Algebra
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8. Two fair dice are rolled. What is the probability that we get the same number on both dice? Express your answer as a common fraction.
1/36
3. What is the area of a right-angled triangle whose two smallest sides are 7 and 16?
56
10. Simplify to a single fraction:
1/2 + 2/3 + 3/4
23/12
Round 243/23 to the nearest integer.
11
Alan bought three textbooks, and spent a total of $210. The calculus book cost $5 more than the economics book, which cost $5 more than the psychology book. How many dollars did the calculus book cost?
$75
What is the sum of all of the prime factors of 2015?
5 + 13 + 31 =49
If the width of a rectangular billboard is 4 times its height, and if it’s area is 25 m^2, what is the value of its width, in metres?
10 metres
1/15 - 1/18 = 1/x
90
5. Let N = 20% of 30% of 200. What is the value of N
12
18. You bought a book at a cost of 19.78 US dollars. If a Canadian dollar is worth 0.92 US dollars, how much did you pay in Canadian dollars? Give the answer to two decimal places.
21.50 Canadian dollars
21. In a class of 29 students, 19 got an A in Math. Of the students who did not get an A in Math, four-fifths did not get an A in Language Arts. Overall, 17 students got an A in Language Arts. If you choose a student at random, what is the probability that the student got an A in both Math and Language Arts? Express the answer as a common fraction.
15/29
The vertices of a triangle have coordinates (-40.3, 0), (40.3, 0), and (0, y). What is the positive value of y such that the area of the triangle is 2015?
y = 50
17. Express 3/(1*2) - 5/(2*3) + 7(3*4) as a common fraction.
5/4
What is the remainder when 202620262026 is divided by 9?
3
If (5x-4)/3 - (x-10)/4 = (x+9)/2 - 3, what is the value of x? Express the answer as a common fraction.
4/11
The centre of a square is at the point (-1, 1). One of the vertices of the square is at the point (6, 4). What is the area of the square?
116
Cone A has height h and base radius r. Cone B has height 4h and base radius r/3. What is the ratio of the volume of the cone A to the volume of cone B? Express your answer as a common fraction.
9/4
Express 1 + 1/2 + 1/4 + 1/8 + … + 1/1024 as a common fraction.
2047/1024
19. Given N = aa1 + bb1 + 1bb, where aa1, bb1, and 1bb are three-digit natural numbers and a < b. Determine b - a if N = 696. (2024 Blitz Provincial questions)
22. The values of the third and sixth terms of a geometric sequence are respectively 15/8 and -405/64. What is the first term of the sequence? Express the answer as a common fraction.
a = 5/6
How many different sums can you get when you throw 3 dice?
A square of side a and an equilateral triangle of side b have the same area. Express the value of b^4/a^4 as a common fraction.
16/3
19. Good garden compound can be made by combining 8 bags of 25 litres topsoil at density of 2/5 kg/litre, 4 bags of 30 litres mushroom compost at density of 1/3 kg/litre, and 1 bag of 25 litres of fertilizer at density of 6/5 kg/litre. By weight, what percentage of the compound is fertilizer? (Blitz, Provincial 2015)
20%
From a group of 6 boys and 5 girls, a delegation of 3 students is chosen, of whom at least one is a girl. In how many ways can this be done?
145