"Geometric and Trigonometry" question number distribution across years

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Mathematics index on skoool nigeria

JAMB questions for "Mathematics :: Geometric and Trigonometry"

Q1

A cylindrical pipe 50m long with radius 7m has one end open. What is the total surface area of the pipe?

A

749π m^{2}

B

700π m^{2}

C

350π m^{2}

D

98π m^{2}

E

**Answer:** A

Q3

The interior angles of a quadrilateral are (x + 15)°, (2x - 45)°, (x - 30)° and (x + 10)°. Find the value of the least interior angle.

A

112°

B

102°

C

82°

D

52°

E

**Answer:** B

Q4

From the cyclic quadrilateral TUVW above, find the value of x.

A

20°

B

23°

C

24°

D

26°

E

**Answer:** C

Q5

If the two smaller size of a a right angled triangle are 4cm and 5cm, find its area.

A

24cm^{2}

B

10cm^{2}

C

8cm^{2}

D

6cm^{2}

E

**Answer:** B

Q6

An arc subtends an angle of 50° at the centre of circle radius 6cm. Calculate the area of the sector formed.

A

80/7cm^{2}

B

90/7cm^{2}

C

100/7cm^{2}

D

110/7cm^{2}

E

**Answer:** D

Q7

What is the locus of points that is equidistant from points P (1, 3) and Q (3, 5)?

A

y = x - 6

B

y = - x + 6

C

y = - x - 6

D

y = x + 6

E

**Answer:** B

Q8

If the area of DPQR above is 12√3cm^{2} find the value of q?

A

5cm

B

6cm

C

7cm

D

8cm

E

**Answer:** B

Q9

What is the locus of the mid - point of all chords of length 6cm with a circle of radius 5cm and with centre O?

A

A circle of radius 4cm and centre O

B

The perpendicular bisector of the chords

C

A straight line passing through centre O

D

A circle of radius 6cm and with centre O

E

**Answer:** B

Q10

Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is constant)

A

x + y = 0

B

x - y = 0

C

x + y + k = 0

D

x - y - k = 0

E

**Answer:** D

Q11

Find the radius of a sphere whose surface area is 154cm². (π = 22/7)

A

7.00 cm

B

3.50 cm

C

3.00 cm

D

1.75 cm

E

**Answer:** B

Q12

A chord is drawn 5cm away from the centre of a circle of radius 13cm. Calculate the length of the chord.

A

7 cm

B

9 cm

C

12 cm

D

24 cm

E

**Answer:** D

Q13

If the hypotenuse of a right-angled isosceles triangle is 2 cm, what is the area of the triangle

A

1/√2 cm²

B

1 cm²

C

2 cm²

D

2√2 cm²

E

**Answer:** B

Q14

In the figure above, **TS**//**XY** and **XY** = **TY**, angle **STZ** = 34°, angle **TXY**= 47°, find the angle marked n.

A

47°

B

52°

C

56°

D

99°

E

**Answer:** B

Q15

A regular polygon has 150° as the size of each interior angle. How many sides does it have?

A

12

B

10

C

9

D

8

E

**Answer:** A

Q16

Find the acute angle between the straight lines y = x and = √3x

A

15°

B

30°

C

45°

D

60°

E

**Answer:** A

Q17

If y = 3 cos 4x, dy/dx equals

A

6 sin 8x

B

-24 sin 4x

C

12 sin 4x

D

-12 sin 4x

E

**Answer:** D

Q18

A cliff on the bank of a river is 300 meters high. If the angle of depression of a point on the opposite side of the river is 60°, find the width of the river.

A

100m

B

75√3m

C

100√3m

D

200√3m

E

**Answer:** C

Q19

Find the value of sin 45° - cos 30°

A

2 + √6/4

B

√2 + √3/4

C

√2 + √3/2

D

√2 - √3/2

E

**Answer:** D

Q20

What is the value of r if the distance between the points (4, 2) and (1, r) is 3 units?

