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Pythagoras & Trigonometry (AQA GCSE Maths: Foundation): Exam Questions

2 hours33 questions
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1
Sme Calculator2 marks
q21b-0580-0980-w20-oct-nov-2020-cie-igcse-maths

Calculate the value of k.

k equals...............................

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2
Sme Calculator2 marks
qp7e-0580-31-paper-3-oct-nov-2019-cie-igcse-maths

The diagram shows a flagpole in a garden.
The flagpole has height 25 m.
A rope from the top of the flagpole is tied to the ground 8m from its base.

Calculate the length of this rope.

................................................ m 

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3
Sme Calculator2 marks

The diagram shows a right-angled triangle.

qp14-0580-13-paper-1-oct-nov-2019-cie-igcse-maths

Show that the value of x is 41.8, correct to 3 significant figures.

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4
Sme Calculator2 marks
q4e-058031-mayjune2019-cie-igcse-maths-core

Calculate P R.

P R = ......................................... cm 

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5
Sme Calculator2 marks
q23-058012-march2018-cie-igcse-maths-core

Calculate A C.

A C space equals........................... m

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6
Sme Calculator2 marks
q21a-0580-0980-w20-oct-nov-2020-cie-igcse-maths

Calculate the value of x.

x equals............................

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7
Sme Calculator2 marks
qp17-0580-12-paper-1-march-2020-cie-igcse-maths

The diagram shows a right-angled triangle A B C.
Calculate A B.

A B space equals..........................m

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8
Sme Calculator2 marks
q12-058011-mayjune2019-cie-igcse-maths-core

The diagram shows a right-angled triangle.

Calculate the value of x.

x = ..................................... 

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9
Sme Calculator2 marks

The diagram shows a right-angled triangle.

q7-058012-octnov2018-cie-igcse-maths-core

Use trigonometry to calculate the value of x.

x space equals .............................. [2]

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10
Sme Calculator2 marks
q16-058013-mayjune2018-cie-igcse-maths-core

The diagram shows a right-angled triangle.

Calculate the value of x.

x space equals............................ [2]

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11
Sme Calculator1 mark

Write down the value of sin 45°.

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1
Sme Calculator3 marks
qp22-0580-13-paper-1-nov-2020-cie-igcse-maths

Calculate P Q.

P Q = ........................................... cm

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2
Sme Calculator3 marks
qp7c-0580-32-paper-3-may-2020-cie-igcse-maths

The diagram shows a rectangle 14cm by w spacecm.
The diagonal is 23 cm.

Calculate the value of w.

w space equals space................................................. space

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3
Sme Calculator3 marks
qp19-0580-12-paper-1-oct-nov-2019-cie-igcse-maths-1

The diagram shows a right-angled triangle.

Calculate the value of x.

x space= ...................................................

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4
Sme Calculator2 marks
q7d-058032-mayjune2019-cie-igcse-maths-core

The diagram shows a right-angled triangle A B C.
Calculate the length of A B.

A B = ................................................m 

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5
Sme Calculator3 marks
q18-058012-mayjune2018-cie-igcse-maths-core

The diagram shows a rectangular playground A B C D. A B space equals space 23.4m and A C space equals space 35.1m.

Calculate B C.

B C space equals ............................ m [3]

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6
Sme Calculator3 marks
qp22-0580-12-paper-1-nov-2020-cie-igcse-maths

Show that the value of x is 27.2, correct to 3 significant figures.

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7
Sme Calculator3 marks
qp8c-0580-33-paper-3-nov-2020-cie-igcse-maths

Calculate the value of x.

x space= ................................................. 

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8
Sme Calculator2 marks
qp8c-0580-03-paper-3-specimen-2020-cie-igcse-maths

Use trigonometry to calculate the value ofspace p.

p = ..............................................

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9
Sme Calculator3 marks
qp21-0580-11-paper-1-oct-nov-2019-cie-igcse-maths

Use trigonometry to calculate the value of x.

x = ................................................... 

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10
Sme Calculator2 marks
q13-058012-mayjune2019-cie-igcse-maths-core

The diagram shows a right-angled triangle.

