Question1
1: C1.10
Write $928$ correct to the nearest ten.
▶️Answer/Explanation
$930$
Rounding 928 to the nearest ten:
Since 8 is 5 or more, round up.
$
928 \approx 930
$
Question2
2: C1.4
Write down a fraction that is equivalent to $\frac{7}{9}.$
▶️Answer/Explanation
$\frac{7k}{9k}$ where $k$ is an integer $> 1$
We can multiply both the numerator and denominator by the same number to get an equivalent fraction.
multiply by 2:
$
\frac{7 \times 2}{9 \times 2} = \frac{14}{18}
$
multiply by 3:
$
\frac{7 \times 3}{9 \times 3} = \frac{21}{27}
$
So, an equivalent fraction is:
$
\frac{14}{18} \quad \text{or} \quad \frac{21}{27}
$
Question3
3: C1.6
Work out.
$-4+6\times3$
▶️Answer/Explanation
$14$
$
-4 + 6 \times 3
$
Order of operations (BIDMAS/BODMAS)
Multiplication comes before addition/subtraction.
$
6 \times 3 = 18
$
$
-4 + 18 = 14
$
Question4
4: C9.1
Bobby records the number of days a shop is open during $30$ days.
Complete the table.
▶️Answer/Explanation
$23, 7,$ 
For “Days open”
$
5 + 5 + 5 + 5 + 3 = 23
$
So, the frequency for Days open is 23.
Total number of days = 30
If the shop is open for 23 days, then the Days not open is
$
30 – 23 = 7
$
Question5
5(a): C4.5
5(b): C4.5
(a) Complete the statement.
The diagram has rotational symmetry of order …………………… . [1]
(b) On the diagram, draw all the lines of symmetry.
▶️Answer/Explanation
(a) $2$
(b) correctly showed
(a)
Rotational symmetry: The shape has rotational symmetry of order 2, meaning it looks the same when rotated 180° and 360°.
(b)
Question6
6: C1.6
Write down the reciprocal of 16 as a decimal.
▶️Answer/Explanation
$0.0625$
The reciprocal of a number is 1 divided by that number
$
\frac{1}{16} = 0.0625
$
Question7
7(a): C9.3
7(b): C9.3
7(c): C9.3
The stem-and-leaf diagram shows the ages of 21 people.
(a) Find the fraction of people who are more than 30 years old.
(b) Work out the range.
(c) Find the median.
▶️Answer/Explanation
(a): $\frac{2}{3}$
(b): 41
(c): 39
The stem-and-leaf diagram shows the ages of 21 people.
$
16, 19, 21, 24, 24, 25, 28, 32, 36, 37, 39, 40, 42, 44, 46, 48, 49, 53, 54, 55, 57
$
(a)
The ages greater than 30 are
$
32, 36, 37, 39, 40, 42, 44, 46, 48, 49, 53, 54, 55, 57
$
Total count: 14
Fraction
$
\frac{14}{21}\Rightarrow \frac{2}{3}
$
(b)
$
\text{Range} = \text{Highest age} – \text{Lowest age}
$
$
= 57 – 16
$
$
= 41
$
(c)
Since there are 21 people, the median is the middle value (11th value).
$
16, 19, 21, 24, 24, 25, 28, 32, 36, 37, \mathbf{39}, 40, 42, 44, 46, 48, 49, 53, 54, 55, 57
$
The 11th value is 39.
Question8
8: C5.4
Find the total surface area of the cuboid.
▶️Answer/Explanation
$158$
$
\text{Total Surface Area (TSA)} = 2(lb + bh + hl)
$
\( l = 8 \, \mathrm{cm} \) (length)
\( b = 3 \, \mathrm{cm} \) (breadth/width)
\( h = 5 \, \mathrm{cm} \) (height)
$
\text{TSA} = 2(8(3) + 3(5) + 5(8))
$
$
= 2(24 + 15 + 40)
$
$
= 2(79)
$
$
= 158 \, \mathrm{cm^2}
$
Question9N
9: C4.2
The diagram shows a triangular prism.
On the 1cm2 grid, draw a net of the prism.
▶️Answer/Explanation
Correct ruled net
Question10
10: C1.1
Olga thinks that $87$ is a prime number.
Is Olga correct?
Give a reason for your answer.
▶️Answer/Explanation
No
87 divides by 3.
No, Olga is not correct.
87 is not a prime number because it has more than two factors.
$87=3×29$
Since 87 is divisible by 3 (and 29), it is not prime.
A prime number only has 2 factors: 1 and itself.
Question11
11: C1.6
A film lasts for $2$ hours $50$ minutes.
The film ends at 23 05.
Find the time the film starts.
▶️Answer/Explanation
$20 ~15$ or $8:15$ pm
The film ends at 23:05, and it lasts for 2 hours 50 minutes.
$
23:05 – 50 \text{ minutes} = 22:15
$
$
22:15 – 2 \text{ hours} = 20:15
$
The film starts at 20:15 (8:15 PM).
