Numbers
A school spends 3/8 of its budget on salaries and 1/5 on utilities. What fraction of the budget remains?
17/40
Solve for x
3x -8 = 19
9
In a right-angled triangle, if the hypotenuse is 10 cm and one side is 6 cm, what is the third side?
8 cm
Find the midpoint of (2, 4) and (8, 10)
(5,7)
The frequencies of five classes are:
12, 18, 31, 24, 15
What is the modal class frequency?
31
A company divides its profits among three departments in the ratio 7 : 4 : 9. If the largest department receives $18,900, what is the total profit?
$42,000
3x/ (x+2) - 2/ (x+2)
(3x-2)/(x+2)
A ladder 10 m long rests against a wall. Its base is 6 m from the wall.
What angle does the ladder make with the ground?
53°
Find the equation of a line with gradient 3 passing through (0,4)
y = 3x + 4
A survey shows:
What angle represents Cricket on a pie chart?
72°
A loan of $25,000 is taken at 8% simple interest for 2½ years. The borrower repays $12,000 after one year. How much remains to be repaid at the end of the loan period?
$18,000
If p*q = 2p+q, find 4*3
11
From a point P, the angle of elevation to the top of a tower is 32°. Moving 20 m closer increases the angle to 48°.
31.4 m
Find the distance between
(-4,7) and (8,-2)
15
Given
f(x)=3x−2 and g(x)=x2
Find f(g(2)).
10
(3.6 x 105 + 2.4 x 104)/ 1.2 x 102
3200
Factorize completely: 8x2 - 18
2(2x-3)(2x+3)
Two right-angled triangles share a common side. One has hypotenuse 13 cm and another has hypotenuse 15 cm. If the shared side is 12 cm, find the total perimeter of the figure formed.
42 cm
Find the gradient of a line perpendicular to the line joining (-3,4) and (5,-8)
2/3
The frequencies of a grouped distribution are:
Class Frequency
10–19 5
20–29 8
30–39 15
40–49 12
What is the mean?
33
A sports field is divided into turf and track in the ratio 11:5. If the track occupies 1,875 m² and 12% of the turf must be resurfaced, find the area to be resurfaced.
495 m²
Karen is x years old. In four years, the product of her age and her brother's age will be 360. Her brother is 8 years older.
Which equation represents the situation?
(x+4)(x+12)=360
A building stands on top of a cliff. The cliff is 80 m high. The angle of elevation from a point on level ground to the top of the cliff is 25°, and to the top of the building is 40°.
If the point is 120 m from the cliff, find the building's height.
20.7 m
A line passes through (3,2) and (7,10). Find the equation of a line parallel to it and passes through the origin.
y=2x
g(x) = (x+2)/(5x+1)
Find g-1(x)
(2-x)/ (5x-1)