12TH ANNUAL NATIONAL MATHEMATICS COMPETITION REVIEW
12TH ANMC-Copyright © NTIC 12TH ANNUAL NATIONAL MATHEMATICS COMPETITION 2ND ROUND, 14TH MARCH 2015
ALGEBRA
Basic Addition Problem
Question: What is $55 + 66$?
Options:
A. 74
B. 82
C. 108
D. 121
E. 172
Equation Solving
Question: Solve for $x$: $x = ?$
Options:
A. 2
B. 4
C. 6
D. 8
E. 9
Multiplication
Question: What is $9 imes 7$?
Options:
A. 42
B. 56
C. 60
D. 63
E. 72
Complex Calculation
Question: Calculate $2040 - 40 + 40 - 2000$.
Options:
A. 10
B. 4040
C. 40
D. 80
E. 2040
Number Range Identification
Question: Which number is not between 5,345 and 7,216?
Options:
A. 5,499
B. 7,539
C. 6,499
D. 5,985
E. 7,198
Sum of Odd Numbers
Question: What is $1 + 3 + 5 + 7 + 9 + 11$?
Options:
A. 8
B. 13
C. 22
D. 28
E. 36
Days Calculation
Question: Today is Saturday. After how many days will it be Saturday again?
Options:
A. 42
B. 36
C. 30
D. 25
E. 18
Subtraction and Fraction
Question: Aisha has 6 apples. How many apples will be left if she eats $\frac{2}{3}$ of the apples?
Options:
A. 0
B. 1
C. 2
D. 3
E. 5
Reading Pace Calculation
Question: Saudatu wants to read a $200$ page book. If she reads $25$ pages a day, how many days to finish the book?
Options:
A. 4
B. 6
C. 8
D. 10
E. 12
Evaluate Expression
Question: Evaluate $1 imes 2 + 3 imes 4 + 5 imes 6$.
Options:
A. 140
B. 100
C. 80
D. 65
E. 44
Logic Problem involving Cats
Question: Dalton has 10 cats. How many white cats should be sent away so that half of the remaining cats will be black?
Options:
A. 1
B. 2
C. 3
D. 4
E. 5
Percentage Calculation
Question: What percentage is shaded in the figure?
Options:
A. 5%
B. 10%
C. 15%
D. 24%
E. 30%
Expanded Multiplication Problem
Question: What is $6 imes 10,000 + 2 imes 1000 + 1 imes 10$?
Options:
A. 62,010
B. 60,021
C. 60,210
D. 62,210
E. 60,201
Percentage Increase Calculation
Question: By what percentage should we increase the number $2$ to make it $2.5$?
Options:
A. 20%
B. 25%
C. 30%
D. 50%
E. 75%
Fraction Comparison
Question: Which of the following is more than $ rac{1}{2}$?
Options:
A. $ rac{2}{5}$
B. $0.3$
C. $0.5$
D. $40 ext{%}$
E. $ rac{4}{7}$
Logic Puzzle with Addition
Question: Which digit is represented by the symbol in the addition given?
Options:
A. 5
B. 6
C. 7
D. 8
E. 9
GEOMETRY
Speed and Distance Problem
Question: A car travels from town A to B at a speed of $50$ km/h, taking $6$ hours. If speed increases by $25$ km/h, how long is the journey?
Options:
A. 8 hours
B. 6 hours
C. 5 hours
D. 4 hours
E. 3 hours
Animal Leg Calculation
Question: Ms. Bryce's farm has $25$ animals: $7$ horses, $6$ sheep, and $3$ cows. How many legs do the animals have in total? (Horses, sheep, cows have $4$ legs each; chickens have $2$ legs.)
Options:
A. 82
B. 75
C. 60
D. 51
E. 43
Sum and Product of Two Numbers
Question: Two positive whole numbers A and B satisfy $A + B = 19$. Find the smallest and greatest possible values of $A imes B$.
Options:
A. Smallest: 18, Greatest: 90
B. Smallest: 20, Greatest: 88
C. Smallest: 18, Greatest: 99
D. Smallest: 12, Greatest: 88
E. Smallest: 34, Greatest: 90
Bell Ringing Problem
Question: Three bells ring every $12$, $18$, and $30$ minutes respectively. If they ring together at $11:00$ am, when will they ring again together?
