Exam Complete
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UKMT JMC 2024
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Topic Breakdown
Algebra
Weak
0/11 · 0%
Geometry
Weak
0/8 · 0%
Number Theory
Weak
0/4 · 0%
UKMT Challenge
Weak
0/1 · 0%
Counting and Probability
Weak
0/1 · 0%
Target your weak topics with focused practice.
Practice weak topics →Results by Question
1
Algebra
Wrong
When the five expressions below are simplified, how many different values are obtained?
\( 2+2 \quad 2\times 2 \quad 2-2 \quad 2 \div 2 \quad 2^2 \)
A
1
B
2
3
Correct Answer
D
4
E
5
No explanation
2
UKMT Challenge
Wrong
Which of the following could have a capacity of 10 litres?
A
An aeroplane
A bucket
Correct Answer
C
A cup
D
A dustpan
E
An egg
No explanation
3
Number Theory
Wrong
Gill is 36 this year. In which year will her age next be a square?
A
2025
2037
Correct Answer
C
2047
D
2052
E
2060
No explanation
4
Algebra
Wrong
A drink is made by mixing one part of cordial with four parts of water. What percentage of the drink is cordial?
20
Correct Answer
B
25
C
40
D
75
E
80
No explanation
5
Algebra
Wrong
What is the value of \(1+2-3\times4\div5\)?
A
0.2
B
0.3
C
0.4
D
0.5
0.6
Correct Answer
No explanation
6
Number Theory
Wrong
Which of the following has the same remainder when divided by 3 as it does when divided by 4?
A
7
B
11
C
17
D
19
25
Correct Answer
No explanation
7
Geometry
Wrong
The diagram shows a large square which has been divided into four smaller squares. It also shows both diagonals of the large square and two diagonals of smaller squares. What fraction of the area of the large square has been shaded?
A
\(\dfrac{1}{4}\)
B
\(\dfrac{9}{32}\)
C
\(\dfrac{5}{16}\)
\(\dfrac{3}{8}\)
Correct Answer
E
\(\dfrac{7}{16}\)
No explanation
8
Algebra
Wrong
Skye has half as many pens as Ishaa. Ana has twice as many pens as Skye. What fraction of all their pens does Skye have?
A
\(\dfrac{1}{2}\)
B
\(\dfrac{1}{3}\)
C
\(\dfrac{1}{4}\)
\(\dfrac{1}{5}\)
Correct Answer
E
\(\dfrac{1}{6}\)
No explanation
9
Geometry
Wrong
The diagram shows the regular hexagon \(PQRSTU\).
What is the size of angle \(UPT\)?
\(30°\)
Correct Answer
B
\(45°\)
C
\(60°\)
D
\(120°\)
E
\(150°\)
No explanation
10
Algebra
Wrong
In Fred's field there are some humans and some horses.
There are 25 heads in total and 60 legs in total.
What is the difference between the number of humans and the number of horses?
A
3
B
7
C
9
D
11
15
Correct Answer
No explanation
11
Geometry
Wrong
A hexagon is formed by arranging three equilateral triangles, as shown in the diagram. The side-length of the largest equilateral triangle is 10 cm.
What is the perimeter, in cm, of the hexagon?
A
45
40
Correct Answer
C
35
D
30
E
more information needed
No explanation
12
Number Theory
Wrong
In the multiplication sum shown, \(y\) represents the same digit each time. What is the value of \(y\)?
A
0
B
1
C
4
D
5
6
Correct Answer
No explanation
13
Geometry
Wrong
In the triangle \(PQR\), the point \(S\) is on the edge \(QR\).
\(\\angle QPS = \\angle SPR\), \(PQ = PS = SR\) and \(\\angle PRQ = x°\).
What is the value of \(x\)?
A
30
B
33
36
Correct Answer
D
40
E
45
No explanation
14
Number Theory
Wrong
The digits 1, 2, 3, 5 and 8 are to be placed in the grid above, one to a cell, to make a correct mathematical statement. Which number should come immediately after the division sign?
A
1
B
2
C
3
D
5
8
Correct Answer
No explanation
15
Geometry
Wrong
In the diagram shown, \(PQRS\) is a rhombus and \(PQT\) is an isosceles triangle in which \(PT = QT\). Angle \(PSR = 110°\).
