Number Sense
Logic Puzzles
Geometry
Statistics & Probability
Math in Everyday Life
100
State the general quadratic formula.
x= 
100
Which is the bigger number? (No calculator)
399, 933
Biggest number = 933
100
In triangle ABC, AB=AC. If ∠B=35∘, a line is drawn from A to BC such that it bisects ∠A. What is each of the two angles at A?
[No Calculator]
55˚
100
A frog jumps from the starting lilypad* and it cannot travel backwards. How many combinations can the frog travel towards land by lilypads?
* “frog” denotes starting point
Number of combinations = 6
100
A rideshare company charges a flat fee of $3.50 plus $1.50 per km. Which equation represents the total cost (C) for a ride of (m) miles?
A) C = 1.50m + 3.50
B) C = 3.50m + 1.50
C) C = 5.00m
D) C = 1.50m - 3.50
[No Calculator]
A
200
How do you check if any integer x is divisible by 12 without a calculator?
Ans: Check if the sum of its digits is divisible by 3, then check whether the digits in the last two places are divisible by 4.
200
A box contains one number from 1 to 20.
The person says:
“The number is a multiple of 3.”
“The number is even.”
“The number is greater than 10.”
“The number is less than 15.”
All is true. What is the number?
[No Calculator]
Number = 12
200
How many triangles are there in the figure?
[No Calculator]
13
200
Consider 64 distinct stones being placed one at a time on an 8x8 board, with exactly one stone eventually occupying each of the 64 squares. How many different orders are possible for placing the stones if, number of combinations = 
where x ≥ 8.
Subsequently, find x.
x = 64
200
A man deposits his $1500 in a bank that charges a 0.5% compound interest rate per annum. What will be his balance at the end of 8 years?
[Calculator Allowed]
$1560
300
Consider a list of six numbers. When the largest number is removed from the list, the average is decreased by 1. When the smallest number is removed, the average is increased by 1. When both the largest and the smallest numbers are removed, the average of the remaining four numbers is 20. Find the product of the largest and the smallest numbers.
(CALC ALLOWED)
Ans: 25 x 15 = 375
300
A well is 20m tall. Given that a frog can jump up 5m on the odd days and will fall 2m on even days.
How many days will it take for the frog to jump out of the well?
[No Calculator]
Number of Days = 11
300
A rectangle has a perimeter of 30 cm. Its length is 3 cm more than its width. What is its area?
[No Calculator]
54 cm2
300
A thief has to enter a 5-pin number lock that has numbers 1 to 5, where each number cannot be repeated more than once. What is the probability that the thief enters an incorrect combination on the first try but gets it on the second try?
[Calculator Allowed]
Probability = 119/14400
300
Explain your answer. [No Calculator]
Tank X
400
1+3+5+7+...+97+99 = 2500.
What is the general formula for the sum of 1+3+5+...+n, where each term has a uniform interval.
(CALC ALLOWED)
(Ans: [(n+1)2/4] or any equivalent answer)
400
5 People got the foods Pizza, Burger, Fries, Fried Rice and Pasta
Only 2 is telling the truth.
Ethan said: “Gabriel got pizza! Also, I got Fries”
Gabriel said: “Ethan is lying! ”
James said: “ I got Pasta or Fries or Pizza!”
Nathan said: “I got Pizza!”
Max said: “I got Pizza or Burger or Fries or Pasta or Fried Rice! I got Fried Rice too!”
What does James have?
[No Calculator]
James has a Burger.
400
A rectangular sheet of paper ABCD is folded as shown in the figure. EF is the crease. The images of points A and B after folding are G and H, respectively. If ∠1=α, express ∠2 in terms of α.
A. 90-a
B. ½ a
C. ⅔ a
D. 180-½ a
[No Calculator]
B
400
A set of two cards is called a “blackjack!” if the combination contains special cards: an ace and either a king, queen, jack, or “10” card. Suppose there are cards {1, 2, 3, …, 10, king, queen, jack, ace} in a game set, with each number card and special cards being distinct and only appearing ONCE. What is the probability a player obtains a “blackjack!” on the first try?
[Calculator Allowed]
Probability = 4/91
400
You are ordering pizza. A medium pizza has a 30 cm diameter, and a large pizza has a 45 cm diameter. If the large pizza is exactly twice the price of the medium, which is the better value in terms of area per dollar?
A) The medium pizza is better value
B) The large pizza is better value
C) Both pizzas have the same exact value
D) Not possible to tell
Explain your answer. [No Calculator]
B
500
3x = 2, leave x correct to 1dp and show reasoning, NO CALCULATOR (half the points if guessed correctly
Ans: (0.6)
500
Prove that (n+1)(n-1) is divisible by 24 given n is a prime number and is bigger than 3.
(Hint: Draw a number line)
[No Calculator]
Either (n+1) or (n-1) is divisible by 3 or 4.
Both (n+1) and (n-1) is divisible by 2.
3 x 4 x2 =24(proven)
500
A horse keeper starts at point A with a horse. Before returning to the stable at point B, the horse must first stop at the river to drink water. Point A is 20 m from the river bank. Point B, the stable, is 10 m from the river bank. The horizontal distance between A and B is 40 m. (The blue solid line is the river bank) What is the shortest possible total distance they travel? [No Calculator]
Shortest Possible Total Distance = 50 m
500
A regular fair dice is thrown twice. Suppose that the first roll lands on the number a while the second roll lands on the number b. What is the probability that a2+b2=c2, for an integer c?
[Calculator Allowed]
Probability = 1/18
500
A long jumper jumped a height of (y-3) cm and a distance of (4x+2) cm. Express the length of his jump in terms of x and y in the simplest form.
*The length of his jump is measured from his initial point before jumping to the highest point in a straight line.
[No Calculator]
