Eisimpleir de cheistean mu ionad grabhataidh

10 Eisimpleirean de Cheistean Meadhan-Tharraing

1. Co-chomharran Meadhan grabhataidh Is e nì a thaobh puing 0…
Deasbad
Tha fios :
Farsaingeachd an nì (A) = (8)(4) = 32
Meadhan-phuing air an x-axis (x) = ½ (8) = 4
Meadhan-phuing air an ais-y (y) = ½ (4) = 2
Chaidh faighneachd Co-chomharran meadhan grabhataidh an nì a thaobh puing 0
Jawab :
2. Àite meadhan grabhataidh nì gu puing 0 tha…
Deasbad
An toiseach, obraich a-mach àirde an nì. Roinn an nì ann an dà thriantan ceart-cheàrnach, far a bheil bonn 4 cm agus hypotenuse 5 cm aig gach triantan ceart-cheàrnach.
Tha fios :
Farsaingeachd nì (A) = ½ (bonn)(àirde) = ½ (8)(3) = (4)(3) = 12
Meadhan-phuing air an x-axis (x) = ½ (8) = 4
Meadhan-phuing air an ais-y (y) = 1/3 (3) = 1
Chaidh faighneachd Co-chomharran meadhan grabhataidh an nì a thaobh puing 0
Jawab :
Is iad co-chomharran meadhan grabhataidh an nì (4, 1) cm.

3. Seall air an ìomhaigh gu h-ìosal! Obraich a-mach (a) suidheachadh meadhan grabhataidh an nì a thaobh puing P (b) suidheachadh meadhan grabhataidh an nì a thaobh taobh PQ.
Deasbad
Tha fios :
Roinn an nì ann an dà phàirt, pàirt 1 = ceart-cheàrnach, pàirt 2 = ceàrnagach.
A₁ = (6)(2) = 12
A₂ = (2)(2) = 4
x₁ = ½ (6) = 3
x₂ = ½ (2) + 2 = 1 + 2 = 3
y₁ = ½ (2) = 1
y₂ = ½ (2) + 2 = 1 + 2 = 3
Chaidh faighneachd Co-chomharran meadhan na grabhataidh an coimeas ri taobh PQ
Jawab :
(a) Tha meadhan grabhataidh an nì an coimeas ri puing P aig (3; 1,5) cm.
(b) Tha suidheachadh meadhan grabhataidh an nì an coimeas ri taobh PQ 1,5 cm

4. Ceist Àir. 10 ann an Deuchainn Nàiseanta SMA/MA Fiosaigs 2015/2016

Seall air an dealbh a leanas!

Is iad co-chomharran meadhan grabhataidh a’ phlèana H-chruthach...

A. (3; 4)

B. (3,5; 2,5)

C. (3,5; 4)

D. (4; 3)

E. (4; 4)

Deasbad

Roinn an nì ann an trì pàirtean.

Raon earrann 1 (A₁) = (2)(6) = 12 cm²

Meadhan-phuing earrann 1 air an x-axis (x₁) = 1/2 (2) = 1 cm

Meadhan-phuing earrann 1 air an ais-y (y₁) = 1/2 (6) = 3 cm

Raon earrann 2 (A₂) = (4)(2) = 8 cm²

Meadhan-phuing earrann 2 air an x-axis (x₂) = 2 + (1/2)(4) = 2 + 2 = 4 cm

Meadhan-phuing earrann 2 air an ais-y (y₂) = 2 + (1/2)(2) = 2 + 1 = 3 cm

Raon earrann 3 (A₃) = (2)(6) = 12

Meadhan-phuing earrann 3 air an x-axis (x₃) = 2 + 4 + (1/2)(2) = 2 + 4 + 1 = 7 cm

Meadhan-phuing earrann 3 air an ais-y (y₃) = 1/2 (6) = 3 cm

Co-chomharran meadhan grabhataidh an nì air an x-axis:

Co-chomharran meadhan grabhataidh an nì air an ais-y:

Is iad co-chomharran meadhan grabhataidh a’ phlèana cumadh-H (x, y) = (4, 3)

Is e D am freagairt cheart.