Question12
12(a): C4.6
12(b): C4.6
Triangle $ABC$ is isosceles.
$\operatorname{Angle}BAC=38^{\circ}$ and $AB=AC.$
Find the value of $x.$
▶️Answer/Explanation
$71$
Triangle \( ABC \) is isosceles, meaning two sides are equal: \( AB = AC \).
Therefore, the base angles are equal
$
\angle ABC = \angle ACB
$
The angles in a triangle add up to \( 180^\circ \):
$
\angle BAC + \angle ABC + \angle ACB = 180^\circ
$
Since \( \angle ABC = \angle ACB \)
$
38^\circ + x + x = 180^\circ
$
$
38^\circ + 2x = 180^\circ
$
$
2x = 142^\circ
$
$
x = 71^\circ
$
Question13
13: C1.9
By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of
$$\frac{6.8\times10.6}{3.2-0.98}.$$
You must show all your working.
Complete the table.
▶️Answer/Explanation
$\frac{7 \times 10}{3-1}$. $35$
$
\frac{6.8 \times 10.6}{3.2 – 0.98}
$
\( 6.8 \approx 7 \)
\( 10.6 \approx 11 \)
\( 3.2 \approx 3 \)
\( 0.98 \approx 1 \)
$
\frac{7 \times 11}{3 – 1}
$
\( 7 \times 11 = 77 \)
\( 3 – 1 = 2 \)
$
= \frac{77}{2} = 38.5
$
$
\approx 38.5
$
Question14
14(a): C9.5
14(b): C9.5
The scatter diagram shows information about the time spent in a shop and the number of items bought.
(a) What type of correlation is shown on the scatter diagram?
(b) Describe the relationship between the time spent in the shop and the number of items bought.
(c) Draw a line of best fit on the scatter diagram.
▶️Answer/Explanation
(a): Positive
(b): Correct description e.g. The longer people spend in the shop the more items they buy.
(c): Correct ruled line
(a)
The scatter diagram shows a positive correlation.
As the time spent in the shop increases, the number of items bought also tends to increase.
(b)
There is a positive relationship between the time spent in the shop and the number of items bought.
People who spend more time in the shop tend to buy more items.
(c)
- A line of best fit should go through the general center of the points, balancing the number of points above and below the line.
- Start the line around the lower points, near (10, 2), and extend it to the upper points, around (75, 14).
Question15
15: C1.8
Simplify $d^8\div d^2.$
▶️Answer/Explanation
$d^6$
Use the rule of indice
$
d^8 \div d^2 = d^{8-2} = d^6
$
Question16
16: C1.5
Maddie changes $4000$ Swiss francs into dollars when the exchange rate is $1=0.913$ Swiss francs
Work out how many dollars she receives.
▶️Answer/Explanation
$4380, 4381, 4381.1, 4381.20, 4381.16$
The exchange rate is
$
1 \text{ dollar} = 0.913 \text{ Swiss francs}
$
For 4000 Swiss francs.
$
\text{Dollars} = \frac{4000}{0.913}
$
$
\text{Dollars} \approx 4381.71
$
Question17
17: C4.6
Find the highest common factor (HCF) of $32$ and $120$
▶️Answer/Explanation
$8$
Prime factorization:
\( 32 =2\times 2\times 2\times 2\times 2 \Rightarrow 2^5 \)
\( 120 = 2\times 2\times 2 \times 3 \times 5 \)
Common factors: \( 2^3 = 8 \)
So, the HCF is 8.
Question18
18: C2.2
The probability that Tom is late for school is $0.12.$
There are $200$ school days this year.
Work out the expected number of times that Tom is late for school this year
▶️Answer/Explanation
$24$
The probability that Tom is late is \( 0.12 \).
Number of school days: \( 200 \).
Expected value = Probability × Total trials
$
= 0.12 \times 200
$
$
= 24
$
Tom is expected to be late 24 times.
Question19
19: C1.4
Expand and simplify.
$$(x-5)(x+8)$$
▶️Answer/Explanation
$x^2 + 3x – 40$
$
(x – 5)(x + 8)
$
Use the distributive property
$
= x(x) + x(8) – 5(x) – 5(8)
$
$
= x^2 + 8x – 5x – 40
$
$
= x^2 + 3x – 40
$
Question20
20: C1.11
The diagram shows a circle, centre $O$, diameter $AB.$
$A,B$ and $C$ lie on the circumference of the circle.
(a) Write down the mathematical name of the line $AC.$
$( \mathbf{b} )$ Find the value of $x.$
Give a geometrical reason for your answer.
▶️Answer/Explanation
(a): Chord
(b): $58$. Angle in a semicircle $= 90^\circ$
(a)
The line \( AC \) is a chord a line segment that connects two points on the circumference of a circle.
If the line passes through the center, it would be a diameter.