Options:
A. 12:00 pm
B. 12:30 pm
C. 1:00 pm
D. 1:30 pm
E. 2:00 pm
Sum of Interior Angles of a Rectangle
Question: What is the sum of the interior angles of a rectangle?
Options:
A. 60°
B. 90°
C. 150°
D. 180°
E. 360°
Triangle Classification Problem
Question: Figure has $b=11$ and $a=8$. Classify the triangle.
Options:
A. Scalene triangle
B. Equilateral triangle
C. Isosceles triangle
D. Right-angled triangle
E. Square
Finding Unknown Angle in Triangle
Question: Find $x$ in the given triangle.
Options:
A. 60°
B. 63°
C. 72°
D. 80°
E. 85°
Volume of a Tank
Question: How many m³ of water can a tank of dimensions $2m × 4m × 5m$ hold?
Options:
A. 11
B. 20
C. 25
D. 30
E. 40
Identify Non-Prism Shape
Question: Which of the following is NOT a prism?
Options:
A. Cylinder
B. Cube
C. Pyramid
D. Cuboid
E. Square based Prism
Perimeter of Composite Shape
Question: If the perimeter of one square is $16$ cm, find the perimeter of the rectangle made from three squares.
Options:
A. 24 cm
B. 32 cm
C. 48 cm
D. 64 cm
E. 81 cm
Perimeter of a Semi-Circle
Question: Find the perimeter of the semi-circle with a $28$ cm diameter ($ rac{22}{7}= ext{π}$).
Options:
A. 28 cm
B. 40 cm
C. 72 cm
D. 80 cm
E. 96 cm
Perimeter of Given Shape
Given dimensions: 8 cm, 5 cm, 7 cm, 3 cm, 21 cm, 10 cm.
Question: Find the perimeter of the shape.
Options:
A. 40 cm
B. 50 cm
C. 48 cm
D. 54 cm
E. 60 cm
Area of a Given Shape
Question: Find the area of the shape.
Options:
A. 105 cm²
B. 109 cm²
C. 118 cm²
D. 124 cm²
E. 136 cm²
Unknown Angle in Isosceles Triangle
Question: Find $x$ in the given isosceles triangle.
Options:
A. 20
B. 30
C. 40
D. 50
E. 60
Area Calculation of Rectangle
Question: Find the area of the given rectangle.
Options:
A. 14
B. 18
C. 21
D. 24
E. 28
ADDITIONAL GEOMETRY QUESTIONS
Quadrilateral Angles Ratio
Question: The interior angles of a quadrilateral are in the ratio of $1:2:3:4$. Find the greatest angle.
Options:
A. 72°
B. 90°
C. 105°
D. 120°
E. 144°
Shaded Area Calculation
Question: What is the shaded area?
Options:
A. 600 cm²
B. 500 cm²
C. 400 cm²
D. 300 cm²
E. 200 cm²
Clock Angle Calculation
Question: What is the smaller angle between the hour and the minute hands of a clock at $9:10$ am?
Options:
A. 60°
B. 90°
C. 120°
D. 145°
E. 170°
Counting Faces of a Pentagonal Pyramid
Question: Amina counts the number of faces on a pentagonal pyramid, Farouk counts vertices, and Tobi counts sides. What is the sum of their counts?
Options:
A. 14
B. 16
C. 18
D. 22
E. 25
APTITUDE QUESTIONS
Series Completion
Question: What is the next number in the series: $1, 4, 7, 10, 13, 16, ?$
Options:
A. 19
B. 18
C. 17
D. 16
E. 15
Next Number in Series
Question: What is the next number in the series: $1, 2, 4, 5, 10, 11, ?$
Options:
A. 12
B. 16
C. 19
D. 22
E. 25
Fibonacci Style Series Completion
Question: What is the next number in the series: $1, 3, 4, 7, 11, 18, ?$
Options:
A. 22
B. 26
C. 29
D. 32
E. 35
Power Series Completion
Question: What is the next number in the series: $1, 2, 2, 4, 8, 32, ?$
Options:
A. 180
B. 212
C. 240
D. 256
E. 298
Number from Series
Question: In series $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, …$, find the 25th number.
Options:
A. 5
B. 6
C. 7
D. 8
E. 9
Position of Number in Series
Question: What is the position that the number $10$ appears for the first time?