Calculate the value of x.

x space equals .............................................. 

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11
Sme Calculator2 marks
q23-058012-march2018-cie-igcse-maths-core

Calculate the size of angle B A C.

Angle B A C = ............................

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12a
Sme Calculator1 mark

Write down the exact value of cos30°

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12b
Sme Calculator2 marks
SjGh85dW_q8b-easy-4-10-right-angled-triangle-edexcel-gcse-maths

Given that sin30° = 0.5,
work out the value of x.

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1
Sme Calculator3 marks

The length of one side of a rectangle is 12cm.
The length of the diagonal of the rectangle is 13cm.

Calculate the area of the rectangle.

.......................................... cm2 

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2
Sme Calculator3 marks
q26-058012-march2019-cie-igcse-maths-core

Triangles A B C and B C D are both right-angled triangles.

Calculate the value of y.

y space equals space................................ 

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3
Sme Calculator6 marks
q9-058031-octnov2018-cie-igcse-maths-core

The diagram shows a field in the shape of a trapezium. A B space equals space 150 space straight m comma space B C space equals space 90 space straight m and C D space equals space 120 space straight m.
Angle A B C = angle B C D = 90 degree.

i) Show that A D space equals space 95 m, correct to the nearest metre.

[3]

ii) A fence is built around the perimeter of the field.
It costs $ 48 to build each 5-metre section of the fence.
Calculate the cost of building this fence.

$ .................................... [3]

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4
Sme Calculator4 marks

Sam has a rectangular pond, A B C D.

q8a-058033-octnov2018-cie-igcse-maths-core

i) Calculate B C.

B C = ...............................m [3]

ii) He puts a fence around the edge of the pond. Calculate the length of the fence.

................................m [1]

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5
Sme Calculator3 marks
cie-igcse-2020-march-p2-tz2-q7a

The diagram shows a right-angled triangle.

Calculate the perimeter.

............................................ cm [3]

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6
Sme Calculator6 marks
qp9b-0580-33-paper-3-may-2020-cie-igcse-maths

A speedboat starts at X and travels to Y, then to Z and then back to X.
Z is due south of X and Y is due west of Z.
X Y = 39km and X Z = 21 km.

i) Calculate Y Z.

Y Z equals.............................km [3]

ii) Calculate angle Y X Z.

Angle Y X Z = ......................[2]

iii) Find the bearing ofspace Y spacefrom X.

[1]

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7a
Sme Calculator2 marks
q24-058013-mayjune2019-cie-igcse-maths-core

A vertical flagpole, B D, stands on horizontal ground and is held by two ropes, A D and C D.
A D space equals space 15 straight m comma space B C space equals space 10.7 straight m and angle D A B space equals space 38 degree.

Using trigonometry, calculate B D.

B D = ...............................m 

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7b
Sme Calculator2 marks

Calculate C D.

C D space equals space.......................... m 

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8a
Sme Calculator3 marks
q26-058012-march2019-cie-igcse-maths-core

Triangles A B C and B C D are both right-angled triangles.

Calculate the value of y.

y space equals space................................

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8b
Sme Calculator2 marks

Calculate the value of x.

x space equals .................................

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9
Sme Calculator9 marks
q9-058031-mayjune2018-cie-igcse-maths-core

A comma space B and C are points on the circumference of a circle, centre O. Angle A B C equals 90 degree.

.[1]

A B space equals space 20 space cm space and space A C space equals space 52 cm.

i) Use trigonometry to calculate angle B A C.

Angle B A C = ............................. [2]

ii) Show that B C = 48cm.

[2]

iii) Work out the area of triangle A B C.

........................... cm2 [2]

iv) Work out the total shaded area.

............................... cm2 [3]

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10
Sme Calculator3 marks

The diagram shows two vertical phone masts, A B and C D, on horizontal ground.

q12-4ma1-2hr-qp-jan22-paper2-igcse-maths

A B equals 6.2 space straight m      A C equals 244 space straight m     C D equals 30.7 space straight m

Work out the size of the angle of depression of B from D
Give your answer correct to one decimal place.

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