(b)
Triangle \( ABC \) is a right-angled triangle (because of the semicircle rule)
$
\angle CAB + \angle ABC + \angle ACB = 180^\circ
$
\( \angle ACB = 90^\circ \) (Angle in a semicircle)
\( \angle CAB = 32^\circ \)
$
32^\circ + x + 90^\circ = 180^\circ
$
$
x = 180^\circ – (32^\circ + 90^\circ)
$
$
x = 180^\circ – 122^\circ
$
$
x = 58^\circ
$
Geometrical reason:
Angle in a semicircle is \( 90^\circ \)
Question21
21(a): C8.3
21(b): C8.3
A spinner has five sides.
Each side is painted red, blue, green, yellow or orange.
The table shows some of the probabilities of the spinner landing on each colour.
(a) Complete the table.
(b) Dan spins the spinner once.
Find the probability that the spinner lands on red or blue.
▶️Answer/Explanation
(a): $0.11$
(b): $0.46$
(a)
Sum of total probabilities 1.
$
0.3 + 0.16 + 0.18 + 0.25 = 0.89
$
$
1 – 0.89 = 0.11
$
The probability for orange is 0.11.
(b)
$
P(\text{Red or Blue}) = P(\text{Red}) + P(\text{Blue}) = 0.3 + 0.16 = 0.46
$
So, the probability is 0.46.
Question22
22: C2.5
Vanessa invests $\$8500$ at a rate of $3.5\%$ per year compound interest.
Calculate the value of her investment at the end of 6 years.
Give your answer correct to the nearest dollar.
▶️Answer/Explanation
$10449$
Compound interest formula
$
A = P \left( 1 + \frac{r}{100} \right)^t
$
\( A \) = Final amount
\( P = 8500 \) (initial investment)
\( r = 3.5\%\) (interest rate)
\( t = 6 \) years
$
A = 8500 \left( 1 + \frac{3.5}{100} \right)^6
$
$
A = 8500 \left( 1.035 \right)^6
$
Vanessa’s investment will be worth *$\$10,449$ at the end of 6 years, rounded to the nearest dollar.
Question23
23: C4.3
The diagram shows three shapes, $A,B$ and $C$,on$\text{1 cm}^2$ grid
Describe fully the single transformation that maps
(a) shape $A$ onto shape $B$
(b) shape $A$ onto shape $C.$
▶️Answer/Explanation
(a): Rotation, centre $(-3, 3)$, $90^\circ$ clockwise
(b): Translation $\begin{pmatrix} 7 \\ -2 \end{pmatrix}$
(a)
Rotation
The angle of rotation is 90° clockwise.
Center of Rotation
The center point where this rotation happens is (-3, 3).
If we rotate A by 90° clockwise around this point, it perfectly aligns with B.
$
\text{Rotation, center } (-3, 3), 90^\circ \text{ clockwise}.
$
(b)
Translation
Shape A slides directly to shape C without rotating or flipping.
Translation Vector
Right by 7 units
Down by 2 units
So, the vector for the translation is
$
\begin{pmatrix} 7 \\ -2 \end{pmatrix}
$
Question24
24: C1.4
\(\begin{aligned}&\textbf{Without using a calculator, work out 5}\frac{11}{12}+2\frac{1}{4}.\\&\text{You must show all your working and give your answer as a mixed number in its simplest form.}\end{aligned}\)
▶️Answer/Explanation
$\frac{k}{12} + \frac{27}{12}$ or $\frac{71}{12} + \frac{c}{12}$.
\( 5 \frac{11}{12} \):
Multiply the whole number by the denominator, then add the numerator
$
5 \times 12 + 11 = 60 + 11 = 71
$
$
5 \frac{11}{12} = \frac{71}{12}
$
2. \( 2 \frac{1}{4} \):
Multiply the whole number by the denominator, then add the numerator
$
2 \times 4 + 1 = 8 + 1 = 9
$
$
2 \frac{1}{4} = \frac{9}{4}
$
The denominators are 12 and 4. The least common denominator (LCD) is 12.
$
\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}
$
$
\frac{71}{12} + \frac{27}{12} = \frac{71 + 27}{12} = \frac{98}{12}
$
Divide both the numerator and denominator by their GCD (2):
$
\frac{98}{12} = \frac{49}{6}
$
$
49 \div 6 = 8 \text{ remainder } 1
$
$
\frac{49}{6} = 8 \frac{1}{6}
$
Question25
25: C2.5
In this question. both lengths are in centimetres.
The diagram shows two lines, $AB$ and $CD.$
The length of $AB$ is 10x-12. The length of $CD$ is $2x+3.$ Line $AB$ is 3 times as long as line $CD$
Work out the value of $x.$
▶️Answer/Explanation
$5.25$
Length of line \( AB = 10x – 12 \)
Length of line \( CD = 2x + 3 \)
Line \( AB \) is 3 times as long as line \( CD \).
Since \( AB = 3 \times CD \),
$
10x – 12 = 3(2x + 3)
$
$
10x – 12 = 6x + 9
$
$
4x – 12 = 9
$
$
4x = 21
$
$
x = \frac{21}{4} = 5.25
$