Question1
The temperature at midnight is $-4^{\circ}C$.
The temperature at noon is $25^{\circ}C$
Work out the difference between these two temperatures.
▶️Answer/Explanation
$29$
Question2
A gardener charges \( \$6.55\) for each hour he works plus a fixed charge of \( \$15.50\) .
Calculate the total amount he charges when he works for 4 hours.
▶️Answer/Explanation
$41.7$
Question3
A delivery driver records the number of pizzas she delivers each month for one year.
(a) Complete the stem-and-leaf diagram.
(b) Find the median.
▶️Answer/Explanation
(a)
(b) $46$
Question4
Jonah has \(\$750\).
He spends $\frac{1}{4}$ of this money on travel and some of this money on food
He now has \(\$437.50\).
Work out the fraction of the \(\$750\) he spends on food
▶️Answer/Explanation
$\frac{1}[6}$
Question5
The table shows part of a tram timetable.
All the trams take the same number of minutes to complete the journey from Newpoint to Westhill.
Complete the table.
▶️Answer/Explanation
$13.05$
Question6
Write $0.04628$ correct to 2 significant figures.
▶️Answer/Explanation
$0.046$
Question7
On the Venn diagram, shade the region $\rm {A} \cap \rm {B}$,
▶️Answer/Explanation
Question8
Kai invests \(\$5000\) in an account paying simple interest at a rate of $r\%$ per year.
At the end of 8 years, the value of his investment is \(\$5700\).
Find the value of r.
▶️Answer/Explanation
$1.75$
Question9
(a) Describe fully the single transformation that maps triangle A onto triangle B.
(b) On the grid, draw the image of triangle A after a translation by the vector $\binom {-4}{3}$
▶️Answer/Explanation
(a) Enlargement
[s f] 2
[centre] $(1,-1)$
(b) image at $(-1,4)(-1,5)(1,4)$
Question10
Write $174000$ in standard form.
▶️Answer/Explanation
$1.74\times 10^5$
Question11
A company surveys $40$ of its employees.
In the survey, $3$ employees say they walk to work.
The company has a total of $1240$ employees.
Find the expected number of employees in the company who walk to work.
▶️Answer/Explanation
$93$
Question12
The diagram shows a right-angled triangle.
Calculate the value of x.
▶️Answer/Explanation
$52.6$ or $52.61$ to $52.62$
Question13
$\begin{aligned}&\textbf{Without using a calculator, work out}\quad2\frac{1}{4}\div1\frac{7}{8}.\\&\text{You must show all your working and give your answer as a mixed number in its simplest form.}\end{aligned}$
▶️Answer/Explanation
$\frac{9}{4}\times\frac{8}{15}$
$\frac{18}{8}\div\frac{15}{8}$ oe with common denominator
Question14
\(\begin{aligned}&A\text{ is the point }(0,2)\mathrm{~and~}B\text{ is the point }(8,6).\\&\text{Find the equation of line }AB.\\&\text{Give your answer in the form }y=mx+c.\end{aligned}\)
▶️Answer/Explanation
$y=\frac{1}{2}x+2$
Question15
Three towns, $A,B$ and $C$, are equidistant from each other.
The bearing of $C$ from $A$ is 104$^\circ.$
Calculate the bearing of $B$ from $C.$
▶️Answer/Explanation
$22$
Question16
The speed–time graph shows information about a car journey.
(a) Find the deceleration of the car between $240$ and $320$ seconds.
(b) Calculate the total distance the car travels during the $320$ seconds.
▶️Answer/Explanation
(a) $0.2$
(b) $4240$
Question17
$W=\{$students who walk to school$\}$
$G=\{$students who wear glasses$\}$
There are 20 students in a class.
- 8 walk to school
- 3 wear glasses and walk to school
- 2 do not wear glasses and do not walk to school.
Complete the Venn diagram.
▶️Answer/Explanation
Question18
The graph of $y=$f$(x)$ is drawn on the grid
(a) Draw the tangent to the graph at the point $x=3.$
(b) Use your tangent to find an estimate for the gradient of the curve at the point $x=3.$
▶️Answer/Explanation
(a) tangent ruled at $x = 3$
(b) $4.8$ to $5.8$
Question19
$\begin{array}{ll}(\mathbf{a})&y~\text{is directly proportional to}\left(x-1\right)^2.\\&\text{When }x=4,\:y=3.\end{array}$
Find $y$ when $x=7.$
(b) m is inversely proportional to the square root of $p.$
Explain what happens to the value of $m$ when the value of $p$ is multiplied by 9
▶️Answer/Explanation
(a) $12$
(b) divided by $3$
Question20
Two parcels are mathematically similar.
The larger parcel has volume 80cm$^{3}$ and height 5.2cm.
The smaller parcel has volume 33.75 cm$^{3}.$ Calculate the height of the smaller parcel.
▶️Answer/Explanation
$3.9$
Question21
Solve the simultaneous equations. You must show all your working.
$4y+3x=13$
$y=x^2-18$
▶️Answer/Explanation
$4x^{2}+3x-85[=0]$
or 16$y^2-113y+7[=0]$
oe simplified
correct method to solve their quadratic equation e.g. factors, quadratic formula, completing the square
$$\begin{aligned}&x=-5\:y=7\\&x=\frac{17}{4}\:\mathrm{oe}\:y=\frac{1}{16}\:\mathrm{oe}\end{aligned}$$
Question22
(a) For each sketch, put a ring around the correct type of function shown.
$\mathbf{( i) }$ On the grid, sketch the curve $y= \sin x$ for $0^\circ\leqslant x\leqslant360^\circ.$
(ii) Solve the equation $\sin x+ 0. 4= 0$ for $0^{\circ}\leqslant x\leqslant360^{\circ}$
▶️Answer/Explanation
(a)(i) cubic
(a)(ii) reciprocal
(b)(i)
(b)(ii) $203.6$ and $336.4$
Question23
The Venn diagram shows information about the number of students in a class.
Some study English $(E)$, some study French $(F)$, some study Spanish $(S)$ and some do not study any of
these languages.
(a) Find n$((E\cup F)^\prime\cup S)$.
(b) One student is picked at random from those who study Spanish.
Find the probability that this student studies exactly two languages.
▶️Answer/Explanation
(a) $15$
(b) $\frac{1}{2}$
Question24
$O$ is the origin and $OPQR$ is a parallelogram
$M$ is the midpoint of $PQ$ and $\hat{N}$ divides $\underline{O}R$ in the ratio 2:1.
$\overrightarrow{OP}=$a and $\overrightarrow OR=\mathbf{b}.$
$( \mathbf{a} )$ Find $\overrightarrow{MN}.$
Give your answer in terms of a and/or b and in its simplest form.
$(\mathbf{b})$ The lines $MN$ and $OR$ are extended to meet at S.
Find the position vector of $S.$
Give your answer in terms of a and/or b and in its simplest form.
▶️Answer/Explanation
(a) $\frac{1}{2}\mathbf{b}-\frac{2}{3}\mathbf{a}$
(b) $\frac{5}{4}\mathbf{b}$