What is the size of angle \(SQT\)?
A
\(5°\)
B
\(10°\)
C
\(12.5°\)
\(15°\)
Correct Answer
E
\(20°\)
No explanation
16
Algebra
Wrong
The world's smallest vertebrate is much shorter than its name! Discovered in 2022, the frog paedophryne amauensis is only 7.7 mm long.
Approximately how many of these frogs, placed end to end, would be needed to make a line 1 metre long?
A
100
130
Correct Answer
C
260
D
390
E
520
No explanation
17
Geometry
Wrong
\(PQRS\) is a square with area \(100 \,\mathrm{cm}^2\). The point \(T\) is inside the square. \(QRT\) is a triangle with area \(24 \text{ cm}^2\).
What is the area, in \(\mathrm{cm}^2\), of the triangle \(PTS\)?
A
24
B
25
26
Correct Answer
D
27
E
28
No explanation
18
Algebra
Wrong
Goldilocks eats three equal-sized bowls of porridge, one after the other. When she has eaten \(\dfrac{3}{7}\) of the total amount of porridge, what fraction of the porridge in the second bowl has she eaten?
A
\(\dfrac{1}{7}\)
\(\dfrac{2}{7}\)
Correct Answer
C
\(\dfrac{3}{7}\)
D
\(\dfrac{1}{3}\)
E
\(\dfrac{2}{3}\)
No explanation
19
Counting and Probability
Wrong
Jokers always lie.
Clowns always tell the truth.
A group of four, each of whom is a Joker or a Clown, make the following statements about each other:
P says, "Q always lies"; Q says, "R always lies";
R says, "P always tells the truth"; S says, "Exactly two of P, Q and R are Jokers".
How many of P, Q, R and S are Clowns?
A
0
B
1
2
Correct Answer
D
3
E
4
No explanation
20
Geometry
Wrong
When you cut a regular hexagon into two pieces with a single straight cut, you get two polygons. Which of these shapes cannot be obtained?
A
A triangle
B
A quadrilateral
C
A pentagon
D
A heptagon
An octagon
Correct Answer
No explanation
21
Geometry
Wrong
The rectangle \(PQRS\) is divided into eight squares: one large unshaded square, four small unshaded squares and three shaded squares, as shown in the diagram. What fraction of the area of rectangle \(PQRS\) is shaded?
A
\(\dfrac{1}{5}\)
\(\dfrac{5}{17}\)
Correct Answer
C
\(\dfrac{2}{7}\)
D
\(\dfrac{3}{10}\)
E
\(\dfrac{1}{3}\)
No explanation
22
Algebra
Wrong
Forty furry ferrets weigh the same as fifty fit ferrets. Forty-five fit ferrets weigh the same as fifty-four friendly ferrets. How many friendly ferrets weigh the same as fifty furry ferrets?
A
40
B
55
C
60
75
Correct Answer
E
80
No explanation
23
Algebra
Wrong
The area of a square is six times the area of a rectangle with a length half that of the square and a width 6 cm less than the width of the square. What is the perimeter of the square?
A
24 cm
B
28 cm
C
32 cm
36 cm
Correct Answer
E
40 cm
No explanation
24
Algebra
Wrong
Rovers, United, City and Wanderers played against each other once in a hockey tournament.
The results table is shown on the right:
What was the score in the match between Rovers and United?
| Team | Win | Draw | Loss | Goals for | Goals against |
|---|---|---|---|---|---|
| Rovers | 3 | 0 | 0 | 5 | 0 |
| United | 0 | 2 | 1 | 3 | 6 |
| City | 1 | 1 | 1 | 4 | 4 |
| Wanderers | 0 | 1 | 2 | 0 | 2 |
A
3 - 1
3 - 0
Correct Answer
C
2 - 1
D
2 - 0
E
1 - 0
No explanation
25
Algebra
Wrong
In a school, one fifth of the students have blue eyes. One tenth of the left-handed students have blue eyes. One quarter of the right-handed students have blue eyes. What fraction of the students are left-handed?
\(\dfrac{1}{3}\)
Correct Answer
B
\(\dfrac{1}{4}\)
C
\(\dfrac{1}{5}\)
D
\(\dfrac{1}{8}\)
E
\(\dfrac{1}{10}\)
No explanation
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