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Mat 12

This document contains a set of sample exam questions focused on quadratic equations and geometry, with a total duration of 50 minutes and a maximum score of 38 marks. It includes various problems requiring the solving of equations, calculating areas, and determining values based on given dimensions. Each question specifies the required working and provides space for answers, emphasizing the need for clear mathematical reasoning.

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pgirly20
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13 views15 pages

Mat 12

This document contains a set of sample exam questions focused on quadratic equations and geometry, with a total duration of 50 minutes and a maximum score of 38 marks. It includes various problems requiring the solving of equations, calculating areas, and determining values based on given dimensions. Each question specifies the required working and provides space for answers, emphasizing the need for clear mathematical reasoning.

Uploaded by

pgirly20
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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SAMPLE QUESTIONS ON EXAMS GO THROUGH PRACTICE AS SET 1234

Quadratic Equations
50 min
38 marks

1. Showing all your working, solve

5x
– 9 = 0,
(a) 2

Answer (a) x = ………………….…………


[2]

2
(b) x + 12x + 3 = 0, giving your answers correct to 1 decimal place.
Answer (b) x = ……..…… or x = …………
[4]
2.

( x + 4 ) cm

R 4 x cm

Q ( x + 2 ) cm

( x + 1 2 ) cm NOT TO SCALE

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

2
Answer (a) (i) …….…………………. cm
[1]

2
(ii) Show that the total area of rectangles R and Q is 5x + 30x + 24 square centimetres.

[1

2
(b) The total area of rectangles R and Q is 64 cm .
Calculate the value of x correct to 1 decimal place.
Answer (b) x = …………………………….
[4]
3.

1 5 0 cm
7 x cm

2 4 x cm NOT TO SCALE

The right-angled triangle in the diagram has sides of length 7x cm, 24x cm and 150 cm.
2
(a) Show that x = 36

[2]

(b) Calculate the perimeter of the triangle.

Answer (b) ……..….………………… cm


[1]
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.
2
(i) Show that 2y – 8y – 3 = 0.

[3]

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

[4]

(iii) Calculate the area of the triangle.


[2]
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.


2
The area of triangle ABC is 40 cm .
2
(i) Show that x + 5x – 36 = 0.

Answer (i) ……..……….………


[3]

2
(ii) Solve the equation x + 5x – 36 = 0.

Answer (ii) x = ….… or x = ……


[2]

(iii) Calculate the length of BC.


Answer (iii) BC = ……..…… cm
[2]

6.

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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