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100
There are 120 shops in the high street, 35% of which sell food. How many high street shops do not sell food? [1 minute]
78
100
Solve the equation, 2x - 5 = -10. [1 minute]
-2.5
100
What is the gradient of the line joining the points, (2, 5) and (4, -9)? [1 minute]
-7
100
What information is needed in order to fully describe a rotation? [1 minute]
(1) the centre, (2) the angle, (3) the direction (ACW or CW)
100
Find the mean, median and mode of 11, 5, 8, 6, 5. [1 minute]
mean = 7, median = 6, mode = 5
200
After paying 20% as a deposit for a car, Geoff still has to pay $140,000. Find the cost of the car. [2 minutes]
$175,000
200
If A = 2, B = 4, C = -5, evaluate C(A - B) - C x C. [1 minute]
-15
200
A line has gradient -1.25. Find the gradient of a line that is perpendicular to this line. [1 minute]
4/5 or 0.8
200
The Sears Tower in Chicago is the tallest skyscraper in the US. If the Sears tower casts a shadow that is 1,160 feet long while a parking meter that is 5 feet tall casts a 4 foot shadow, how tall is the Sears Tower? [2 minutes]
1,450 feet
200
The mean of 10 numbers is 8. If an eleventh number is now included in the data set, the mean increases by 2. Find the eleventh number. [1 minute]
30
300
Last year, the ratio of girls to boys in the Maths Club was 2:5. This year, there are 22 new members. As a result, there are 4 times as many girls, and twice the number of boys, as last year. How many students are there in the Maths Club now? [3 minutes]
36
300
Factorise fully the expression, pa - qb - pb + qa. (Hint: you must end up with a PRODUCT.) [3 minutes]
(p + q) (a - b)
300
Find the equation of the line which passes through (-4, 7) and which is parallel to line with equation, 1/2 x + y = 11. [2 minutes]
y = -0.5x +5
300
In triangle ABC, angle B = 100 degrees, angle C = 30 degrees, AB = 11 cm, BC = 18 cm and AC = 23 cm. In triangle PQR, angle Q = 50 degrees, angle R = 100 degrees and QR = 16.5 cm. Find PQ. [4 minutes]
34.5 cm
300
What are the conditions for an Euler route to exist? [2 minutes]
EITHER the degree of every vertex has to be even (=> circuit) OR there have to be exactly two vertices of odd degree (=> path).
400
A car travels 120 km in four and a quarter hours and a train travels 800 m in 40 secs. Find the ratio of the speed of the car to the speed of the train in the form a:b, where a and b are whole numbers. [4 minutes]
20 : 51
400
Solve the equation, 2/3 (x - 5) + 2x = 7 - 3(6 - x). [4 minutes]
23
400
The line with equation y = 0.25x - 6 cuts the coordinate axes at P and Q. Find the area of triangle POQ, where O is the origin. [4 minutes]
72 units squared
400
There is a single transformation which is equivalent to: a reflection in the y-axis, followed by a 90 degree ACW rotation about the origin. What is this single transformation? [4 minutes]
Reflection in y = -x
400
5, 6, 7, 6, 2, 8, 9, 8, 4, 6, 20, 4, 5, 4, 3, 6, 6. Find the range and the IQR for the above set of data. Explain which of these two measures of spread is more appropriate in this case. [4 minutes]
Range = 18, IQR = 3.5; IQR is more appropriate because it ignores the anomalous data value, 20.
500
Lucy bought 200 belts at a cost price of $15 each. She sold 2/5 of them for $x and the rest at 20% more than the cost price. She made a profit of $456. Find what percentage x is above the cost price. [5 minutes]
8%
500
A sparrow flies to see a friend at a speed of 4 km/h. His friend is out, so the sparrow immediately returns home at a speed of 6 km/h. The complete journey took 60 minutes. How far way does his friend live? [6 minutes]
2.4 km
500
The point (-36, k) lies on the line joining the points (1, 2) and (10, -5). Find k. [5 minutes]
277/9 (or 30 7/9)
500
One of the vertices of a square has coordinates, A(2, -3). The square is translated by vector [-5, -1], followed by a reflection in the x-axis, followed by an enlargement, centre (-1, 1), scale factor 2, followed by a 90 degree CW rotation about the origin. Find the coordinates of A', the image of A, after these 4 transformations. [5 minutes]
(7, 5)
500
Three positive integers p, q and r, where p < q < r, are such that their median is 17, their mean is 19 and their range is 12. Find p. [4 minutes]
14