5. Ceist Àir. 6 ann an Deuchainn Nàiseanta SMA/MA Fiosaigs 2014/2015

Thoir sùil air an raon aon-ghnèitheach leis na tomhasan mar a chithear san dealbh!

Is e suidheachadh meadhan grabhataidh a’ chruth gu h-àrd an coimeas ris an x-axis….

A. 2,0 cm

B. 2,5 cm

C. 3,0 cm

Trast-thomhas 3,5 cm

4,0 cm a dh'fhaid

Deasbad

Roinn an nì ann an 4 pàirtean, is iad sin A, B, C agus D.

Obraich a-mach farsaingeachd gach earrainn.

A_A = ½ (bonn)(àirde) = ½ (1,5)(3) = (1,5)(1,5) = 2,25

A_B = (fad)(leud) = (4,5-1,5)(1) = (3)(1) = 3

A_C = ½ (bonn)(àirde) = ½ (6-4,5)(3) = (1,5)(1,5) = 2,25

A_D = ½ (bonn)(àirde) = ½ (4,5-1,5)(6-3) = ½ (3)(3) = (1,5)(3) = 4,5

y_A = 1/3 (3) = 1

y_B = 1/2 (1) = 0,5

y_C = 1/3 (3) = 1

y_D = 3 + (1/3)(6-3) = 3 + (1/3)(3) = 3 + 1 = 4

Co-chomharran meadhan grabhataidh an nì air an ais-y:

Tha suidheachadh meadhan grabhataidh a’ chumaidh an coimeas ris an x-axis 2 cm.

Is e A am freagairt cheart.

6. Ceist Àir. 6 ann an Deuchainn Nàiseanta SMA/MA Fiosaigs 2014/2015

Seall air an dealbh!

Is iad co-chomharran meadhan grabhataidh na h-ìomhaigh sgìre a leanas….

Deasbad

Roinn an nì ann an 4 pàirtean, is iad sin A, B, C agus D.

Obraich a-mach farsaingeachd gach earrainn.

A_A = (fad)(leud) = (4)(3) = 12

A_B = ½ (bonn)(àirde) = ½ (6-4)(3) = ½ (2)(3) = (1)(3) = 3

A_C = ½ (bonn)(àirde) = ½ (8-6)(3) = ½ (2)(3) = (1)(3) = 3

A_D = (fad)(leud) = (8)(6-3) = (8)(3) = 24

y_A = 1/2 (3) = 1,5

y_B = 3 – (1/3)(3) = 3 – 1 = 2

y_C = 3 – (1/3)(3) = 3 – 1 = 2

y_D = 3 + (1/2)(6-3) = 3 + (1/2)(3) = 3 + 1,5 = 4,5

x_A = 1/2 (4) = 2

x_B = 4 + (1/2)(6-4) = 4 + (1/2)(2) = 4 + 1 = 5

x_C = 6 + (1/2)(8-6) = 6 + (1/2)(2) = 6 + 1 = 7

x_D = 1/2 (8) = 4

Co-chomharran meadhan grabhataidh an nì air an x-axis:

Co-chomharran meadhan grabhataidh an nì air an ais-y:

Is e am freagairt cheart B.

7. Is iad co-chomharran meadhan grabhataidh an nì aon-ghnèitheach san ìomhaigh gu h-ìosal...
A. (14, 15)
B. (17, 11)
C. (15, 11)
D. (15, 7)
E. (11, 7)

Deasbad:
Roinn an nì ann an trì pàirtean, gach pàirt le farsaingeachd (10-0)x(10-0), (20-10)x(30-0), (30-20)x(10-0)
Co-chomharran meadhan grabhataidh an nì a thaobh an x-axis:

x₁ = astar meadhan sgìre 1 bho phuing 0, x₂ = astar meadhan sgìre 2 bho phuing 0, x₃ = astar meadhan sgìre 3 bho phuing 0.
Co-chomharran meadhan grabhataidh an nì a thaobh an ais-y:

y₁ = astar meadhan sgìre 1 bho phuing 0, y₂ = astar meadhan sgìre 2 bho phuing 0, y₃ = astar meadhan sgìre 3 bho phuing 0.

