June 2023 Paper 3 Foundation

Three thousand = 3 in the thousands column, one hundred = 1 in the hundreds, no tens so 0, and 7 units.

So the number is $3107$.

$\frac{3}{10} = \frac{30}{100}$

So it is $30\%$.

Four lots of $m$ added together is $4 \times m$, written $4m$.

There are 1000 g in 1 kg.

$4000 \div 1000 = 4$ kg

The negatives are smallest, and $-5$ is further below zero than $-2$.

Then the positives in order: $-5, -2, 3, 7, 9$

(a) Count the squares: a 2 by 6 block (12) plus a 1 by 2 block (2), so $12 + 2 = 14$ cm².

(b) Go round the edge: $2 + 6 + 3 + 2 + 1 + 4 = 18$ cm.

(a) Two of the four sections show 2, so the chance is $\frac{2}{4} = \frac{1}{2}$: evens.

(b) Every number on the spinner is less than 4, so it is certain.

(c) $1 - 0.4 = 0.6$

(a) Four right angles and four equal sides make a square.

(b) The solid has six rectangular faces, so it is a cuboid.

(a) In order: 1, 5, 7, 9. The middle two are 5 and 7, so the median is $(5 + 7) \div 2 = 6$.

(b) Range $= 9 - 1 = 8$

(c) Label each bar with a name, use an evenly spaced scale up the side, and draw bars of heights 7, 9, 1 and 5.

8:30 am + 1 h 45 min = 10:15 am

Rest 15 min: 10:30 am

85 min = 1 h 25 min, so 10:30 + 1 h 25 min = 11:55 am

11:55 am is before noon, so yes.

Work backwards: $72 - 7 = 65$

$65 \div 5 = 13$

(a) The largest sector (150°) is Merit.

(b) Distinction is 105° for 7 students, so each student is $105 \div 7 = 15°$.

Total $= 360 \div 15 = 24$ students.

(a)(i) The first line goes from 12:00 to 12:30, so 30 minutes.

(a)(ii) The flat section is at 10 miles.

(b) She reaches the beach at 13:30; draw a flat line at 35 miles to 15:00, then a straight line to 0 at 16:00.

(c) 35 miles in 1 hour, so $35 \div 1 = 35$ mph.

One box: $600 \div 120 = 5$p

One bag: $1000 \div 270 = 3.7037...$p

Difference: $5 - 3.7037... = 1.296...$, which is $1.3$p to 1 d.p.

1 part is 35 beads, and there are $1 + 4 = 5$ parts.

$35 \times 5 = 175$

The shape has turned, so it is a rotation.

The vertex $(2, -2)$ goes to $(2, 2)$, $(5, -2)$ to $(2, 5)$ and $(2, -4)$ to $(4, 2)$: each point $(x, y)$ becomes $(-y, x)$.

That is a rotation of $90°$ anticlockwise about the origin $(0, 0)$.

Scale: 55 km $\div$ 10 = 5.5 cm.

Put the protractor on T, measure 65° clockwise from North, and mark a cross 5.5 cm from T along that line.

$8x - 12 = 20$

$8x = 32$

$x = 4$

Interest each year: $450 \div 6 = £75$

As a percentage of £3000: $75 \div 3000 \times 100 = 2.5$

$y = 2.5$

(a) Multiply the powers: $(m^2)^3 = m^{2 \times 3} = m^6$

(b) Add the powers: $x^{5+8} = x^{13}$

(c) $4p \times p^2 = 4p^3$ and $4p \times 3p = 12p^2$, so $4p^3 + 12p^2$

(a) $0.68 \times 800 = 544$ people

$544 \times 2 = 1088$ cups

$1088 \times 10.6 = 11532.8$, so $11533$ g

(b) More people drink coffee, so he needs more than in (a).

Angle $CFG = 180 - 125 = 55°$ (angles on a straight line add to 180°).

Angle $ACD = 55°$ (corresponding angles are equal).

Angle $ADC = 180 - 110 = 70°$ (angles on a straight line).

Angle $CAD = 180 - 55 - 70 = 55°$ (angles in a triangle add to 180°).

Two angles are equal, so triangle $ACD$ is isosceles.

Total work: $5 \times 14 = 70$ pump-hours.

With 4 pumps: $70 \div 4 = 17.5$ hours

(a) Take the lowest power of each shared prime: $3^2 \times 7 = 63$

(b) Take the highest power of every prime: $2^2 \times 3^4 \times 7^2 = 4 \times 81 \times 49 = 15876$

Seconds: $67\,205\,600 \div 11.9 = 5\,647\,529.4...$

Seconds in a day: $24 \times 60 \times 60 = 86\,400$

$5\,647\,529.4 \div 86\,400 = 65.36...$, so $65$ days

(a) The lowest point of the curve is at $(1, -3)$.

(b) The roots are where the curve crosses the $x$-axis: about $x = -0.7$ or $x = 2.7$.

Mass = density × volume

$9 \times 72 = 648$ g

(a) $90\,000 : 4\,500\,000$. Divide both by 90 000: $1 : 50$

(b) As ordinary numbers: $56\,250$, $5625$, $56.25$, $562.5$

Smallest first: $56250 \times 10^{-3}$, $0.005625 \times 10^{5}$, $5625$, $5.625 \times 10^{4}$