A

1

B

2

C

3

D

4

E

**Answer:** B

Q21

What is the value of p if the gradient of the line joining (-1, p) and (p, 4) is 2/3?

A

-2

B

-1

C

1

D

2

E

**Answer:** D

Q22

Find the exterior angle of a 12 sided regular polygon

A

12°

B

24°

C

25°

D

30°

E

**Answer:** D

Q23

Find the number of ways of selecting 6 out of 10 subject for an examination.

A

218

B

216

C

215

D

210

E

**Answer:** D

Q24

A student sitting on a tower 68 meters high observes his principal's car at an angle of depression 20°. How far is the car from the bottom of the tower to the nearest metre?

A

184m

B

185m

C

186m

D

187m

E

**Answer:** D

Q26

Calculate the distance between points L (-1, -6) and M (-3, -5)

A

√5

B

2√3

C

√20

D

√53

E

**Answer:** A

Q27

Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

A

3/2

B

2/3

C

-2/3

D

-3/2

E

**Answer:** B

Q28

The locus of a point equidistant from two points P(6,2) and R (4, 2) is a perpendicular bisector or PR passing through

A

(2, 5)

B

(5, 2)

C

(1, 0)

D

(0, 1)

E

**Answer:** B

Q29

Find the capacity in litres of a cylindrical well of radius 1 metre and depth 14 metres

A

44000 litres

B

4400 litres

C

440 litres

D

44 litres

E

**Answer:** A

Q30

Find the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle.

A

30°

B

45°

C

60°

D

90°

E

**Answer:** C

Q31

Find the area of the figure beside

A

12.5 cm²

B

75.0 cm²

C

78.5 cm²

D

84.8 cm²

E

**Answer:** D

Q33

If the lines 2y - kx + 2 = 0 and y + k - k/2 = 0 intersect at (1, 2), find the value of k.

A

-4

B

-3

C

-2

D

-1

E

**Answer:** C

Q34

A particle P moves between points S and T such that angle SPT is always constant. Find the locus of P

A

It is a semi-circle with ST as diameter

B

It is a perpendicular bisector of ST

C

It is a quadrant of a circle with ST as diameter

D

It is a straight line perpendicular to ST

E

**Answer:** A

Q35

Make L the subject of the formula if d = √(42W/5L)

A

√(42W/5d)

B

(42W/5d²)

C

42/5dW

D

1/d√42W/5

E

**Answer:** B

Q36

Calculate the length of an arc of a circle of diameter 14cm, which subtends an angle of 90° at the centre of the circle.

A

7π/2 cm

B

7π cm

C

14π cm

D

7π/4 cm

E

**Answer:** A

Q37

In the parallelogram PQRS above, find angle SQR.

A

100°

B

80°

C

50°

D

30°

E

**Answer:** A

Q38

A man 40m from the foot of a tower observes the angle of elevation of the tower to be 30°. Determine the height of the tower.

A

^{40√3}/_{3} m

B

20 m

C

40√3 m

D

40 m

E

**Answer:** A

Q39

Find the locus of points equidistant from two straight lines y - 5 = 0 and y - 3 = 0

A

y -2 = 0

B

y - 4 = 0

C

y - 1 = 0

D

y - 3 = 0

E

**Answer:** B

Q40

What is the value of k if the mid-point of the line joining (1 - k, -4) and (2, k + 1) is ( -k, k)?

A

-3

B

-1

C

-4

D

-2

E

**Answer:** A

Q41

Find the size of each exterior angle of a regular octagon.

A

51°

B

45°

C

40°

D

36°

E

**Answer:** B

Q42

Find the value of tan 60° - tan 30°/ tan 60° + tan 30°

A

4/√3

B

2/√3

C

1

D

1/2

E

**Answer:** D

Q43

The area of a square is 144 sqcm. Find the length of the diagonal.

