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
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].
[-0.5, 1.25, -1, 2] or 0.25x[-2, 5, -4, 8]
100
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
100
A triangle has sides 5 cm, 8 cm and 11 cm. Find the area of the triangle, giving your answer to 1 decimal place.
18.3
200
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)
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
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
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
When 2x^3 + x^2 + bx + 58 is divided by (x + 3) the remainder is 4. Find b.
b = 3
300
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
300
Make X the subject of the following matrix equation, 5XA - B = C.
X = (C + B) (A^-1) / 5
300
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
300
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
400
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
400
The 3rd term of an arithmetic series is 2 and the 6th term is -7. Find the sum from the 10th term to the 20th term inclusive.
-374
400
Solve the simultaneous equations, x + 2y = 7 *** -3x + y – z = 10 *** 2x – 2y + z = –12.
x = -3 *** y = 5 *** z = 4
400
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.
400
In a triangle ABC, a = 10 cm, c = 6 cm and angle C = 30 degrees. Find two possible values of side b, giving the answers to 2 d.p.
5.34 and 11.98 cm
500
Given f (x) = x^2 + (2 – k)x + k^2, find the range of values of k for which f (x) > 0 for all real values of x.
k > 2/3 , k < –2
500
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
500
Make X the subject of the following matrix equation, ABX + 2X = C.
X = [(AB + 2I)^-1] C
500
A regular tetrahedron is inscribed in a sphere (all four vertices are on the sphere). Determine the exact radius of the sphere, if the edges of the tetrahedron are 12 cm long.
3 times sq.rt. of 6
500
In a quadrilateral ABCD, AB = 5 m, AD = 2 m, angle A = 50 degrees, angle B = 80 degrees and angle C = 100 degrees. Find the area of this quadrilateral. Give your answer to 1d.p.