November 2019 Paper 3 Foundation

The factor pairs of 12 are $1\times12$, $2\times6$ and $3\times4$.

So any two of 1, 2, 3, 4, 6, 12 will do, for example 3 and 4.

To find $\frac{1}{3}$ of an amount, divide by 3.

$30 \div 3 = 10$

The 7 is in the tenths column, so $0.7 = \frac{7}{10}$.

The 6 times table goes 6, 12, 18, 24, ...

The only one in the list is 18.

There are 1000 metres in a kilometre.

$4 \times 1000 = 4000$ metres

Count: 3 squares are shaded and $8 - 3 = 5$ are not.

Shaded : unshaded $= 3 : 5$

Replace $u$ with 8:

$w = 4 \times 8 + 3 = 32 + 3 = 35$

The gaps go up by one each time: $+2, +3, +4, +5$.

Next gaps are $+6$ and $+7$: $15 + 6 = 21$, $21 + 7 = 28$

(a) Count each pet: dog 8, rabbit 3, cat 5, hamster 2 (total 18).

(b) Put the pets along the bottom, a frequency scale going up in 1s, and draw bars of heights 8, 3, 5 and 2.

(c) Dog has the tallest bar, so it is the most popular.

(a) A diameter is a straight line from one side of the circle to the other that passes through the centre.

(b) Draw any chord (a line joining two points on the circle), then shade the smaller region between the chord and the curved edge. That region is a segment.

(a) Cost: $13 \times 7.50 = £97.50$. Paid: $5 \times 20 = £100$.

Change $= 100 - 97.50 = £2.50$

(b) $\frac{1}{5}$ of 120 $= 24$, so the sale price is $120 - 24 = £96$.

Small boxes: $3 \times 450 = 1350$ g

Left for large boxes: $5850 - 1350 = 4500$ g

$4500 \div 750 = 6$ large boxes

Smallest age: stem 3, leaf 1, which is 31.

Largest age: stem 7, leaf 4, which is 74.

Range $= 74 - 31 = 43$ years

(a) $7 \times 3$ is the area of the rectangle. Perimeter means adding all four sides: $7 + 3 + 7 + 3 = 20$ cm.

(b) One side is $x$ cm. If $x = -2$, that side would be $-2$ cm long, and a length must be positive.

Boys: $0.55 \times 800 = 440$

Boys with packed lunch: $0.4 \times 440 = 176$

All packed lunches: $0.31 \times 800 = 248$

Girls with packed lunch: $248 - 176 = 72$

Probabilities add to 1: $1 - 0.4 - 0.25 = 0.35$

Share 0.35 in the ratio $3 : 4$: one part $= 0.35 \div 7 = 0.05$

Blue $= 3 \times 0.05 = 0.15$, green $= 4 \times 0.05 = 0.2$

(a) Put each $x$ into $4x - 6$:

$x=-1$: $-4-6=-10$; $x=0$: $-6$; $x=2$: $2$; $x=3$: $6$

(b) Plot the six points from $(-1,-10)$ to $(4,10)$ and join them with a single ruled straight line.

Each point moves to the same distance on the other side of $y = 3$.

$(1, 4)$ is 1 above, so it goes to $(1, 2)$. $(2, 4)$ goes to $(2, 2)$. $(1, 7)$ is 4 above, so it goes to $(1, -1)$.

Divide both sides by 4: $x - 6 = 11$

Add 6: $x = 17$

Multiples of 3: 3, 6, 9, 12. Even: 2, 4, 6, 8, 10, 12.

In both (overlap): 6, 12

Multiples of 3 only: 3, 9. Even only: 2, 4, 8, 10

Outside both circles: 1, 5, 7, 11, 13

Profit: $158\,220 - 146\,500 = 11\,720$

Percentage profit $= \frac{11\,720}{146\,500} \times 100 = 8\%$

(a) $x \times x = x^2$, $x \times (-9) = -9x$, $5 \times x = 5x$, $5 \times (-9) = -45$

$x^2 - 9x + 5x - 45 = x^2 - 4x - 45$

(b) The highest common factor of $9x^2$ and $6x$ is $3x$: $3x(3x + 2)$

(a) Top: $29^2 - 4.6 = 836.4$. Bottom: $\sqrt{35 - 6.859} = \sqrt{28.141} = 5.30481...$

$836.4 \div 5.30481... = 157.668255...$

(b) The 4th significant figure is 6 and the next digit is 6, so round up: $157.7$

Draw a line of best fit through the middle of the crosses.

Go up from 34 on the Science axis to the line, then across to the Maths axis. This reads about 40.

Midpoints: 7.5, 12.5, 17.5, 22.5

$\sum fx = 7.5 + 25 + 122.5 + 180 = 335$

Mean $\approx 335 \div 18 = 18.61... = 18.6$ seconds

1 cm $= 10$ mm, so $1\text{ cm}^3 = 10 \times 10 \times 10 = 1000\text{ mm}^3$.

$37 \times 1000 = 37\,000\text{ mm}^3$

Time: 13 30 to 14 48 is 1 hour 18 minutes $= 78$ minutes.

In hours: $78 \div 60 = 1.3$

Speed $= 65 \div 1.3 = 50$ mph

(a) Put the decimal point after the first digit: $3.246$. It moves 7 places, so $3.246 \times 10^7$.

(b) Move the point 3 places left: $0.00496$

(c) No. $A = 621\,200\,000$ and $B = 4\,730\,000\,000$, so $B$ is bigger. Compare the powers first.

Co-interior angles in the parallelogram add to 180°: $180 - 117 = 63°$

Interior angle of a regular pentagon: $(5-2) \times 180 \div 5 = 108°$

$x = 108 - 63 = 45°$

Area of A $= \frac{1}{4} \times \pi \times 15^2 = 56.25\pi$

Area of B $= 56.25\pi \div 9 = 6.25\pi$

$\pi r^2 = 6.25\pi$, so $r^2 = 6.25$ and $r = \sqrt{6.25} = 2.5$ cm