Is iad co-chomharran meadhan grabhataidh an nì (15, 11)
Is e C am freagairt cheart.

8. Is iad co-chomharran meadhan grabhataidh an nì san ìomhaigh gu h-ìosal...
A. (3; 2,7) m
B. (3; 3,6) m
C. (3; 4,0) m
D. (3; 4,5) m
E. (3; 5,0) m
Deasbad:

Roinn an nì ann an dà phàirt, gach pàirt le farsaingeachd de (5-1)x(3-0), ½ (6-0)x(9-3)
Co-chomharran meadhan grabhataidh an nì a thaobh an x-axis:

Co-chomharran meadhan grabhataidh an nì a thaobh an ais-y:

Is iad co-chomharran meadhan grabhataidh an nì (3; 3,6)
Is e am freagairt cheart B.

9. Is iad co-chomharran meadhan grabhataidh nì aon-ghnèitheach an coimeas ri puing O san ìomhaigh a leanas...

A. (4 3/5, 3 3/5)
B. (4 1/3, 3 1/3)
C. (4 1/3, 3)
D. (3 1/3, 4 1/3)
E. (3, 3 2/3)

Deasbad
Roinn an nì ann an trì pàirtean, pàirt 1 = ceart-cheàrnach, pàirt 2 = ceàrnag, pàirt 3 = ceart-cheàrnach.

Raon earrann 1 (A₁) = (2-0)(8-0) = (2)(8) = 16
Meadhan-phuing earrann 1 air an x-axis (x₁) =1
Meadhan-phuing earrann 1 air an ais-y (y₁) =4

Raon earrann 2 (A₂) = (4-2)(2-0) = (2)(2) = 4
Meadhan-phuing earrann 2 air an x-axis (x₂) =3
Meadhan-phuing earrann 2 air an ais-y (y₂) =1

Raon earrann 3 (A₃) = (6-4)(8-0) = (2)(8) = 16
Meadhan-phuing earrann 3 air an x-axis (x₃) =5
Meadhan-phuing earrann 3 air an ais-y (y₃) =4

Co-chomharran meadhan grabhataidh an nì air an x-axis:
Co-chomharran meadhan grabhataidh an nì air an ais-y:
Is iad co-chomharran meadhan grabhataidh an nì a thaobh puing O (x, y) = (3, 3 2/3)
Is e E am freagairt cheart.

10. Is iad co-chomharran meadhan grabhataidh figear a’ phlèana gu h-ìosal….

A. (1 1/2, 1 1/2) cm
B. (2.1/2) cm
C. (2, 1 1/2) cm
D. (2 1/2, 1 1/2) cm
O. (2 1/2, 2 1/2) cm

Deasbad
Roinn an nì ann an trì pàirtean, pàirt 1 = ceart-cheàrnach, pàirt 2 = ceart-cheàrnach, pàirt 3 = ceart-cheàrnach.

Raon earrann 1 (A₁) = (1-0)(3-0) = (1)(3) = 3
Meadhan-phuing earrann 1 air an x-axis (x₁) =0,5
Meadhan-phuing earrann 1 air an ais-y (y₁) =1,5

Raon earrann 2 (A₂) = (3-1)(2-1) = (2)(1) = 2
Meadhan-phuing earrann 2 air an x-axis (x₂) =2
Meadhan-phuing earrann 2 air an ais-y (y₂) =1,5

Raon earrann 3 (A₃) = (4-3)(3-0) = (1)(3) = 3
Meadhan-phuing earrann 3 air an x-axis (x₃) =3,5
Meadhan-phuing earrann 3 air an ais-y (y₃) =1,5

Co-chomharran meadhan grabhataidh an nì air an x-axis:
Co-chomharran meadhan grabhataidh an nì air an ais-y:

Is iad co-chomharran meadhan grabhataidh an nì (x, y) = (2, 1 1/2)
Is e C am freagairt cheart.

Stòr na ceiste:

Ceistean Fiosaigs airson Àrd-sgoil Àrd-ìre/Àrd-sgoil Dreuchdail