A

13cm

B

12√2 cm

C

12 cm

D

11√3 cm

E

**Answer:** B

Q44

The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). Find the equation of the curve.

A

y = x^{2} + 14x + 11

B

y = x^{2} + 7x + 9

C

y = x^{2} + 7x - 18

D

y = x^{2} +7x +18

E

**Answer:** C

Q45

What is the locus of points equidistant from the line ax + by + c = 0?

A

A line ax + by + q = 0

B

A line ax - by + q = 0

C

A line bx - ay + q = 0

D

A line bx + ay + q = 0

E

**Answer:** B

Q46

In the Diagram above , POQ is a diameter of the circle PQRS. If ‹PSR = 145°, find x°

A

45°

B

25°

C

55°

D

35°

E

**Answer:** C

Q47

In the diagram above, /QR/ is the diameter of the semicircle QR. Find the area of the figure to the nearest whole number.

A

80 cm^{2}

B

70 cm^{2}

C

90 cm^{2}

D

89 cm^{2}

E

**Answer:** D

Q48

**PQRSTW** is a regular hexagon and QS intersects **RT** at **V**. Calculate ‹ **TVS.**

A

60°

B

90°

C

120°

D

30°

E

**Answer:** B

Q49

If the locus of the points which are equidistant from points** P **and** Q **meets line **PQ** at point** N**, then **PN **equals

A

1/2** NQ **

B

2**NQ**

C

1/4**NQ**

D

**NQ**

E

**Answer:** D

Q50

In the diagram above, **PQ** = 10cm, **PS** = 8cm and ‹**PSR** is 60° while ‹**SRQ** is a right angle. Find **SR **

A

14√3cmB

B

14cm

C

10√3cmD

D

10cm

E

**Answer:** B

Q51

In the diagram above, find the value of x/.

A

45°

B

55°

C

40°

D

50°

E

**Answer:** A

Q52

In triangle **XYZ**, <**XYZ** = 15°, <**XYZ** = 45° and /**XY**/ = 7cm. Find /**YZ**/.

A

7√2cm

B

7cm

C

14√2cm

D

^{7/2 }√^{ }6cm

E

**Answer:** D

Q53

The solution set of the faded area above is

A

y = x ≥ 4, y ≤ x

B

y ≤ x, y + x ≤ 4 and y ≥ 0

C

y ≥ 0, y ≥ x and y + x ≤ 4

D

y ≤ x, y + x ≤ 4

E

**Answer:** B

Q54

The sum of the first n positve integers is

A

n(n-1)

B

n(n+1)

C

1/2n(n+1)

D

1/2n(n-1)

E

**Answer:** C

Q55

The sum of the interior angles of a regular polygon is 1800°. Calculate the size of one exterior angle of the polygon.

A

12°

B

18°

C

30°

D

24°

E

**Answer:** C

Q56

Two lines PQ and ST intersect at 75°. The locus of points equidistant from PQ and ST lies on the

A

bisector of the angles between lines PQ and ST

B

bisector of the angles between lines PT and QS

C

perpendicular bisector of ST

D

perpendicular bisector of PQ

E

**Answer:** A

Q57

A chord of a circle substends angle of 60° at the centre of a circle of radius 14cm. Find the length of the chord.

A

21cm

B

7cm

C

28cm

D

14 cm

E

**Answer:** D

Q58

From the diagram below, find the bearing of **R** and **S **

A

224°

B

136°

C

134°

D

226°

E

**Answer:** A

Q59

In the diagram below, **O** is the centre of the circle <**UOT** = 70° and <**RST** = 100°. Calculate <**RUO**.

A

50°

B

20°

C

80°

D

25°

E

**Answer:** B

Q60

A sector of a circle has an area of 55cm^{2}. If the radius of the circle is 10cm, calculate the angle of the sector.

A

90°

B

75°

C

63°

D

45°

E

**Answer:** C