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ALGEBRA1

The document contains a series of algebra problems requiring the solution of equations, calculation of areas, and determination of perimeters involving rectangles, triangles, and trapeziums. Each problem includes specific tasks such as showing work, solving quadratic equations, and providing answers to a specified number of decimal places. The problems are structured to test understanding of algebraic concepts and geometric properties.

Uploaded by

Shweta Bhasker.
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15 views6 pages

ALGEBRA1

The document contains a series of algebra problems requiring the solution of equations, calculation of areas, and determination of perimeters involving rectangles, triangles, and trapeziums. Each problem includes specific tasks such as showing work, solving quadratic equations, and providing answers to a specified number of decimal places. The problems are structured to test understanding of algebraic concepts and geometric properties.

Uploaded by

Shweta Bhasker.
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ALGEBRA1

1. Showing all your working, solve

5x
(a) – 9 = 0,
2

Answer (a) x = ………………….…………


[2]

(b) x2 + 12x + 3 = 0, giving your answers correct to 1 decimal place.

Answer (b) x = ……..…… or x = …………


[4]

1
2.

(x + 4) cm

R 4x cm

Q (x + 2) cm

(x + 12) cm NOT TO SCALE

(a) (i) Write down an expression for the area of rectangle R.

Answer (a) (i) …….…………………. cm2


[1]

(ii) Show that the total area of rectangles R and Q is 5x2 + 30x + 24 square centimetres.

[1

(b) The total area of rectangles R and Q is 64 cm2.


Calculate the value of x correct to 1 decimal place.

Answer (b) x = …………………………….


[4]

2
3.

150 cm
7x cm

24x cm NOT TO SCALE

The right-angled triangle in the diagram has sides of length 7x cm, 24x cm and 150 cm.

(a) Show that x2 = 36

[2]

(b) Calculate the perimeter of the triangle.

Answer (b) ……..….………………… cm


[1]

3
4.

2y – 1
y

y+2 NOT TO SCALE

The diagram shows a right-angled triangle.


The lengths of the sides are given in terms of y.

(i) Show that 2y2 – 8y – 3 = 0.

[3]

(ii) Solve the equation 2y2 – 8y – 3 = 0, giving your answers to 2 decimal places.

[4]

(iii) Calculate the area of the triangle.

[2]

4
5.

(x + 1) cm

A (x + 6) cm D (x + 2) cm C NOT TO SCALE

In triangle ABC, the line BD is perpendicular to AC.

AD = (x + 6) cm, DC = (x + 2) cm and the height BD = (x + 1) cm.

The area of triangle ABC is 40 cm2.

(i) Show that x2 + 5x – 36 = 0.

Answer (i) ……..……….………


[3]

(ii) Solve the equation x2 + 5x – 36 = 0.

Answer (ii) x = ….… or x = ……


[2]

(iii) Calculate the length of BC.

Answer (iii) BC = ……..…… cm


[2]

6.

5
2x + 4

x+2 x

x2 – 40 NOT TO SCALE

The diagram shows a trapezium.


Two of its angles are 90°.
The lengths of the sides are given in terms of x
The perimeter is 62 units.

(i) Write down a quadratic equation in x to show this information. Simplify your equation.

[2]

(ii) Solve your quadratic equation.

[2]

(iii) Write down the only possible value of x.

[1]

(iv) Calculate the area of the trapezium.

[2]

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