Algebraic Techniques
Algebraic Techniques
Right Angled Triangles
Right Angled Triangles
Equations
100
Simplify the following expression:
4x + 3y -x +2 + 6y
3x + 9y + 2
100
Solve the following expression when
x = 4
2x^2 -7
25
100
What is the Pythagoras' Theorem for the triangle below?
b^2+c^2=a^2
100
Find c:
c = 15
100
A school purchases science kits for a class. The total cost is $432 and the school bought 18 kits. How much did each science kit cost?
$24
200
A phone company charges a monthly fee of $18 plus $4 for every gigabyte (g) of data used. Write an expression that represents the total monthly cost
18 + 4g
200
A rectangular garden has a length of 3a meters and a width of 2a meters. Write an expression that represents the area of the rectangle.
6a^2
200
Find c. Leave your answer in surd form.
c = sqrt(98)
200
Find c correct to 1 decimal place.
c = 12.5
200
A rectangular garden has a perimeter of 60 meters. The garden is 14 meters long. What is the width of the garden?
16m
300
A school buys 3(x + 5) rulers and 2(x - 4) protractors.
Write a simplified expression for the total number of items purchased.
5x + 7
300
Simplify the following expression:
(4w^5xy^3)/(2w^2x^2y^5)
(2w^3)/(xy^2)
300
Is the triangle below right angled?
No
300
A man flies a kite on a 14m long string. Above him, the kite is 9m away horizontally. What is the vertical height of the kite from the ground? Leave your answer in surd form.
sqrt115 m
300
The area of a rectangle is 84 square centimeters. One side has a length of (x + 2) cm, while the other side is 7 cm. Find the value of x.
x = 10
400
The perimeter of a rectangle is represented by:
6x+18
The width is
x+2
2x + 7
400
Write an algebraic expression and expand it to represent the area of the triangle below:
m+3m^2
400
A rectangular park has an area of 240 square meters. Find the diagonal length of the park if the width of the park is 15m. Give your answer in cm to 1 dp.
2193.2cm
400
Two trees are 12 meters apart, joined by a cable. It is attached two meters above the ground to one tree and 11 meters above the ground to the other. Find the length of the cable.
15 m
400
A school bus can carry 48 students. There are already 15 students on the bus. At the next stop, the same number of students get on at each of 3 bus stops. After the 3rd stop, the bus is full. How many students get on at each stop?
11 students.
500
Yesterday, Gareth walked x kilometers in a National Park. The first day he completed 1/5 of the total distance. The second day he walked a further 1/3 of the total distance. Write a simplified algebraic fraction to represent the total distance covered by Gareth in the first two days.
(8x)/15
500
Fully factorise the following expression:
24p^2qr^3+18p^3q^2 +6p^2qr^2
6p^2q(4r^3+3pq+r^2)
500
An isoceles triangle has two equal sides of length 10cm, and a third side of length 15cm. Find the perpendicular height to 1 dp.
6.6 cm
500
A builder has a 7.5m ladder to reach the roof of a garage. The roof is 6.4m high and the base of the ladder must be placed 4.2m from the wall. He finds that the ladder is too short to reach the roof. By how many cm is the ladder too short?
15cm
500
A taxi company charges a fixed booking fee plus a per-kilometer rate. A 14km trip costs $33.20. The booking fee is $5. What is the cost per km? Give your answer to the nearest cent.
$2.01