Options:
A. 52nd
B. 46th
C. 39th
D. 36th
E. 30th
Sum of First 20 Numbers in Series
Question: What is the sum of the first 20 numbers in the series?
Options:
A. 68
B. 77
C. 85
D. 90
E. 99
Counting Sweets Consumed
Question: Michael starts at $11:10$ am to $2:25$ pm. How many sweets did he eat if he has one every 5 minutes?
Options:
A. 41
B. 40
C. 37
D. 35
E. 33
Balloon Count
Question: Abel has various colored balloons. Which color does he have the most?
Options:
A. Blue
B. Green
C. Yellow
D. Red
E. White
Balloon Comparison
Question: How many more blue balloons than white does Abel have?
Options:
A. 17
B. 19
C. 21
D. 23
E. 25
Balloon Count Range
Question: Abel has more than $123$ but less than $139$ of which color?
Options:
A. Blue
B. Green
C. Yellow
D. Red
E. White
Balloon Loss Calculation
Question: If Abel loses $3$ blue, $9$ green, $38$ yellow, and $26$ red balloons, which color will he have the most?
Options:
A. Blue
B. Green
C. Yellow
D. Red
E. White
Weight Calculation of Box with Balls
Question: When Mr. Kenneth puts $4$ balls inside a box, it weighs $3$ kg total. When he puts $8$ balls, it weighs $4$ kg total. How heavy will it be for $16$ balls?
Options:
A. 5 kg
B. 6 kg
C. 7 kg
D. 8 kg
E. 10 kg
Midpoint on Number Line
Question: On the number line, point L is the midpoint between…
Options:
A. $104$ and $120$
B. $100$ and $120$
C. $108$ and $120$
D. $100$ and $108$
E. $104$ and $108$
Geometric Shapes Count
Question: How many parallelograms are there in the figure?
Options:
A. 3
B. 5
C. 6
D. 7
E. 9
Counting in a Sequence
Question: How many numbers are in the sequence $20, 22, 24, 26, 28, … , 100$?
Options:
A. 30
B. 37
C. 41
D. 43
E. 47
Story Problem Representation
Question: Which of the following statement can be described by the equation $7 - 4 = ?$
Options:
A. Tope has $4$ movies and $7$ books.
B. Tope has $7$ books. The number of movies he has is $4$ less than the books.
C. Tope has $4$ shelves with $7$ books each.
D. Tope has $7$ books on $4$ shelves.
E. Tope has $7$ blue books and $4$ green books.
Floor Function Evaluation
Question: Evaluate $\text{floor}\left(\frac{33}{4}\right)\frac{25}{7}\text{floor}$
Options:
A. 1
B. 2
C. 3
D. 4
E. 5
Competition Prize Arrangement
Question: If $4$ contestants compete in a math tournament, how many different ways can the $3$ medals be awarded?
Options:
A. 30
B. 24
C. 20
D. 16
E. 15
Pattern Recognition
Question: If $7948=LIKE$ and $51326=MATHS$, what does $5148$ equal?
Options:
A. MAKE
B. TASK
C. MASK
D. TAKE
E. LIST
OPERATIONS AND LOGIC
Defined Operations Calculation
Operation $A ullet B$ is defined as the smaller of the two numbers.
Example: $3 ullet 4 = 3$ and $7 ullet 2 = 2$.
Question: Calculate $5 ullet 7$.
Options:
A. 2
B. 5
C. 7
D. 12
E. 35
Combined Operations Calculation
Using operations defined above, solve for $(2 ullet 4) + (7 ullet 6)$.
Options:
A. 8
B. 9
C. 10
D. 11
E. 12
Complex Nested Operations Calculation
Evaluate $[(3 ullet 4) ullet (8 ullet 1)] ullet [(6 ullet 3) ullet (7 ullet 8)]$.
Options:
A. 1
B. 3
C. 4
D. 7
E. 8
CATERPILLAR PROBLEM
Shortest Distance Calculation
A caterpillar moves from point A to point B on a cube's edges of length $10$ cm. Find the shortest distance.
Options:
A. 30 cm
B. 40 cm
C. 50 cm
D. 60 cm
E. 70 cm
Longest Possible Distance Calculation
Find the longest possible distance the caterpillar can travel.
Options:
A. 40 cm
B. 50 cm
C. 60 cm
D. 70 cm
E. 80 cm
END OF THE EXAM
WORKING AREA (You can use this space for rough work)