Oct/Nov 2017

Evaluate $1\frac{3}{8}-\frac{2}{3}$.

Fractions, decimals and percentages

Over one week, the midnight temperatures, measured in degrees Celsius, were noted. The recorded values were $-1,-3,2,5,-2,1,-2$.

Averages and measures of spread

Express the number $0.00012$ in standard form.

Standard form

Solve the pair of simultaneous equations $2y=x+12$ and $3y=11-2x$.

Equations

In a survey, respondents were asked which of three teas, labelled $X$, $Y$ and $Z$, they liked best. The sector for the people who preferred $Y$ has an angle of $168^\circ$.

Statistical charts and diagrams

This table lists square roots, correct to $4$ significant figures, for a selection of numbers from $31.0$ up to $32.9$.

Powers and roots

Evaluate the expression $9^2-9^0$.

Powers and roots

Calculate the simple interest earned on $\$200$ for $3$ years at $4\%$ per year.

Rates

Use numbers rounded correctly to $1$ significant figure to calculate an estimate for the value of $\frac{987.65}{0.0193}$.

Estimation

The diagram contains part of a figure with $AB$ as its line of symmetry. Complete the figure.

Symmetry

As part of her training, Samantha covers $2$ hours of running. During the first $1\frac{1}{2}$ hours, her average speed is $10\text{ km/h}$. In the final $\frac{1}{2}$ hour, she covers $7\text{ km}$.

Rates

The function is $f(x)=3x+7$.

Functions

The quantity $y$ is directly proportional to the square of $x$. It is given that $y=\frac{1}{5}$ when $x=\frac{1}{2}$.

Ratio and proportion

Solve $12-2x<x$.

Inequalities

Evaluate the difference $\frac{6}{7} - \frac{3}{5}$.

Fractions, decimals and percentages

Using appropriate approximations, calculate an estimate of $\frac{40.32 \times \sqrt{35.7}}{2980}$. Make the approximations you choose clear and give your answer to $1$ significant figure.

Estimation

Ali, Ben and Chris have a mean age of $14$ years $3$ months, while Dai is $15$ years and $3$ months old.

Averages and measures of spread

$a^x = 5$.

Indices I

The information provided gives the distribution of how long each member of a group of students spent on the internet on a Monday.

Statistical charts and diagrams

Find the two negative integers that solve $\frac{x}{3} - 1 < \frac{3x}{4}$.

Inequalities

This diagram is a shape built from five identical triangles, and it has rotational symmetry.

Transformations

Write $360$ million in standard form.

Standard form

The masses, measured in kilograms, of 20 parcels dispatched by a dispatch centre are shown.

Statistical charts and diagrams

$y$ varies inversely with $x$.

Ratio and proportion

Here, $f(x)=\frac{x}{4}$.

Functions

The bus timetable from A to E, with stops at B, C and D, is shown.

Time

The scale in the diagram runs from $3.8$ to $3.9$ and is divided into five equal intervals. What value is shown at the mark labelled $P$?

Ratio and proportion

From the diagram, $ABC$ runs parallel to $DEFG$. Also, $BC = BE$, $\angle ACE = 35^\circ$ and $\angle BFG = 102^\circ$.

Angles

Thirty students were surveyed about the number of days on which they ate pasta during the previous week.

Averages and measures of spread

The rectangle's area is stated as $8\text{ cm}^2$, rounded to the nearest $\text{cm}^2$.

Limits of accuracy

Jasmine is paid $12.50 for every hour she works. She works 38 hours each week. Her pay is increased by 6%. Calculate how much Jasmine earns in total each week after the increase.

Percentages

Sunil noted the call lengths, in minutes, for the 150 phone calls he made during one month. These results are shown in the table.

Statistical charts and diagrams

The diagram indicates the locations of the three towns, $A$, $B$ and $C$. $B$ lies due north of $A$, and the bearing of $C$ from $A$ is $220^\circ$. $AB = 25$ km and $AC = 38$ km.

Non-right-angled triangles

Adam has a bag with 9 balls, labelled from 1 to 9. Adam chooses a ball at random from the bag and then puts it back. Find the probability that the ball has an odd number.

Probability of combined events

Solve $\frac{y}{2y + 3} = \frac{2}{y + 5}$.

Algebraic fractions

Points A, B, C, D and E lie on the circumference of the circle with centre $O$. $AC$ is a diameter, and $AC$ is parallel to $ED$. The lines $AC$ and $BE$ intersect at $F$. $\angle BAC$ is $52^\circ$ and $\angle CBE$ is $68^\circ$.

Circle theorems I

Sara purchases a brand-new car. Its cash price is $4500. She may pay for it by using option A or option B.

Percentages

A rectangular picture $ABCD$ sits within a rectangular frame. Its length $AB$ is three times the height $x\,\text{cm}$. The frame has width $2\,\text{cm}$.

Equations

A vertical mast, $XY$, stands on horizontal ground. Four cables hold the mast, each fixed to the mast at $P$ and to the ground at points $A$, $B$, $C$ and $D$. $Y$ is the centre of square $ABCD$. $PY = 7.50\text{ m}$.

Pythagoras' theorem and trigonometry in 3D

A company carried out a survey asking staff how long they spent travelling to work on one day. The table below summarises the times for 120 employees.

Cumulative frequency diagrams

Anya manufactures T-shirts. Matrix $M$ displays how many T-shirts of each type she makes in one week.

Algebraic manipulation

The grid displays triangle $A$.

Transformations

Express $\frac{4}{x-2}-\frac{5}{x+1}$ as a single fraction in simplest form.

Algebraic manipulation

Take $\mathcal{E}=\{x:x\text{ is an integer and }10\le x\le 20\}$, $A=\{x:x\text{ is an odd number}\}$, and $B=\{x:x\text{ is a multiple of }5\}$.

Sets

The variables $x$ and $y$ satisfy the equation $y=3+x-\frac{x^2}{2}$.

Sketching curves

The diagram displays two circles, each with centre $O$.

Similarity

The ventilation shaft has a cylindrical shape, with radius $0.4\,\text{m}$ and length $15\,\text{m}$. Calculate the volume of the cylinder.

Surface area and volume