Real distance $= 5 \times 25\,000 = 125\,000$ cm $= 1250$ m $= 1.25$ km.

Males: $30 - 20 = 10$. Two chose tennis, leaving 8 split equally: 4 cricket, 4 swimming.

Females: cricket $5 - 4 = 1$, swimming 11, so tennis $20 - 1 - 11 = 8$.

Totals: cricket 5, tennis $2 + 8 = 10$, swimming $4 + 11 = 15$ (sum 30).

Water: $750 \times 9 = 6750$ ml.

Total drink: $750 + 6750 = 7500$ ml $= 7.5$ litres.

Only whole bottles count, so he can fill 7 bottles.

(a) Nobody scored more than 4 points, so the middle value cannot be 5. The 8th and 9th scores are both 2, so the median is 2.

(b) $0 \times 1 = 0$, not 1. The correct total is $0 + 3 + 10 + 12 + 12 = 37$.

Monday: $\frac{1}{10}$ of £500 is £50, so the price is $500 - 50 = £450$.

Tuesday: 20% of £450 is $0.2 \times 450 = £90$, so the price is $450 - 90 = £360$.

£360 is less than £400, so yes, Chris can buy it.

Round to 1 significant figure: $790 \approx 800$, $289 \approx 300$, $49 \approx 50$.

$\frac{800 \times 300}{50} = \frac{240\,000}{50} = 4800$

(a) $x \times x - x \times 4 = x^2 - 4x$

(b) The highest common factor of 15 and 10 is 5: $5(3y - 2)$.

(c) Divide by 7: $f - 5 = 4$, so $f = 9$.

The terms go up by 3, so start with $3n$: 3, 6, 9, ...

Each term is 2 less than that, so the nth term is $3n - 2$.

Change to improper fractions: $2\frac{1}{3} = \frac{7}{3}$ and $3\frac{3}{4} = \frac{15}{4}$.

Multiply: $\frac{7 \times 15}{3 \times 4} = \frac{105}{12} = \frac{35}{4}$.

$35 \div 4 = 8$ remainder 3, so $\frac{35}{4} = 8\frac{3}{4}$.

$y = x^2$ is the U shape: D.

$y = \frac{1}{x}$ has two separate branches and never touches the axes: A.

$y = x^3$ rises from bottom left to top right: C.

$y = -x^3$ is its reflection, falling from top left: B.

Triangle D has angles 80° and 45°, so its third angle is $180 - 80 - 45 = 55°$.

In D the 10 cm side lies between the 45° and 55° angles, just as in A. Same two angles and the side between them (ASA), so A and D are congruent.

Selling price: $24 \times 50$p $= 1200$p $= £12$.

Profit: $12 - 10 = £2$.

Percentage profit: $\frac{2}{10} \times 100 = 20\%$.

Angle $AEB = 63°$ (corresponding angles are equal).

Angle $ABE = 180 - 148 = 32°$ (angles on a straight line add up to $180°$).

Angle $EAB = 180 - 63 - 32 = 85°$ (angles in a triangle add up to $180°$).

Girls: median 165 cm, range $170 - 150 = 20$ cm.

Boys: 15 values, so the median is the 8th: 168 cm. Range $182 - 158 = 24$ cm.

On average the boys are taller (168 > 165), and their heights are more spread out (24 > 20).

Base area $= \frac{18}{3} = 6\text{ m}^2$.

Force $=$ pressure $\times$ area $= 75 \times 6 = 450$ N.

Write each as an ordinary number:

$67.2 \times 10^{-4} = 0.00672$, $6.72 \times 10^5 = 672\,000$, $672 \times 10^4 = 6\,720\,000$.

So: 0.000672, $67.2 \times 10^{-4}$, $6.72 \times 10^5$, $672 \times 10^4$.

$\frac{a}{b} = \frac{2}{5}$ gives $a : b = 2 : 5$, and $\frac{b}{c} = \frac{3}{4}$ gives $b : c = 3 : 4$.

Make b the same in both (15): $a : b = 6 : 15$ and $b : c = 15 : 20$.

So $a : b : c = 6 : 15 : 20$.

(a) $p = 6q + 7$. Subtract 7: $p - 7 = 6q$. Divide by 6: $q = \frac{p - 7}{6}$.

(b) Multiply the powers: $(-2) \times (-3) = 6$, so $(m^{-2})^{-3} = m^6$.