ALGEBRA
NUMBER
PROBLEM SOLVING
TRIGONOMETRY
GEOMETRY
100
3x=1/243. Find x
(30 seconds)
-5
100
An engine pulls four identical carriages. The engine is ⅔ the length of a carriage and the total length of the train is 86.8 m. Find the length of the engine.
(45 seconds)
12.4 m
100
Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did Mary pick?
(45 seconds)
12 kg
100
If sin(x°)=0.5, then find the value of the constant a when sin(ax°)=1.
(60 seconds)
a = 3
100
Find x:
(30 seconds)
31
200
Rationalise the denominator and simplify.
1/(√x-√8)
(60 seconds)
(√x+√8)/(x-8)
200
A sum of $5000 is invested in a bank offering a simple interest rate of 8% per annum. How many years will it take for the amount to double?
(75 seconds)
12.5 years
200
50 students are asked about their preferred movie categories. 26 like comedy, 15 like both and 8 like neither action nor comedy. Using a Venn diagram or otherwise, find the number of students who like action but not comedy.
(45 seconds)
16
200
If A is acute and cos(A)=⅘, find the value of tan(A)
(45 seconds)
3/4
200
Given that triangle XYZ is similar to triangle ABC, and the ratio of XY to AB is 3:5, if AB = 15 cm, find the length of XY.
(30 seconds)
9 cm
300
Given that x+1 is a factor of 3x3 -14x2 - 7x + d, find the value of d.
(60 seconds)
10
300
A new scooter is values $15 000. At the end of each year its value is reduced by 15% of its value at the start of the year. What will it be worth after 3 years?
(60 seconds)
$9211. 88
300
All of 60 different vitamin pills contain at least one of the vitamins A, B and C. 12 have A only, 7 have B only, and 11 have C only. If 6 have all three vitamins and there are x having A and B only, B and C only and A and C only, how many pills contain vitamin A?
(75 seconds)
34
300
A triangle ABC has angle A as 30° and angle B as 45°. Side AC has the length of 12 cm. Find the area of the triangle ABC (give in the form of a decimal up to two d.p. or in the form a√b + c)
(75 seconds)
18√3 + 18 cm2
49.18 cm2
300
Find a and b:
(30 seconds)
A = 63 b =59
400
Factorise the following cubic polynomial:
3x3 - 10x2 + 9x - 2
(75 seconds)
(x-1)(x-2)(3x-1)
400
The ratio of the number of marbles that Alice, Bob, and Carol have is 5:3:2. If Alice has 50 marbles more than Bob, how many marbles does Carol have?
(60 seconds)
20 marbles
400
The perimeters of a square and a rectangle are equal. One side of the rectangle is 11 cm and the area of the square is 4 cm2 more than the area of the rectangle. Find the length of the side of the square given it is less than 20cm.
(75 seconds)
9 cm.
400
Given that cot2θ = 1/(y+2) and secθ = x - 4, find y in terms of x.
(90 seconds)
y = (x-4)2 - 3 OR
y = x2-8x+13
400
Triangles ABC and DEF are similar.Side AB of triangle ABC corresponds to side DE of triangle DEF and so on. If the length of AB is 10 cm and the length of DE is 4 cm, express the area of triangle DEF as a fraction, percentage or decimal of triangle ABC.
(60 seconds)
4/25ths of ABC or 16% of 0.16
500
Find the coefficient of x6 in the expansion of (1+2x)8
(90 seconds)
1792
500
Evaluate 7321 mod 11
(105 seconds)
6
500
The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2,the fraction is increased by 1/12 Find the original fraction.
(90 seconds)
3/4
500
By finding the value of dy/dx for y=1-3cos(2x) at the point where x= pi/12, Obtain the approximate change in y when x increases from pi/12 to pi/11
(90 seconds)
pi/44
500
In the xy-plane, the graph of 2x2-6x+2y2+2y=45 is a circle. What is the radius of this circle (in units)?
(120 seconds)
5 units