NO CALCULATOR. The height, h metres, of a ball t secs after being launched into the air is given by, h = -2t^2 + 8t +7. Find the maximum height reached by the ball.
15 m
100
Phil goes swimming every week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for one year (52 weeks). How far does he swim in the final week?
1730 m or 1.73 km
100
READ MATRICES ACROSS. Find the inverse of the 2x2 matrix [-2, 5, -4, 8].
[2, -5/4, 1, -1/2] *** or *** 1/4 x [8, -5, 4, -2]
100
The bearing of P from Q is 247 degrees. What is the bearing of Q from P?
067 degrees
100
A triangle has sides 5 cm, 8 cm and 11 cm. Find the largest angle in the triangle, giving your answer to 1 decimal place.
113.6 degrees
200
NO CALCULATOR. Solve 2x^2 + 5x - 12 = 0.
(2x - 3)(x + 4) = 0 *** therefore, x = 1.5 or x = -4
200
Find 19 + 23 + 27 + ... + 383.
18,492
200
READ MATRICES ACROSS. The 2x2 matrix [k-2, 8, 3, k] is singular. Find the value(s) of k.
k = -4 or k = 6
200
PQ is a chord of a circle with centre O. PQ has length 12 cm and the circle has radius 7 cm. What angle does PQ subtend at the centre of the circle, i.e. what is the size of angle POQ? Give your answer to 2 decimal places.
117.99 degrees
200
To calculate the height of a building, Andrea measures the angle of elevation of the top of the building as 52 degrees. She then walks 20 meters closer to the building and measures the angle of elevation as 60 degrees. What is the height of the building, correct to 1 decimal place?
98.1 m
300
NO CALCULATOR. A quadratic graph has x-intercepts, -4 and 6. The y-intercept is 6. Find the equation of the graph.
y = a(x + 4)(x - 6) *** substitute x = 0, y = 6 *** a = -0.25 *** therefore, y = -0.25(x + 4)(x - 6)
300
Find 54 + 36 + 24 + ...
162
300
Make X the subject of the following matrix equation, 5XA - B = C.
X = (C + B) (A^-1) / 5
300
Staring at point A, a hiker walks 10 km east and then 3 km southeast finishing at point B. Find the bearing of B from A. Give your answer to 1 decimal place.
099.9 degrees
300
A boat sets sail at 10:00 am from P and travels at 120 km/h on a bearing of 225 degrees. A second boat sets sail at 10:10 am from P and travels at 90 km/h on a bearing of 100 degrees. How far apart are the boats at 10:25 am? Give your answer to 1 decimal place.
71.6 km
400
NO CALCULATOR. Write y = 3x^2 - 12x + 5 in the form, y = a(x - h)^2 + k [i.e. vertex form].
y = 3(x - 2)^2 - 7
400
In a geometric series, the sum of the first two terms is 28. The sum of the second and third terms is 84. Find the sum of the first eight terms.
22,960
400
Solve the simultaneous equations, x + 2y = 7 *** -3x + y – z = 10 *** 2x – 2y + z = –12.
x = -3 *** y = 5 *** z = 4
400
A cuboid has sides 2 cm, 3 cm and 6 cm. Find the angle between the internal diagonal of the cuboid and the face of the cuboid with the largest area. Give your answer to 1 decimal place.
16.6 degrees
400
In a triangle, angle A is 45 degrees, angle B is 60 degrees and side BC is 5 cm. What is the EXACT length of side AC?
5 (sq. root 6) / 2
500
A quadratic graph, y = ax^2 + bx + c, opens downwards, and is tangent to the x-axis. The line of symmetry of the graph is on the right of the y-axis. Determine whether a, b, c and (b^2 - 4ac) are positive, negative or zero.
a ~ negative *** b ~ positive *** c ~ negative *** b^2 - 4ac ~ zero
500
Scheme A offers a starting salary of $11,000 in the first year and then an annual increase of $400 per year. Scheme B offers a starting salary of $10,000 dollars in the first year and then an annual increase of 4% of the previous year’s salary. Find the minimum number of years needed for the total salary earned under Scheme B to exceed the total salary earned under Scheme A.
20 years
500
Make X the subject of the following matrix equation, ABX + 2X = C.
X = [(AB + 2I)^-1] x C
500
From the top of a cliff 100 m above sea level a boat is observed due south at an angle of depression of 30 degrees. The boat travels due east at constant speed and 5 minutes later its angle of depression is 18 degrees. Find the speed of the boat. Give your answer to 2 decimal places.
50.88 m/min.
500
In a triangle ABC, a = 10 cm, c = 6 cm and angle C = 30 degrees. Find the two possible values of angle B. Give your answers to 1 decimal place.