Oct/Nov 2015

Calculate $12 + 6 \div 3 + 1 \times 5$.

The four operations

The numbers in the list are $-8, -5, -3, -2, 0, 2, 4, 9$.

Inequalities

An empty box is given a mass of 0.8 kg, rounded to the nearest 0.1 kg.

Limits of accuracy

A set of five numbers has a mean of 3.8 and a median of 3. The numbers 3 and 6 are added to the set.

Averages and measures of spread

ABCD is a quadrilateral in which BC is parallel to AD. CD is perpendicular to BC. BC = 5 cm and AD = 12 cm. The area of triangle BCD is 20 cm$^2$.

Area and perimeter

One number expressed as a product of prime factors is $2^2 \times 5^2 \times 7$.

Types of number

The conversion rate from pounds (£) into dollars ($) is £1 = $1.60.

Money

The diagram depicts a square PQRS and a right-angled triangle PST. The area of the square is 50 cm$^2$. $ST = \sqrt{34}$ cm.

Pythagoras' theorem

Write $30\,682$ rounded to three significant figures.

Limits of accuracy

Paul sits examinations in Maths and Physics. The chance that he passes Maths is 0.7. The chance that he passes Physics is 0.6. The outcomes in each subject are independent of one another.

Probability of combined events

$\cos y^\circ = -0.54$ with $90 \le y \le 180$. A solution of $\cos x^\circ = 0.54$ is $x = 57$, correct to the nearest whole number. Find $y$, correct to the nearest whole number.

Right-angled triangles

Because $p$ is directly proportional to $q$, work out the value of $r$.

Ratio and proportion

Tim places $2500$ in a bank account that earns simple interest at $2.3\%$ per year. What total amount will be in the bank after $4$ years?

Percentages

ABCD is a trapezium with $AB$ parallel to $DC$. $DC = 15\text{ cm}$ and $AB = x\text{ cm}$. The perpendicular distance between $AB$ and $DC$ is $3\text{ cm}$ shorter than the length of $AB$. The area of $ABCD$ is $75\text{ cm}^2$.

Area and perimeter

The diagram depicts a solid triangular prism. Every length is measured in centimetres.

Surface area and volume

ABCDE is a pentagon that has one line of symmetry. $BC = DE = 10\text{ cm}$, $DC = 30\text{ cm}$ and $\angle BCD = \angle CDE = 90^\circ$. The minimum distance from $A$ to $DC$ is $22\text{ cm}$.

Non-right-angled triangles

The matrices $A = \begin{pmatrix} 1 & 3 \\ -2 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} -1 & 2 \\ -3 & 2 \end{pmatrix}$ are provided.

Algebraic manipulation

Shade the set $(A \cap B) \cup C$.

Sets

Write $6x^2y^3 - 15x^3y$ in fully factorised form.

Inequalities

The diagram displays the vectors $\vec{PQ}$ and $\vec{QR}$. $\vec{PQ} = \begin{pmatrix}5 \\ 2\end{pmatrix}$ and $\vec{QR} = \begin{pmatrix}a \\ b\end{pmatrix}$.

Vectors in two dimensions

The shaded triangle, shown on the grid, is one part of a quadrilateral with a single line of symmetry. The area of the quadrilateral is twice the area of the triangle. Since the line of symmetry is not vertical, finish the quadrilateral.

Transformations

The diagram depicts a solid cone with radius $r$ cm, height $h$ cm and slant height $l$ cm. Each cone’s slant height is $4$ cm greater than its radius. Use $\pi = 3$ throughout this question.

Surface area and volume

The cumulative frequency graph for the lengths of the $50$ tracks on Abi's MP3 player is displayed.

Cumulative frequency diagrams

Fatima and Mohammed purchase new bikes.

Percentages

The table below summarises the time taken by $80$ drivers to complete one particular journey.

Statistical charts and diagrams

ABCDE is a pentagon. $AFB$, $AHE$ and $BGC$ lie on straight lines.

Vectors in two dimensions

$A$ is located at $(8, 7)$, $B$ at $(-2, 11)$, and $C$ at $(1, 7)$.

Length and midpoint

In the circle with centre $O$, $AC$ is a diameter. $BCD$ and $OED$ are straight lines. $AC = 6\text{ cm}$ and $CD = 3\text{ cm}$. $\angle BAC = 34^{\circ}$.

Circle theorems I

This cookery measuring spoon is made up of a hemispherical bowl and a handle. The bowl has an internal volume of $20\text{ cm}^3$, and the handle measures $5\text{ cm}$ in length.

Surface area and volume

The diagram illustrates a vertical radio mast, $AB$. Three of the supporting wires are fixed to it at $F$, $H$ and $D$. The foot of the mast, $A$, and the far ends $E$, $G$ and $C$ of the wires lie on one straight line on horizontal ground.

Right-angled triangles

Solve the equation $(x + \frac{7}{2})^2 = \frac{\sqrt{5}}{2}$. Provide both solutions correct to $2$ decimal places.

Equations

The points $A$, $B$ and $D$ lie on one straight line, while $A$, $C$ and $E$ lie on another. $BD = 12\text{ cm}$ and $CE = 4\text{ cm}$. $AB = x\text{ cm}$ and $AC = (2x - 5)\text{ cm}$. Angle $BAC = \theta^{\circ}$.

Non-right-angled triangles

$OAB$ forms a sector of a circle, with centre $O$ and radius $6\text{ cm}$. $\angle AOB = 25^{\circ}$.

Circles, arcs and sectors

For a moving object, its distance, $d$ metres, from an observer after $t$ minutes is given by $d = t^2 + \frac{48}{t} - 20$.

Graphs in practical situations