ALGERBA
NUMBERS
PROBLEM SOLVING
TRIGONOMETRY
GEOMETRY
100
The sum of the areas of two squares is 818 cm sq. The sum of the perimeters is 160cm. Find the lengths of the sides of squares.
(30 seconds)
17 cm and 23 cm
100
Using all the letters of the word GIFT how many distinct words can be formed? (They do not have to actually be real words)
(30 seconds)
24
100
Two girls have $76 between them. If the first gave the second $7, they would each have the same amount of money. How much did each girl have?
(30 seconds)
$45, $31
100
If sin(45)/cos(45)=tan(x). What is the value of x in the first quadrant?
(30 seconds)
45
100
If a polygon has 12 sides, what is it called?
(30 seconds)
a dodecagon
200
Find the dimensions of the rectangle whose perimeter is 36 m and which is such that the square of the length of one of the diagonals is 170 m sq.
(60 seconds)
7m , 11m
200
A sum of money is divided among three persons in the ratio 4:5:7. If the difference between the shares of the first and the second person is $240, find the total sum of money
(45 seconds)
$1560
200
A bag contains red, blue and yellow counters. There are 60 counters in the bag. Probability that a counter taken at random from the bag is red is 2/5 and probability that a counter taken at random from the bag is blue is 5/12. How many yellow counters are in the bag?
(45 seconds)
11 yellow counters
200
From an observer, the angle of elevation of the top of a tree is 50°. If the observer is 8 metres from the tree, find the height of the tree.
(60 seconds)
9.53 (8 tan 50°)
200
Find a:
(30 seconds)
105
300
In three years time a pet mouse will be as old as his owner was 4 years ago. Their present ages total 13 years. Find the age of each.
(45 seconds)
Boy = 10
Mouse = 3
300
If 15% of a number is 90, find 25% of that number.
(30 seconds)
150
300
Alex and Daniel travel to England. Alex exchanges Rs. 20,500 and receives £250. Daniel exchanges Rs. 26,650 into pounds (£) at the same exchange rate. How many pounds does Daniel receive?
(45 seconds)
£325
300
Simplify sec(X)*cos(X)
(30 seconds)
1
300
Calculate the numbers of sides of a regular polygon whose interior angles are 1560 each.
(60 seconds)
15 sides
400
Find the remainder when 4x^3 - 5x + 1 is divided by 2x - 1
(30 seconds)
-1
400
The 15th term of an arithmetic sequence is 75, and the 25th term is 125. What is the fifth term of the sequence?
(30 seconds)
25
400
Luis works in an office and for normal time, he is paid $8 per hour. For overtime, he is paid the same plus an extra 50%. One month he works 140 hours of normal time and then 10 hours overtime. Work out how much he is paid for that month’s work.
(60 seconds)
$1240
400
Differentiate [3sin(x)+2]2 with respect to x
(60 seconds)
[6cos(x)][3sin(x)+2]
400
A student creates a challenge for his friend. He first draws a square, the adds the line for each of the 2 diagonals. Finally, he asks his friend to draw the circle that has the most intersections possible. How many intersections will this circle have?
(45 seconds)
12
500
A curve has equation y = (3x+1)^2/60 and a point is moving along the curve. Find the x-coordinate of the point on the curve at which the x- and y-coordinates are increasing at the same rate.
(75 seconds)
x = 3
500
The population of a city increased by 25% in one year. The next year, it decreased by 20% of the new population. This new population was increased by 50% in the year after that. If the initial population was 40,000 people, what is the final population?
(75 seconds)
60,000
500
A car manufacturer states that a particular car uses 5 litres of fuel in travelling 100 km and produces 110 g of Carbon Dioxide for each km travelled. Use this information to calculate the mass of Carbon Dioxide for each litre used. Give your answer in kilograms.
(90 seconds)
2.2 kg
500
Given that y= x+cos(x), by finding dy/dx, evaluate the approximate change in y when x increases from pi/6 to pi/5
(90 seconds)
pi/60
500
The diagonal of a rectangle exceeds the length by 2. If the width is 10 cm, find the length
(75 seconds)
24 cm